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Introduction

\n", + "

Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations?

\n", + "\n", + "

Machine learning technics allow computers to automatically learn from a historical dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our past dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm:

\n", + "\n", + "\n", + "

History

\n", + "

The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief:

\n", + "
  • 1834: Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure.
  • \n", + "
  • 1936: Alan Turing gave a theory about how machines can execute a set of instructions.
  • \n", + "
  • 1940: First manually operated computer named \"ENIAC\" was invented.
  • \n", + "
  • 1943: The first model of human neural network was modeled with electronic circuits.
  • \n", + "
  • 1950: \"Computer Machinery and Intelligence,\" was published by Alan Turing on the topic of AI with this question, \"Can machines think?\".
  • \n", + "
  • 1952: Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more.
  • \n", + "
  • 1959: Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter.
  • \n", + "
  • 1974 to 1980: These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced.
  • \n", + "
  • 1985: A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week.
  • \n", + "
  • 1997: The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov.
  • \n", + "
  • 2006: Geoffrey Hinton has first used name of \"deep learning\" instead of neural net research.
  • \n", + "
  • 2012: Google developed a deep neural network system to distinguish cat and human images in a YouTube video.
  • \n", + "
  • 2016: AlphaGo won a Go game against number one and number second player of Go.
  • \n", + "\n", + "

    ML Applications

    \n", + "

    The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are:

    \n", + "
  • Image recognition:

    One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms.

  • \n", + "
  • Speech Recognition:

    This project converts your voice to text and is also known as \"Computer speech recognition.\" Some examples of this technology are Google assistant, Siri, Cortana, and Alexa.

  • \n", + "
  • Traffic prediction:

    Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users.

  • \n", + "
  • Product recommendations:

    Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its last searches or other features that are used in dataset.

  • \n", + "\n", + "

    Types of Machine Learning

    \n", + "

    There are three major recognized categories for ML:

    \n", + "\n", + "\n", + "

    Supervised Learning

    \n", + "

    In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless.\n", + "The supervised algorithms are grouped in two main categories:\n", + "

    \n", + "\n", + "\n", + "

    Classification

    \n", + "

    In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that the output of classification algorithm is a label or category, but the output of a regression algorithm is a value. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem:

    \n", + "
  • Lazy Learners: \n", + "
  • \n", + "
  • Eager Learners: \n", + "
  • \n", + "\n", + "

    Naïve Bayes Classifier Algorithm

    \n", + "

    Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem.

    \n", + " \n", + "\n", + "

    Unsupervised Learning

    \n", + "

    In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format.\n", + "The supervised algorithms are grouped in two main categories:\n", + "

    \n", + " \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "\n", + "

    Bias and Variance

    \n", + "\n", + "

    \n", + "if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors shows small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    \n", + "

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    \n", + "\n", + "\n", + "

    What is Bias?

    \n", + "

    \n", + "In general, a machine learning model analyses the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction.\n", + "While the model in making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors\n", + "It can be defined as an inability of ml algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ml has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either:\n", + "

    \n", + "linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias.\n", + "

    \n", + "\n", + "

    Machine learning algorithm with low bias:

    \n", + "\n", + "\n", + "

    Machine learning algorithm with high bias:

    \n", + "\n", + "\n", + "\n", + "

    What is variance?

    \n", + "\n", + "

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    \n", + "\n", + "

    low varince means that we have small variation in the changes of training data with prediction in target function!\n", + "high variance means there is a high variation in the prediction of the target function with changes in the training dataset

    \n", + "\n", + "

    a model that has high variance is well-performed with training data but can not generalize unseen dataset as well.\n", + "high variance leads to overfitting and increases model complexities!\n", + "

    \n", + "\n", + "

    machine learning algorithms with low variance:

    \n", + "\n", + "\n", + "

    machine learning algorithms with high variance:

    \n", + "\n", + "\n", + "in general variance shows us how much our model is dependent to our dataset!\n", + "\n", + "

    in the following image you can see the impact of bias and variance in machine learning model:

    \n", + "\n", + "\n", + "\n", + "

    Bias and Variance Trade-Off

    \n", + "

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically!\n", + "low-bias and high-variance leads to overfitting, high-bias and low-variance leads to unferfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off.\n", + "in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    OverFitting and Underfitting

    \n", + "

    Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

    \n", + "\n", + "

    An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

    \n", + "\n", + "\n", + "

    The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

    \n", + "\n", + "

    There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

    \n", + "\n", + "

    Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

    \n", + "\n", + "\n", + "

    So what is overfitting?

    \n", + "

    when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
    \n", + "This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.\n", + "An overfitted model is said to have low bias and high variance.\n", + "

    \n", + "

    To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

    \n", + "\n", + "\n", + "

    What is underfiting?

    \n", + "

    Underfitting refers to a model that can neither model the training data nor generalize to new data.\n", + "An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

    \n", + "\n", + "\n", + "

    and how to prevent overfitting?

    \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    Parameter Estiamtion

    \n", + "\n", + "\n", + "

    What is MLE?

    \n", + "\n", + "

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    \n", + "\n", + "

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    \n", + "

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    \n", + "L(x1,x2,⋯,xn;θ) = P(X1=x1,X2=x2,⋯,Xn=xn;θ)\n", + "\n", + "

      \n", + "
    1. If Xi's are discrete, then the likelihood function is defined as\n", + "L(x1,x2,⋯,xn;θ) = PX1X2⋯Xn(x1,x2,⋯,xn;θ).
    2. \n", + "\n", + "
    3. If Xi's are jointly continuous, then the likelihood function is defined as\n", + "L(x1,x2,⋯,xn;θ)=fX1X2⋯Xn(x1,x2,⋯,xn;θ).
    4. \n", + "
    \n", + "

    \n", + "\n", + "

    In some problems, it is easier to work with the log likelihood function given by\n", + "ln L(x1,x2,⋯,xn;θ).

    \n", + "\n", + "

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1, X2=x2, ⋯, Xn=xn. The maximum likelihood estimate of θ, shown by θ^ML is the value that maximizes the likelihood function\n", + "L(x1,x2,⋯,xn;θ).\n", + "

    \n", + "\n", + "

    Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

    \n", + "\n", + "\n", + "

    Waht is MAP?

    \n", + "\n", + "

    we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

    \n", + "\n", + "

    in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution.
    \n", + "After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y,\n", + "we use bayes formula for calculating posterior distribution.\n", + "

    \n", + "\n", + "\n", + "

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we explained it later!

    \n", + "\n", + "

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    \n", + "\n", + "

    Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:\n", + "
    fY|X(y|x)fX(x)
    \n", + "

    \n", + "\n", + "


    in many cases we choose alpha-beta distribution for prior distribution

    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    Handle unseen events

    \n", + "\n", + "

    One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example.\n", + "

    \n", + "\n", + "
    \n", + "\n", + "

    Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset.

    \n", + "\n", + "
    \n", + "\n", + "| data | label |\n", + "| :-----------: | :-----------: |\n", + "|[1, 1, 1, 0, 1]| a |\n", + "|[1, 0, 1, 0, 0]| a |\n", + "|[0, 0, 1, 0, 1]| a |\n", + "|[0, 1, 1, 0, 0]| a |\n", + "|[0, 0, 1, 0, 0]| a |\n", + "|[0, 0, 0, 0, 1]| b |\n", + "|[0, 1, 1, 0, 1]| b |\n", + "|[0, 1, 0, 1, 1]| b |\n", + "|[0, 1, 1, 1, 1]| b |\n", + "|[0, 0, 0, 1, 1]| b |\n", + "\n", + "

    We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset.

    \n", + " \n", + "\n", + "\n", + "

    Now, we calculate the probability of each label based on the created naïve Bayes model.

    \n", + "\n", + "
    \n", + "\n", + "$P\\left(label=a\\right)\\propto\\frac{2}{5}\\times\\frac{2}{5}\\times0\\times1\\times\\frac{2}{5}=0$\n", + "\n", + "
    \n", + "\n", + "$P\\left(label=b\\right)\\propto0\\times\\frac{3}{5}\\times\\frac{3}{5}\\times\\frac{2}{5}\\times1=0$\n", + "\n", + "

    If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b.

    \n", + "\n", + "
    \n", + "\n", + "So, what would we do to handle this situation?\n", + "\n", + "\n", + "

    Laplace Smoothing

    \n", + "

    One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is:\n", + "

    \n", + "\n", + "$P\\left(color=green\\right)=1$\n", + "\n", + "
    \n", + "\n", + "$P\\left(color=yellow\\right)=0$\n", + "

    Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows:

    \n", + "\n", + "$P\\left(color=green\\right)=\\frac{4}{5}$\n", + "\n", + "
    \n", + "\n", + "$P\\left(color=yellow\\right)=\\frac{1}{5}$\n", + "\n", + "

    In general:

    \n", + "$P_{LAP,k}\\left(x\\right)=\\frac{c\\left(x\\right)+k}{N+k\\left|X\\right|}$\n", + "\n", + "
    \n", + "\n", + "

    And for conditional probabilities:

    \n", + "$P_{LAP,k}\\left(x|y\\right)=\\frac{c\\left(x,y\\right)+k}{c\\left(y\\right)+k\\left|X\\right|}$\n", + "\n", + "Using Laplace smoothing with large k is not appropriate as it ignores the prior belief.\n", + "\n", + "\n", + " \n", + "\n", + "

    Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data:

    \n", + "\n", + "| data | label |\n", + "| :-----------: | :-----------: |\n", + "|[1, 1, 1, 1, 1]| a |\n", + "|[1, 1, 1, 1, 1]| b |\n", + "|[0, 0, 0, 0, 0]| a |\n", + "|[0, 0, 0, 0, 0]| b |\n", + "\n", + "\n", + "\n", + "$P\\left(label=a\\right)\\propto\\frac{3}{7}\\times\\frac{3}{7}\\times\\frac{1}{7}\\times\\frac{6}{7}\\times\\frac{3}{7}=\\frac{162}{16807}$\n", + "\n", + "
    \n", + "\n", + "$P\\left(label=b\\right)\\propto\\frac{1}{7}\\times\\frac{4}{7}\\times\\frac{4}{7}\\times\\frac{3}{7}\\times\\frac{6}{7}=\\frac{288}{16807}$\n", + "\n", + "\n", + "\n", + "

    Linear interpolation

    \n", + "\n", + "

    In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large.

    \n", + "\n", + "

    Another useful method is linear interpolation. Linear interpolation (also known as Lerp) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line.

    \n", + "\n", + "

    In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$

    \n", + "
    \n", + "

    In general:

    \n", + "$P_{LIN}\\left(x\\middle|\\ y\\right)=\\alpha P\\left(x\\middle|\\ y\\right)+\\left(1-\\alpha\\right)P\\left(x\\right),\\ 0<\\alpha<1$\n", + "\n", + "

    By choosing an appropriate value for $\\alpha$, we can handle unseen events.

    \n", + "\n", + "\n", + "\n", + "

    More about dataset

    \n", + "\n", + "

    In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\\alpha$ and k?

    \n", + "\n", + "
    \n", + "\n", + "

    We introduce three datasets:

    \n", + "\n", + "\n", + "

    Training Dataset

    \n", + "The sample of data used to fit the model.\n", + "

    The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data.

    \n", + "\n", + "\n", + "

    Validation Dataset

    \n", + "The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.\n", + "

    The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\\alpha$ and $k$.

    \n", + "\n", + "
    \n", + "\n", + "\n", + "\n", + "
    \n", + "\n", + "\n", + "

    Test Dataset

    \n", + "The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset.\n", + "

    The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world.

    \n", + "\n", + "\n", + "

    About the dataset split ratio

    \n", + "

    Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets.


    \n", + "

    This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training.


    \n", + "

    Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too!

    \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    Conclusion

    \n", + "

    so in this chapter, we introduced key concepts of machine learning.\n", + "we learned about the applications of ML, supervised and unsupervised in ML, and some algorithms like naive Bayes.\n", + "after these primary concepts, we learned about some problems like bias and variance and their relations to overfitting and underfitting.\n", + "for parameter estimation, we learned two statistical approaches like Bayesian and frequentist approach and after that, we used these two frameworks and some formulas like Laplace and linear interpolation which are based on MLE and MAP.\n", + "we also learned about how to work with datasets in machine learning

    " + ] + } + ], + "metadata": { + "interpreter": { + "hash": "63fd5069d213b44bf678585dea6b12cceca9941eaf7f819626cde1f2670de90d" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/notebooks/12_Intro_to_machine_learning/images/balls_1.png b/notebooks/12_Intro_to_machine_learning/images/balls_1.png new file mode 100644 index 0000000000000000000000000000000000000000..78a1976b0e20243441a0d760557944a95aec2891 GIT binary patch literal 5809 zcmYjV2|QHq*B{0>R~nNoW6Lu3u`d~8l#xB6A}Tvs8ly7AWcy`JwhSh+4HDTJ zB9lU8Pm(Oj&U^ir_kHK{nR}k+p68x>p7WgZJ?GqHI~y}Dc42l92*hQMGIjugz;IwZ 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    Introduction

    \n", + "

    Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations?

    \n", + "\n", + "

    Machine learning technics allow computers to automatically learn from a historical dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our past dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm:

    \n", + "\n", + "\n", + "

    History

    \n", + "

    The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief:

    \n", + "
  • 1834: Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure.
  • \n", + "
  • 1936: Alan Turing gave a theory about how machines can execute a set of instructions.
  • \n", + "
  • 1940: First manually operated computer named \"ENIAC\" was invented.
  • \n", + "
  • 1943: The first model of human neural network was modeled with electronic circuits.
  • \n", + "
  • 1950: \"Computer Machinery and Intelligence,\" was published by Alan Turing on the topic of AI with this question, \"Can machines think?\".
  • \n", + "
  • 1952: Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more.
  • \n", + "
  • 1959: Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter.
  • \n", + "
  • 1974 to 1980: These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced.
  • \n", + "
  • 1985: A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week.
  • \n", + "
  • 1997: The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov.
  • \n", + "
  • 2006: Geoffrey Hinton has first used name of \"deep learning\" instead of neural net research.
  • \n", + "
  • 2012: Google developed a deep neural network system to distinguish cat and human images in a YouTube video.
  • \n", + "
  • 2016: AlphaGo won a Go game against number one and number second player of Go.
  • \n", + "\n", + "

    ML Applications

    \n", + "

    The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are:

    \n", + "
  • Image recognition:

    One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms.

  • \n", + "
  • Speech Recognition:

    This project converts your voice to text and is also known as \"Computer speech recognition.\" Some examples of this technology are Google assistant, Siri, Cortana, and Alexa.

  • \n", + "
  • Traffic prediction:

    Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users.

  • \n", + "
  • Product recommendations:

    Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its last searches or other features that are used in dataset.

  • \n", + "\n", + "

    Types of Machine Learning

    \n", + "

    There are three major recognized categories for ML:

    \n", + "\n", + "\n", + "

    Supervised Learning

    \n", + "

    In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless.\n", + "The supervised algorithms are grouped in two main categories:\n", + "

    \n", + "
      \n", + "
    • Classification
    • \n", + "
    • Regression
    • \n", + "
    \n", + "\n", + "

    Classification

    \n", + "

    In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that the output of classification algorithm is a label or category, but the output of a regression algorithm is a value. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem:

    \n", + "
  • Lazy Learners:

      These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are:

      \n", + "
    • K-NN algorithm
    • \n", + "
    • b.\tCase-based reasoning
    • \n", + "
    \n", + "
  • \n", + "
  • Eager Learners:

      In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are:

      \n", + "
    • Decision Trees
    • \n", + "
    • Naïve Bayes
    • \n", + "
    • ANN
    • \n", + "
    \n", + "
  • \n", + "\n", + "

    Naïve Bayes Classifier Algorithm

    \n", + "

    Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem.

    \n", + "
      \n", + "

      Advantages of Naïve Bayes Classifier

      \n", + "
        \n", + "
      • It is fast and not that much complicated.
      • \n", + "
      • It can be used for Binary as well as Multi-class Classifications.
      • \n", + "
      • It is the most popular choice for text classification problems.
      • \n", + "
      \n", + "

      Disadvantages of Naïve Bayes Classifier

      \n", + "
        \n", + "
      • Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact.
      • \n", + "
      \n", + "
    \n", + "\n", + "

    Unsupervised Learning

    \n", + "

    In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format.\n", + "The supervised algorithms are grouped in two main categories:\n", + "

    \n", + "
      \n", + "
    • Clustering
    • \n", + "
    • Association
    • \n", + "
    \n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [] + }, + "source": [ + "\n", + "

    Bias and Variance

    \n", + "\n", + "

    \n", + "if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors shows small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    \n", + "

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    \n", + "\n", + "\n", + "

    What is Bias?

    \n", + "

    \n", + "In general, a machine learning model analyses the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction.\n", + "While the model in making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors\n", + "It can be defined as an inability of ml algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ml has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either:\n", + "

      \n", + "
    • High Bias: A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data.
    • \n", + "
    • Low Bias: A low bias model has fewer assumptions about the form of the function of dataset.
    • \n", + "
    \n", + "linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias.\n", + "

    \n", + "\n", + "

    Machine learning algorithm with low bias:

    \n", + "
      \n", + "
    • Decision Trees
    • \n", + "
    • k-Nearest Neighbours
    • \n", + "
    \n", + "\n", + "

    Machine learning algorithm with high bias:

    \n", + "
      \n", + "
    • Linear Regression
    • \n", + "
    • Logistic Regression
    • \n", + "
    \n", + "\n", + "\n", + "

    What is variance?

    \n", + "\n", + "

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    \n", + "\n", + "

    low varince means that we have small variation in the changes of training data with prediction in target function!\n", + "high variance means there is a high variation in the prediction of the target function with changes in the training dataset

    \n", + "\n", + "

    a model that has high variance is well-performed with training data but can not generalize unseen dataset as well.\n", + "high variance leads to overfitting and increases model complexities!\n", + "

    \n", + "\n", + "

    machine learning algorithms with low variance:

    \n", + "
      \n", + "
    • Linear Regression
    • \n", + "
    • Logistic Regression
    • \n", + "
    \n", + "\n", + "

    machine learning algorithms with high variance:

    \n", + "
      \n", + "
    • decision tree
    • \n", + "
    • K-nearest neighbours
    • \n", + "
    \n", + "\n", + "in general variance shows us how much our model is dependent to our dataset!\n", + "\n", + "

    in the following image you can see the impact of bias and variance in machine learning model:

    \n", + "\n", + "\n", + "\n", + "

    Bias and Variance Trade-Off

    \n", + "

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically!\n", + "low-bias and high-variance leads to overfitting, high-bias and low-variance leads to unferfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off.\n", + "in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    OverFitting and Underfitting

    \n", + "

    Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

    \n", + "\n", + "

    An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

    \n", + "
      \n", + "
    • Generalization: It shows how well a model is trained to predict unseen data.

    • \n", + "
    • Noise: Noise is meaningless or irrelevant data present in the dataset. It affects the performance of the model if it is not removed.
    • \n", + "
    \n", + "\n", + "

    The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

    \n", + "\n", + "

    There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

    \n", + "\n", + "

    Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

    \n", + "\n", + "\n", + "

    So what is overfitting?

    \n", + "

    when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
    \n", + "This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.\n", + "An overfitted model is said to have low bias and high variance.\n", + "

    \n", + "

    To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

    \n", + "\n", + "\n", + "

    What is underfiting?

    \n", + "

    Underfitting refers to a model that can neither model the training data nor generalize to new data.\n", + "An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

    \n", + "\n", + "\n", + "

    and how to prevent overfitting?

    \n", + "
      \n", + "
    • cross validation: In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds.
    • \n", + "
    • regularization: in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function
    • \n", + "
    • ...
    • \n", + "
    \n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    Parameter Estiamtion

    \n", + "\n", + "\n", + "

    What is MLE?

    \n", + "\n", + "

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    \n", + "\n", + "

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    \n", + "

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    \n", + "L(x1,x2,⋯,xn;θ) = P(X1=x1,X2=x2,⋯,Xn=xn;θ)\n", + "\n", + "

      \n", + "
    1. If Xi's are discrete, then the likelihood function is defined as\n", + "L(x1,x2,⋯,xn;θ) = PX1X2⋯Xn(x1,x2,⋯,xn;θ).
    2. \n", + "\n", + "
    3. If Xi's are jointly continuous, then the likelihood function is defined as\n", + "L(x1,x2,⋯,xn;θ)=fX1X2⋯Xn(x1,x2,⋯,xn;θ).
    4. \n", + "
    \n", + "

    \n", + "\n", + "

    In some problems, it is easier to work with the log likelihood function given by\n", + "ln L(x1,x2,⋯,xn;θ).

    \n", + "\n", + "

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1, X2=x2, ⋯, Xn=xn. The maximum likelihood estimate of θ, shown by θ^ML is the value that maximizes the likelihood function\n", + "L(x1,x2,⋯,xn;θ).\n", + "

    \n", + "\n", + "

    Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

    \n", + "\n", + "\n", + "

    Waht is MAP?

    \n", + "\n", + "

    we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

    \n", + "\n", + "

    in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution.
    \n", + "After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y,\n", + "we use bayes formula for calculating posterior distribution.\n", + "

    \n", + "\n", + "\n", + "

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we explained it later!

    \n", + "\n", + "

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    \n", + "\n", + "

    Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:\n", + "
    fY|X(y|x)fX(x)
    \n", + "

    \n", + "\n", + "


    in many cases we choose alpha-beta distribution for prior distribution

    " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    Handle unseen events

    \n", + "\n", + "

    One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example.\n", + "

    \n", + "\n", + "
    \n", + "\n", + "

    Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset.

    \n", + "\n", + "
    \n", + "\n", + "| data | label |\n", + "| :-----------: | :-----------: |\n", + "|[1, 1, 1, 0, 1]| a |\n", + "|[1, 0, 1, 0, 0]| a |\n", + "|[0, 0, 1, 0, 1]| a |\n", + "|[0, 1, 1, 0, 0]| a |\n", + "|[0, 0, 1, 0, 0]| a |\n", + "|[0, 0, 0, 0, 1]| b |\n", + "|[0, 1, 1, 0, 1]| b |\n", + "|[0, 1, 0, 1, 1]| b |\n", + "|[0, 1, 1, 1, 1]| b |\n", + "|[0, 0, 0, 1, 1]| b |\n", + "\n", + "

    We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset.

    \n", + " \n", + "\n", + "\n", + "

    Now, we calculate the probability of each label based on the created naïve Bayes model.

    \n", + "\n", + "
    \n", + "\n", + "$P\\left(label=a\\right)\\propto\\frac{2}{5}\\times\\frac{2}{5}\\times0\\times1\\times\\frac{2}{5}=0$\n", + "\n", + "
    \n", + "\n", + "$P\\left(label=b\\right)\\propto0\\times\\frac{3}{5}\\times\\frac{3}{5}\\times\\frac{2}{5}\\times1=0$\n", + "\n", + "

    If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b.

    \n", + "\n", + "
    \n", + "\n", + "So, what would we do to handle this situation?\n", + "\n", + "\n", + "

    Laplace Smoothing

    \n", + "

    One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is:\n", + "

    \n", + "\n", + "$P\\left(color=green\\right)=1$\n", + "\n", + "
    \n", + "\n", + "$P\\left(color=yellow\\right)=0$\n", + "

    Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows:

    \n", + "\n", + "$P\\left(color=green\\right)=\\frac{4}{5}$\n", + "\n", + "
    \n", + "\n", + "$P\\left(color=yellow\\right)=\\frac{1}{5}$\n", + "\n", + "

    In general:

    \n", + "$P_{LAP,k}\\left(x\\right)=\\frac{c\\left(x\\right)+k}{N+k\\left|X\\right|}$\n", + "\n", + "
    \n", + "\n", + "

    And for conditional probabilities:

    \n", + "$P_{LAP,k}\\left(x|y\\right)=\\frac{c\\left(x,y\\right)+k}{c\\left(y\\right)+k\\left|X\\right|}$\n", + "\n", + "Using Laplace smoothing with large k is not appropriate as it ignores the prior belief.\n", + "\n", + "\n", + " \n", + "\n", + "

    Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data:

    \n", + "\n", + "| data | label |\n", + "| :-----------: | :-----------: |\n", + "|[1, 1, 1, 1, 1]| a |\n", + "|[1, 1, 1, 1, 1]| b |\n", + "|[0, 0, 0, 0, 0]| a |\n", + "|[0, 0, 0, 0, 0]| b |\n", + "\n", + "\n", + "\n", + "$P\\left(label=a\\right)\\propto\\frac{3}{7}\\times\\frac{3}{7}\\times\\frac{1}{7}\\times\\frac{6}{7}\\times\\frac{3}{7}=\\frac{162}{16807}$\n", + "\n", + "
    \n", + "\n", + "$P\\left(label=b\\right)\\propto\\frac{1}{7}\\times\\frac{4}{7}\\times\\frac{4}{7}\\times\\frac{3}{7}\\times\\frac{6}{7}=\\frac{288}{16807}$\n", + "\n", + "\n", + "\n", + "

    Linear interpolation

    \n", + "\n", + "

    In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large.

    \n", + "\n", + "

    Another useful method is linear interpolation. Linear interpolation (also known as Lerp) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line.

    \n", + "\n", + "

    In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$

    \n", + "
    \n", + "

    In general:

    \n", + "$P_{LIN}\\left(x\\middle|\\ y\\right)=\\alpha P\\left(x\\middle|\\ y\\right)+\\left(1-\\alpha\\right)P\\left(x\\right),\\ 0<\\alpha<1$\n", + "\n", + "

    By choosing an appropriate value for $\\alpha$, we can handle unseen events.

    \n", + "\n", + "\n", + "\n", + "

    More about dataset

    \n", + "\n", + "

    In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\\alpha$ and k?

    \n", + "\n", + "
    \n", + "\n", + "

    We introduce three datasets:

    \n", + "\n", + "\n", + "

    Training Dataset

    \n", + "The sample of data used to fit the model.\n", + "

    The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data.

    \n", + "\n", + "\n", + "

    Validation Dataset

    \n", + "The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.\n", + "

    The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\\alpha$ and $k$.

    \n", + "\n", + "
    \n", + "\n", + "\n", + "\n", + "
    \n", + "\n", + "\n", + "

    Test Dataset

    \n", + "The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset.\n", + "

    The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world.

    \n", + "\n", + "\n", + "

    About the dataset split ratio

    \n", + "

    Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets.


    \n", + "

    This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training.


    \n", + "

    Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too!

    \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

    Conclusion

    \n", + "

    so in this chapter, we introduced key concepts of machine learning.\n", + "we learned about the applications of ML, supervised and unsupervised in ML, and some algorithms like naive Bayes.\n", + "after these primary concepts, we learned about some problems like bias and variance and their relations to overfitting and underfitting.\n", + "for parameter estimation, we learned two statistical approaches like Bayesian and frequentist approach and after that, we used these two frameworks and some formulas like Laplace and linear interpolation which are based on MLE and MAP.\n", + "we also learned about how to work with datasets in machine learning

    " + ] + } + ], + "metadata": { + "interpreter": { + "hash": "63fd5069d213b44bf678585dea6b12cceca9941eaf7f819626cde1f2670de90d" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} From 69b98741afcb98cd7f6106650a44f578255f16d7 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 17 Dec 2021 20:55:39 +0330 Subject: [PATCH 02/21] metadata.yml added --- .../12_Intro_to_machine_learning/metadata.yml | 40 +++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 notebooks/12_Intro_to_machine_learning/metadata.yml diff --git a/notebooks/12_Intro_to_machine_learning/metadata.yml b/notebooks/12_Intro_to_machine_learning/metadata.yml new file mode 100644 index 00000000..d7caabb6 --- /dev/null +++ b/notebooks/12_Intro_to_machine_learning/metadata.yml @@ -0,0 +1,40 @@ +title: LN | introduction to machine learning (key concepts) + +header: + title: Intro to machine learning + +authors: + label: + position: top + text: Authors + kind: people + content: + - name: Alireza Eiji + role: Author + contact: + - icon: fas fa-envelope + link: mailto:alirezaeiji151379@gmail.com + - icon: fas fa-github + link: https://github.com/AlirezaEiji191379 + + - name: Mohammad Ali Khodabandeloo + role: Author + contact: + - icon: fab fa-github + link: https://github.com/MohammadAli-Khodabandelou + - icon: fas fa-envelope + link: mailto:mohammadali.khodabandelou@gmail.com + + - name: Ahmad Reza Hamzei + role: Author + contact: + - icon: fas fa-envelope + link: mailto:hamzei@ce.sharif.edu + - icon: fas fa-github + link: https://github.com/ARH80 + + - name: Sepehr Amini Afshar + role: Supervisor + contact: + - icon: fas fa-envelope + link: mailto:sepehramini83@gmail.com \ No newline at end of file From cab98a6006e2629f7ed841ac18695d1fafb37e58 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Sat, 25 Dec 2021 19:34:54 +0330 Subject: [PATCH 03/21] changing ipynb to md --- .../.ipynb_checkpoints/index-checkpoint.ipynb | 510 ------------------ .../12_Intro_to_machine_learning/index.ipynb | 510 ------------------ .../12_Intro_to_machine_learning/index.md | 483 +++++++++++++++++ 3 files changed, 483 insertions(+), 1020 deletions(-) delete mode 100644 notebooks/12_Intro_to_machine_learning/.ipynb_checkpoints/index-checkpoint.ipynb delete mode 100644 notebooks/12_Intro_to_machine_learning/index.ipynb create mode 100644 notebooks/12_Intro_to_machine_learning/index.md diff --git a/notebooks/12_Intro_to_machine_learning/.ipynb_checkpoints/index-checkpoint.ipynb b/notebooks/12_Intro_to_machine_learning/.ipynb_checkpoints/index-checkpoint.ipynb deleted file mode 100644 index 21d9ce97..00000000 --- a/notebooks/12_Intro_to_machine_learning/.ipynb_checkpoints/index-checkpoint.ipynb +++ /dev/null @@ -1,510 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Table of contents\n", - "1. [Introduction](#Introduction)\n", - " 1. [History](#History)\n", - " 2. [ML Applications](#Applications)\n", - "2. [Types of Machine Learning](#Types)\n", - " 1. [Supervised Learning](#Supervised)\n", - " 1. [Classification](#Classification)\n", - " 2. [Naïve Bayes Classifier Algorithm](#Naïve)\n", - " 2. [Unsupervised Learning](#Unsupervised)\n", - "3. [Bias and Variance](#Bias)\n", - " 1. [What is Bias?](#What)\n", - " 2. [What is variance?](#variance)\n", - " 3. [Bias and Variance Trade-Off](#Trade)\n", - "4. [OverFitting and Underfitting](#and)\n", - " 1. [So what is overfitting?](#overfitting)\n", - " 2. [What is underfiting?](#underfiting)\n", - " 3. [and how to prevent overfitting?](#prevent)\n", - "5. [Parameter Estiamtion](#Estiamtion)\n", - " 1. [What is MLE?](#MLE)\n", - " 2. [Waht is MAP?](#MAP)\n", - "6. [Handle unseen events](#Handle)\n", - " 1. [Laplace Smoothing](#Laplace)\n", - " 2. [Linear interpolation](#Linear)\n", - "7. [More about dataset](#More)\n", - " 1. [Training Dataset](#Training)\n", - " 2. [Validation Dataset](#Validation)\n", - " 3. [Test Dataset](#Test)\n", - " 4. [About the dataset split ratio](#ratio)\n", - "8. [Conclusion](#Conclusion)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Introduction

    \n", - "

    Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations?

    \n", - "\n", - "

    Machine learning technics allow computers to automatically learn from a historical dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our past dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm:

    \n", - "\n", - "\n", - "

    History

    \n", - "

    The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief:

    \n", - "
  • 1834: Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure.
  • \n", - "
  • 1936: Alan Turing gave a theory about how machines can execute a set of instructions.
  • \n", - "
  • 1940: First manually operated computer named \"ENIAC\" was invented.
  • \n", - "
  • 1943: The first model of human neural network was modeled with electronic circuits.
  • \n", - "
  • 1950: \"Computer Machinery and Intelligence,\" was published by Alan Turing on the topic of AI with this question, \"Can machines think?\".
  • \n", - "
  • 1952: Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more.
  • \n", - "
  • 1959: Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter.
  • \n", - "
  • 1974 to 1980: These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced.
  • \n", - "
  • 1985: A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week.
  • \n", - "
  • 1997: The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov.
  • \n", - "
  • 2006: Geoffrey Hinton has first used name of \"deep learning\" instead of neural net research.
  • \n", - "
  • 2012: Google developed a deep neural network system to distinguish cat and human images in a YouTube video.
  • \n", - "
  • 2016: AlphaGo won a Go game against number one and number second player of Go.
  • \n", - "\n", - "

    ML Applications

    \n", - "

    The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are:

    \n", - "
  • Image recognition:

    One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms.

  • \n", - "
  • Speech Recognition:

    This project converts your voice to text and is also known as \"Computer speech recognition.\" Some examples of this technology are Google assistant, Siri, Cortana, and Alexa.

  • \n", - "
  • Traffic prediction:

    Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users.

  • \n", - "
  • Product recommendations:

    Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its last searches or other features that are used in dataset.

  • \n", - "\n", - "

    Types of Machine Learning

    \n", - "

    There are three major recognized categories for ML:

    \n", - "\n", - "\n", - "

    Supervised Learning

    \n", - "

    In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless.\n", - "The supervised algorithms are grouped in two main categories:\n", - "

    \n", - "
      \n", - "
    • Classification
    • \n", - "
    • Regression
    • \n", - "
    \n", - "\n", - "

    Classification

    \n", - "

    In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that the output of classification algorithm is a label or category, but the output of a regression algorithm is a value. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem:

    \n", - "
  • Lazy Learners:

      These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are:

      \n", - "
    • K-NN algorithm
    • \n", - "
    • b.\tCase-based reasoning
    • \n", - "
    \n", - "
  • \n", - "
  • Eager Learners:

      In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are:

      \n", - "
    • Decision Trees
    • \n", - "
    • Naïve Bayes
    • \n", - "
    • ANN
    • \n", - "
    \n", - "
  • \n", - "\n", - "

    Naïve Bayes Classifier Algorithm

    \n", - "

    Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem.

    \n", - "
      \n", - "

      Advantages of Naïve Bayes Classifier

      \n", - "
        \n", - "
      • It is fast and not that much complicated.
      • \n", - "
      • It can be used for Binary as well as Multi-class Classifications.
      • \n", - "
      • It is the most popular choice for text classification problems.
      • \n", - "
      \n", - "

      Disadvantages of Naïve Bayes Classifier

      \n", - "
        \n", - "
      • Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact.
      • \n", - "
      \n", - "
    \n", - "\n", - "

    Unsupervised Learning

    \n", - "

    In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format.\n", - "The supervised algorithms are grouped in two main categories:\n", - "

    \n", - "
      \n", - "
    • Clustering
    • \n", - "
    • Association
    • \n", - "
    \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "tags": [] - }, - "source": [ - "\n", - "

    Bias and Variance

    \n", - "\n", - "

    \n", - "if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors shows small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    \n", - "

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    \n", - "\n", - "\n", - "

    What is Bias?

    \n", - "

    \n", - "In general, a machine learning model analyses the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction.\n", - "While the model in making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors\n", - "It can be defined as an inability of ml algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ml has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either:\n", - "

      \n", - "
    • High Bias: A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data.
    • \n", - "
    • Low Bias: A low bias model has fewer assumptions about the form of the function of dataset.
    • \n", - "
    \n", - "linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias.\n", - "

    \n", - "\n", - "

    Machine learning algorithm with low bias:

    \n", - "
      \n", - "
    • Decision Trees
    • \n", - "
    • k-Nearest Neighbours
    • \n", - "
    \n", - "\n", - "

    Machine learning algorithm with high bias:

    \n", - "
      \n", - "
    • Linear Regression
    • \n", - "
    • Logistic Regression
    • \n", - "
    \n", - "\n", - "\n", - "

    What is variance?

    \n", - "\n", - "

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    \n", - "\n", - "

    low varince means that we have small variation in the changes of training data with prediction in target function!\n", - "high variance means there is a high variation in the prediction of the target function with changes in the training dataset

    \n", - "\n", - "

    a model that has high variance is well-performed with training data but can not generalize unseen dataset as well.\n", - "high variance leads to overfitting and increases model complexities!\n", - "

    \n", - "\n", - "

    machine learning algorithms with low variance:

    \n", - "
      \n", - "
    • Linear Regression
    • \n", - "
    • Logistic Regression
    • \n", - "
    \n", - "\n", - "

    machine learning algorithms with high variance:

    \n", - "
      \n", - "
    • decision tree
    • \n", - "
    • K-nearest neighbours
    • \n", - "
    \n", - "\n", - "in general variance shows us how much our model is dependent to our dataset!\n", - "\n", - "

    in the following image you can see the impact of bias and variance in machine learning model:

    \n", - "\n", - "\n", - "\n", - "

    Bias and Variance Trade-Off

    \n", - "

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically!\n", - "low-bias and high-variance leads to overfitting, high-bias and low-variance leads to unferfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off.\n", - "in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    \n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    OverFitting and Underfitting

    \n", - "

    Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

    \n", - "\n", - "

    An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

    \n", - "
      \n", - "
    • Generalization: It shows how well a model is trained to predict unseen data.

    • \n", - "
    • Noise: Noise is meaningless or irrelevant data present in the dataset. It affects the performance of the model if it is not removed.
    • \n", - "
    \n", - "\n", - "

    The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

    \n", - "\n", - "

    There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

    \n", - "\n", - "

    Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

    \n", - "\n", - "\n", - "

    So what is overfitting?

    \n", - "

    when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
    \n", - "This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.\n", - "An overfitted model is said to have low bias and high variance.\n", - "

    \n", - "

    To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

    \n", - "\n", - "\n", - "

    What is underfiting?

    \n", - "

    Underfitting refers to a model that can neither model the training data nor generalize to new data.\n", - "An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

    \n", - "\n", - "\n", - "

    and how to prevent overfitting?

    \n", - "
      \n", - "
    • cross validation: In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds.
    • \n", - "
    • regularization: in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function
    • \n", - "
    • ...
    • \n", - "
    \n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Parameter Estiamtion

    \n", - "\n", - "\n", - "

    What is MLE?

    \n", - "\n", - "

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    \n", - "\n", - "

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    \n", - "

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    \n", - "L(x1,x2,⋯,xn;θ) = P(X1=x1,X2=x2,⋯,Xn=xn;θ)\n", - "\n", - "

      \n", - "
    1. If Xi's are discrete, then the likelihood function is defined as\n", - "L(x1,x2,⋯,xn;θ) = PX1X2⋯Xn(x1,x2,⋯,xn;θ).
    2. \n", - "\n", - "
    3. If Xi's are jointly continuous, then the likelihood function is defined as\n", - "L(x1,x2,⋯,xn;θ)=fX1X2⋯Xn(x1,x2,⋯,xn;θ).
    4. \n", - "
    \n", - "

    \n", - "\n", - "

    In some problems, it is easier to work with the log likelihood function given by\n", - "ln L(x1,x2,⋯,xn;θ).

    \n", - "\n", - "

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1, X2=x2, ⋯, Xn=xn. The maximum likelihood estimate of θ, shown by θ^ML is the value that maximizes the likelihood function\n", - "L(x1,x2,⋯,xn;θ).\n", - "

    \n", - "\n", - "

    Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

    \n", - "\n", - "\n", - "

    Waht is MAP?

    \n", - "\n", - "

    we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

    \n", - "\n", - "

    in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution.
    \n", - "After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y,\n", - "we use bayes formula for calculating posterior distribution.\n", - "

    \n", - "\n", - "\n", - "

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we explained it later!

    \n", - "\n", - "

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    \n", - "\n", - "

    Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:\n", - "
    fY|X(y|x)fX(x)
    \n", - "

    \n", - "\n", - "


    in many cases we choose alpha-beta distribution for prior distribution

    " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Handle unseen events

    \n", - "\n", - "

    One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example.\n", - "

    \n", - "\n", - "
    \n", - "\n", - "

    Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset.

    \n", - "\n", - "
    \n", - "\n", - "| data | label |\n", - "| :-----------: | :-----------: |\n", - "|[1, 1, 1, 0, 1]| a |\n", - "|[1, 0, 1, 0, 0]| a |\n", - "|[0, 0, 1, 0, 1]| a |\n", - "|[0, 1, 1, 0, 0]| a |\n", - "|[0, 0, 1, 0, 0]| a |\n", - "|[0, 0, 0, 0, 1]| b |\n", - "|[0, 1, 1, 0, 1]| b |\n", - "|[0, 1, 0, 1, 1]| b |\n", - "|[0, 1, 1, 1, 1]| b |\n", - "|[0, 0, 0, 1, 1]| b |\n", - "\n", - "

    We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset.

    \n", - " \n", - "\n", - "\n", - "

    Now, we calculate the probability of each label based on the created naïve Bayes model.

    \n", - "\n", - "
    \n", - "\n", - "$P\\left(label=a\\right)\\propto\\frac{2}{5}\\times\\frac{2}{5}\\times0\\times1\\times\\frac{2}{5}=0$\n", - "\n", - "
    \n", - "\n", - "$P\\left(label=b\\right)\\propto0\\times\\frac{3}{5}\\times\\frac{3}{5}\\times\\frac{2}{5}\\times1=0$\n", - "\n", - "

    If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b.

    \n", - "\n", - "
    \n", - "\n", - "So, what would we do to handle this situation?\n", - "\n", - "\n", - "

    Laplace Smoothing

    \n", - "

    One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is:\n", - "

    \n", - "\n", - "$P\\left(color=green\\right)=1$\n", - "\n", - "
    \n", - "\n", - "$P\\left(color=yellow\\right)=0$\n", - "

    Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows:

    \n", - "\n", - "$P\\left(color=green\\right)=\\frac{4}{5}$\n", - "\n", - "
    \n", - "\n", - "$P\\left(color=yellow\\right)=\\frac{1}{5}$\n", - "\n", - "

    In general:

    \n", - "$P_{LAP,k}\\left(x\\right)=\\frac{c\\left(x\\right)+k}{N+k\\left|X\\right|}$\n", - "\n", - "
    \n", - "\n", - "

    And for conditional probabilities:

    \n", - "$P_{LAP,k}\\left(x|y\\right)=\\frac{c\\left(x,y\\right)+k}{c\\left(y\\right)+k\\left|X\\right|}$\n", - "\n", - "Using Laplace smoothing with large k is not appropriate as it ignores the prior belief.\n", - "\n", - "\n", - " \n", - "\n", - "

    Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data:

    \n", - "\n", - "| data | label |\n", - "| :-----------: | :-----------: |\n", - "|[1, 1, 1, 1, 1]| a |\n", - "|[1, 1, 1, 1, 1]| b |\n", - "|[0, 0, 0, 0, 0]| a |\n", - "|[0, 0, 0, 0, 0]| b |\n", - "\n", - "\n", - "\n", - "$P\\left(label=a\\right)\\propto\\frac{3}{7}\\times\\frac{3}{7}\\times\\frac{1}{7}\\times\\frac{6}{7}\\times\\frac{3}{7}=\\frac{162}{16807}$\n", - "\n", - "
    \n", - "\n", - "$P\\left(label=b\\right)\\propto\\frac{1}{7}\\times\\frac{4}{7}\\times\\frac{4}{7}\\times\\frac{3}{7}\\times\\frac{6}{7}=\\frac{288}{16807}$\n", - "\n", - "\n", - "\n", - "

    Linear interpolation

    \n", - "\n", - "

    In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large.

    \n", - "\n", - "

    Another useful method is linear interpolation. Linear interpolation (also known as Lerp) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line.

    \n", - "\n", - "

    In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$

    \n", - "
    \n", - "

    In general:

    \n", - "$P_{LIN}\\left(x\\middle|\\ y\\right)=\\alpha P\\left(x\\middle|\\ y\\right)+\\left(1-\\alpha\\right)P\\left(x\\right),\\ 0<\\alpha<1$\n", - "\n", - "

    By choosing an appropriate value for $\\alpha$, we can handle unseen events.

    \n", - "\n", - "\n", - "\n", - "

    More about dataset

    \n", - "\n", - "

    In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\\alpha$ and k?

    \n", - "\n", - "
    \n", - "\n", - "

    We introduce three datasets:

    \n", - "\n", - "\n", - "

    Training Dataset

    \n", - "The sample of data used to fit the model.\n", - "

    The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data.

    \n", - "\n", - "\n", - "

    Validation Dataset

    \n", - "The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.\n", - "

    The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\\alpha$ and $k$.

    \n", - "\n", - "
    \n", - "\n", - "\n", - "\n", - "
    \n", - "\n", - "\n", - "

    Test Dataset

    \n", - "The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset.\n", - "

    The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world.

    \n", - "\n", - "\n", - "

    About the dataset split ratio

    \n", - "

    Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets.


    \n", - "

    This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training.


    \n", - "

    Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too!

    \n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Conclusion

    \n", - "

    so in this chapter, we introduced key concepts of machine learning.\n", - "we learned about the applications of ML, supervised and unsupervised in ML, and some algorithms like naive Bayes.\n", - "after these primary concepts, we learned about some problems like bias and variance and their relations to overfitting and underfitting.\n", - "for parameter estimation, we learned two statistical approaches like Bayesian and frequentist approach and after that, we used these two frameworks and some formulas like Laplace and linear interpolation which are based on MLE and MAP.\n", - "we also learned about how to work with datasets in machine learning

    " - ] - } - ], - "metadata": { - "interpreter": { - "hash": "63fd5069d213b44bf678585dea6b12cceca9941eaf7f819626cde1f2670de90d" - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.10" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/notebooks/12_Intro_to_machine_learning/index.ipynb b/notebooks/12_Intro_to_machine_learning/index.ipynb deleted file mode 100644 index 21d9ce97..00000000 --- a/notebooks/12_Intro_to_machine_learning/index.ipynb +++ /dev/null @@ -1,510 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Table of contents\n", - "1. [Introduction](#Introduction)\n", - " 1. [History](#History)\n", - " 2. [ML Applications](#Applications)\n", - "2. [Types of Machine Learning](#Types)\n", - " 1. [Supervised Learning](#Supervised)\n", - " 1. [Classification](#Classification)\n", - " 2. [Naïve Bayes Classifier Algorithm](#Naïve)\n", - " 2. [Unsupervised Learning](#Unsupervised)\n", - "3. [Bias and Variance](#Bias)\n", - " 1. [What is Bias?](#What)\n", - " 2. [What is variance?](#variance)\n", - " 3. [Bias and Variance Trade-Off](#Trade)\n", - "4. [OverFitting and Underfitting](#and)\n", - " 1. [So what is overfitting?](#overfitting)\n", - " 2. [What is underfiting?](#underfiting)\n", - " 3. [and how to prevent overfitting?](#prevent)\n", - "5. [Parameter Estiamtion](#Estiamtion)\n", - " 1. [What is MLE?](#MLE)\n", - " 2. [Waht is MAP?](#MAP)\n", - "6. [Handle unseen events](#Handle)\n", - " 1. [Laplace Smoothing](#Laplace)\n", - " 2. [Linear interpolation](#Linear)\n", - "7. [More about dataset](#More)\n", - " 1. [Training Dataset](#Training)\n", - " 2. [Validation Dataset](#Validation)\n", - " 3. [Test Dataset](#Test)\n", - " 4. [About the dataset split ratio](#ratio)\n", - "8. [Conclusion](#Conclusion)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Introduction

    \n", - "

    Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations?

    \n", - "\n", - "

    Machine learning technics allow computers to automatically learn from a historical dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our past dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm:

    \n", - "\n", - "\n", - "

    History

    \n", - "

    The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief:

    \n", - "
  • 1834: Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure.
  • \n", - "
  • 1936: Alan Turing gave a theory about how machines can execute a set of instructions.
  • \n", - "
  • 1940: First manually operated computer named \"ENIAC\" was invented.
  • \n", - "
  • 1943: The first model of human neural network was modeled with electronic circuits.
  • \n", - "
  • 1950: \"Computer Machinery and Intelligence,\" was published by Alan Turing on the topic of AI with this question, \"Can machines think?\".
  • \n", - "
  • 1952: Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more.
  • \n", - "
  • 1959: Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter.
  • \n", - "
  • 1974 to 1980: These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced.
  • \n", - "
  • 1985: A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week.
  • \n", - "
  • 1997: The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov.
  • \n", - "
  • 2006: Geoffrey Hinton has first used name of \"deep learning\" instead of neural net research.
  • \n", - "
  • 2012: Google developed a deep neural network system to distinguish cat and human images in a YouTube video.
  • \n", - "
  • 2016: AlphaGo won a Go game against number one and number second player of Go.
  • \n", - "\n", - "

    ML Applications

    \n", - "

    The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are:

    \n", - "
  • Image recognition:

    One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms.

  • \n", - "
  • Speech Recognition:

    This project converts your voice to text and is also known as \"Computer speech recognition.\" Some examples of this technology are Google assistant, Siri, Cortana, and Alexa.

  • \n", - "
  • Traffic prediction:

    Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users.

  • \n", - "
  • Product recommendations:

    Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its last searches or other features that are used in dataset.

  • \n", - "\n", - "

    Types of Machine Learning

    \n", - "

    There are three major recognized categories for ML:

    \n", - "\n", - "\n", - "

    Supervised Learning

    \n", - "

    In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless.\n", - "The supervised algorithms are grouped in two main categories:\n", - "

    \n", - "
      \n", - "
    • Classification
    • \n", - "
    • Regression
    • \n", - "
    \n", - "\n", - "

    Classification

    \n", - "

    In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that the output of classification algorithm is a label or category, but the output of a regression algorithm is a value. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem:

    \n", - "
  • Lazy Learners:

      These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are:

      \n", - "
    • K-NN algorithm
    • \n", - "
    • b.\tCase-based reasoning
    • \n", - "
    \n", - "
  • \n", - "
  • Eager Learners:

      In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are:

      \n", - "
    • Decision Trees
    • \n", - "
    • Naïve Bayes
    • \n", - "
    • ANN
    • \n", - "
    \n", - "
  • \n", - "\n", - "

    Naïve Bayes Classifier Algorithm

    \n", - "

    Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem.

    \n", - "
      \n", - "

      Advantages of Naïve Bayes Classifier

      \n", - "
        \n", - "
      • It is fast and not that much complicated.
      • \n", - "
      • It can be used for Binary as well as Multi-class Classifications.
      • \n", - "
      • It is the most popular choice for text classification problems.
      • \n", - "
      \n", - "

      Disadvantages of Naïve Bayes Classifier

      \n", - "
        \n", - "
      • Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact.
      • \n", - "
      \n", - "
    \n", - "\n", - "

    Unsupervised Learning

    \n", - "

    In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format.\n", - "The supervised algorithms are grouped in two main categories:\n", - "

    \n", - "
      \n", - "
    • Clustering
    • \n", - "
    • Association
    • \n", - "
    \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "tags": [] - }, - "source": [ - "\n", - "

    Bias and Variance

    \n", - "\n", - "

    \n", - "if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors shows small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    \n", - "

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    \n", - "\n", - "\n", - "

    What is Bias?

    \n", - "

    \n", - "In general, a machine learning model analyses the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction.\n", - "While the model in making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors\n", - "It can be defined as an inability of ml algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ml has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either:\n", - "

      \n", - "
    • High Bias: A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data.
    • \n", - "
    • Low Bias: A low bias model has fewer assumptions about the form of the function of dataset.
    • \n", - "
    \n", - "linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias.\n", - "

    \n", - "\n", - "

    Machine learning algorithm with low bias:

    \n", - "
      \n", - "
    • Decision Trees
    • \n", - "
    • k-Nearest Neighbours
    • \n", - "
    \n", - "\n", - "

    Machine learning algorithm with high bias:

    \n", - "
      \n", - "
    • Linear Regression
    • \n", - "
    • Logistic Regression
    • \n", - "
    \n", - "\n", - "\n", - "

    What is variance?

    \n", - "\n", - "

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    \n", - "\n", - "

    low varince means that we have small variation in the changes of training data with prediction in target function!\n", - "high variance means there is a high variation in the prediction of the target function with changes in the training dataset

    \n", - "\n", - "

    a model that has high variance is well-performed with training data but can not generalize unseen dataset as well.\n", - "high variance leads to overfitting and increases model complexities!\n", - "

    \n", - "\n", - "

    machine learning algorithms with low variance:

    \n", - "
      \n", - "
    • Linear Regression
    • \n", - "
    • Logistic Regression
    • \n", - "
    \n", - "\n", - "

    machine learning algorithms with high variance:

    \n", - "
      \n", - "
    • decision tree
    • \n", - "
    • K-nearest neighbours
    • \n", - "
    \n", - "\n", - "in general variance shows us how much our model is dependent to our dataset!\n", - "\n", - "

    in the following image you can see the impact of bias and variance in machine learning model:

    \n", - "\n", - "\n", - "\n", - "

    Bias and Variance Trade-Off

    \n", - "

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically!\n", - "low-bias and high-variance leads to overfitting, high-bias and low-variance leads to unferfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off.\n", - "in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    \n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    OverFitting and Underfitting

    \n", - "

    Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

    \n", - "\n", - "

    An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

    \n", - "
      \n", - "
    • Generalization: It shows how well a model is trained to predict unseen data.

    • \n", - "
    • Noise: Noise is meaningless or irrelevant data present in the dataset. It affects the performance of the model if it is not removed.
    • \n", - "
    \n", - "\n", - "

    The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

    \n", - "\n", - "

    There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

    \n", - "\n", - "

    Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

    \n", - "\n", - "\n", - "

    So what is overfitting?

    \n", - "

    when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
    \n", - "This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize.\n", - "An overfitted model is said to have low bias and high variance.\n", - "

    \n", - "

    To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

    \n", - "\n", - "\n", - "

    What is underfiting?

    \n", - "

    Underfitting refers to a model that can neither model the training data nor generalize to new data.\n", - "An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

    \n", - "\n", - "\n", - "

    and how to prevent overfitting?

    \n", - "
      \n", - "
    • cross validation: In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds.
    • \n", - "
    • regularization: in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function
    • \n", - "
    • ...
    • \n", - "
    \n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Parameter Estiamtion

    \n", - "\n", - "\n", - "

    What is MLE?

    \n", - "\n", - "

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    \n", - "\n", - "

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    \n", - "

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    \n", - "L(x1,x2,⋯,xn;θ) = P(X1=x1,X2=x2,⋯,Xn=xn;θ)\n", - "\n", - "

      \n", - "
    1. If Xi's are discrete, then the likelihood function is defined as\n", - "L(x1,x2,⋯,xn;θ) = PX1X2⋯Xn(x1,x2,⋯,xn;θ).
    2. \n", - "\n", - "
    3. If Xi's are jointly continuous, then the likelihood function is defined as\n", - "L(x1,x2,⋯,xn;θ)=fX1X2⋯Xn(x1,x2,⋯,xn;θ).
    4. \n", - "
    \n", - "

    \n", - "\n", - "

    In some problems, it is easier to work with the log likelihood function given by\n", - "ln L(x1,x2,⋯,xn;θ).

    \n", - "\n", - "

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1, X2=x2, ⋯, Xn=xn. The maximum likelihood estimate of θ, shown by θ^ML is the value that maximizes the likelihood function\n", - "L(x1,x2,⋯,xn;θ).\n", - "

    \n", - "\n", - "

    Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

    \n", - "\n", - "\n", - "

    Waht is MAP?

    \n", - "\n", - "

    we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

    \n", - "\n", - "

    in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution.
    \n", - "After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y,\n", - "we use bayes formula for calculating posterior distribution.\n", - "

    \n", - "\n", - "\n", - "

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we explained it later!

    \n", - "\n", - "

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    \n", - "\n", - "

    Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:\n", - "
    fY|X(y|x)fX(x)
    \n", - "

    \n", - "\n", - "


    in many cases we choose alpha-beta distribution for prior distribution

    " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Handle unseen events

    \n", - "\n", - "

    One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example.\n", - "

    \n", - "\n", - "
    \n", - "\n", - "

    Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset.

    \n", - "\n", - "
    \n", - "\n", - "| data | label |\n", - "| :-----------: | :-----------: |\n", - "|[1, 1, 1, 0, 1]| a |\n", - "|[1, 0, 1, 0, 0]| a |\n", - "|[0, 0, 1, 0, 1]| a |\n", - "|[0, 1, 1, 0, 0]| a |\n", - "|[0, 0, 1, 0, 0]| a |\n", - "|[0, 0, 0, 0, 1]| b |\n", - "|[0, 1, 1, 0, 1]| b |\n", - "|[0, 1, 0, 1, 1]| b |\n", - "|[0, 1, 1, 1, 1]| b |\n", - "|[0, 0, 0, 1, 1]| b |\n", - "\n", - "

    We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset.

    \n", - " \n", - "\n", - "\n", - "

    Now, we calculate the probability of each label based on the created naïve Bayes model.

    \n", - "\n", - "
    \n", - "\n", - "$P\\left(label=a\\right)\\propto\\frac{2}{5}\\times\\frac{2}{5}\\times0\\times1\\times\\frac{2}{5}=0$\n", - "\n", - "
    \n", - "\n", - "$P\\left(label=b\\right)\\propto0\\times\\frac{3}{5}\\times\\frac{3}{5}\\times\\frac{2}{5}\\times1=0$\n", - "\n", - "

    If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b.

    \n", - "\n", - "
    \n", - "\n", - "So, what would we do to handle this situation?\n", - "\n", - "\n", - "

    Laplace Smoothing

    \n", - "

    One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is:\n", - "

    \n", - "\n", - "$P\\left(color=green\\right)=1$\n", - "\n", - "
    \n", - "\n", - "$P\\left(color=yellow\\right)=0$\n", - "

    Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows:

    \n", - "\n", - "$P\\left(color=green\\right)=\\frac{4}{5}$\n", - "\n", - "
    \n", - "\n", - "$P\\left(color=yellow\\right)=\\frac{1}{5}$\n", - "\n", - "

    In general:

    \n", - "$P_{LAP,k}\\left(x\\right)=\\frac{c\\left(x\\right)+k}{N+k\\left|X\\right|}$\n", - "\n", - "
    \n", - "\n", - "

    And for conditional probabilities:

    \n", - "$P_{LAP,k}\\left(x|y\\right)=\\frac{c\\left(x,y\\right)+k}{c\\left(y\\right)+k\\left|X\\right|}$\n", - "\n", - "Using Laplace smoothing with large k is not appropriate as it ignores the prior belief.\n", - "\n", - "\n", - " \n", - "\n", - "

    Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data:

    \n", - "\n", - "| data | label |\n", - "| :-----------: | :-----------: |\n", - "|[1, 1, 1, 1, 1]| a |\n", - "|[1, 1, 1, 1, 1]| b |\n", - "|[0, 0, 0, 0, 0]| a |\n", - "|[0, 0, 0, 0, 0]| b |\n", - "\n", - "\n", - "\n", - "$P\\left(label=a\\right)\\propto\\frac{3}{7}\\times\\frac{3}{7}\\times\\frac{1}{7}\\times\\frac{6}{7}\\times\\frac{3}{7}=\\frac{162}{16807}$\n", - "\n", - "
    \n", - "\n", - "$P\\left(label=b\\right)\\propto\\frac{1}{7}\\times\\frac{4}{7}\\times\\frac{4}{7}\\times\\frac{3}{7}\\times\\frac{6}{7}=\\frac{288}{16807}$\n", - "\n", - "\n", - "\n", - "

    Linear interpolation

    \n", - "\n", - "

    In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large.

    \n", - "\n", - "

    Another useful method is linear interpolation. Linear interpolation (also known as Lerp) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line.

    \n", - "\n", - "

    In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$

    \n", - "
    \n", - "

    In general:

    \n", - "$P_{LIN}\\left(x\\middle|\\ y\\right)=\\alpha P\\left(x\\middle|\\ y\\right)+\\left(1-\\alpha\\right)P\\left(x\\right),\\ 0<\\alpha<1$\n", - "\n", - "

    By choosing an appropriate value for $\\alpha$, we can handle unseen events.

    \n", - "\n", - "\n", - "\n", - "

    More about dataset

    \n", - "\n", - "

    In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\\alpha$ and k?

    \n", - "\n", - "
    \n", - "\n", - "

    We introduce three datasets:

    \n", - "\n", - "\n", - "

    Training Dataset

    \n", - "The sample of data used to fit the model.\n", - "

    The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data.

    \n", - "\n", - "\n", - "

    Validation Dataset

    \n", - "The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.\n", - "

    The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\\alpha$ and $k$.

    \n", - "\n", - "
    \n", - "\n", - "\n", - "\n", - "
    \n", - "\n", - "\n", - "

    Test Dataset

    \n", - "The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset.\n", - "

    The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world.

    \n", - "\n", - "\n", - "

    About the dataset split ratio

    \n", - "

    Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets.


    \n", - "

    This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training.


    \n", - "

    Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too!

    \n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "

    Conclusion

    \n", - "

    so in this chapter, we introduced key concepts of machine learning.\n", - "we learned about the applications of ML, supervised and unsupervised in ML, and some algorithms like naive Bayes.\n", - "after these primary concepts, we learned about some problems like bias and variance and their relations to overfitting and underfitting.\n", - "for parameter estimation, we learned two statistical approaches like Bayesian and frequentist approach and after that, we used these two frameworks and some formulas like Laplace and linear interpolation which are based on MLE and MAP.\n", - "we also learned about how to work with datasets in machine learning

    " - ] - } - ], - "metadata": { - "interpreter": { - "hash": "63fd5069d213b44bf678585dea6b12cceca9941eaf7f819626cde1f2670de90d" - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.10" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md new file mode 100644 index 00000000..794be0cc --- /dev/null +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -0,0 +1,483 @@ +# Table of contents +1. [Introduction](#Introduction) + 1. [History](#History) + 2. [ML Applications](#Applications) +2. [Types of Machine Learning](#Types) + 1. [Supervised Learning](#Supervised) + 1. [Classification](#Classification) + 2. [Naïve Bayes Classifier Algorithm](#Naïve) + 2. [Unsupervised Learning](#Unsupervised) +3. [Bias and Variance](#Bias) + 1. [What is Bias?](#What) + 2. [What is variance?](#variance) + 3. [Bias and Variance Trade-Off](#Trade) +4. [OverFitting and Underfitting](#and) + 1. [So what is overfitting?](#overfitting) + 2. [What is underfiting?](#underfiting) + 3. [and how to prevent overfitting?](#prevent) +5. [Parameter Estiamtion](#Estiamtion) + 1. [What is MLE?](#MLE) + 2. [Waht is MAP?](#MAP) +6. [Handle unseen events](#Handle) + 1. [Laplace Smoothing](#Laplace) + 2. [Linear interpolation](#Linear) +7. [More about dataset](#More) + 1. [Training Dataset](#Training) + 2. [Validation Dataset](#Validation) + 3. [Test Dataset](#Test) + 4. [About the dataset split ratio](#ratio) +8. [Conclusion](#Conclusion) +9. [References](#References) + + +

    Introduction

    +

    Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations?

    + +

    Machine learning technics allow computers to automatically learn from a historical dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our past dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm:

    + + +

    History

    +

    The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief:

    +
  • 1834: Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure.
  • +
  • 1936: Alan Turing gave a theory about how machines can execute a set of instructions.
  • +
  • 1940: First manually operated computer named "ENIAC" was invented.
  • +
  • 1943: The first model of human neural network was modeled with electronic circuits.
  • +
  • 1950: "Computer Machinery and Intelligence," was published by Alan Turing on the topic of AI with this question, "Can machines think?".
  • +
  • 1952: Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more.
  • +
  • 1959: Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter.
  • +
  • 1974 to 1980: These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced.
  • +
  • 1985: A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week.
  • +
  • 1997: The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov.
  • +
  • 2006: Geoffrey Hinton has first used name of "deep learning" instead of neural net research.
  • +
  • 2012: Google developed a deep neural network system to distinguish cat and human images in a YouTube video.
  • +
  • 2016: AlphaGo won a Go game against number one and number second player of Go.
  • + +

    ML Applications

    +

    The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are:

    +
  • Image recognition:

    One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms.

  • +
  • Speech Recognition:

    This project converts your voice to text and is also known as "Computer speech recognition." Some examples of this technology are Google assistant, Siri, Cortana, and Alexa.

  • +
  • Traffic prediction:

    Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users.

  • +
  • Product recommendations:

    Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its last searches or other features that are used in dataset.

  • + +

    Types of Machine Learning

    +

    There are three major recognized categories for ML:

    + + +

    Supervised Learning

    +

    In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless. +The supervised algorithms are grouped in two main categories: +

    +
      +
    • Classification
    • +
    • Regression
    • +
    + +

    Classification

    +

    In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that the output of classification algorithm is a label or category, but the output of a regression algorithm is a value. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem:

    +
  • Lazy Learners:

      These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are:

      +
    • K-NN algorithm
    • +
    • b. Case-based reasoning
    • +
    +
  • +
  • Eager Learners:

      In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are:

      +
    • Decision Trees
    • +
    • Naïve Bayes
    • +
    • ANN
    • +
    +
  • + +

    Naïve Bayes Classifier Algorithm

    +

    Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem.

    +
      +

      Advantages of Naïve Bayes Classifier

      +
        +
      • It is fast and not that much complicated.
      • +
      • It can be used for Binary as well as Multi-class Classifications.
      • +
      • It is the most popular choice for text classification problems.
      • +
      +

      Disadvantages of Naïve Bayes Classifier

      +
        +
      • Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact.
      • +
      +
    + +

    Unsupervised Learning

    +

    In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format. +The supervised algorithms are grouped in two main categories: +

    +
      +
    • Clustering
    • +
    • Association
    • +
    + + + +

    Bias and Variance

    + +

    +if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors shows small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    +

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    + + +

    What is Bias?

    +

    +In general, a machine learning model analyses the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. +While the model in making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors +It can be defined as an inability of ml algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ml has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either: +

      +
    • High Bias: A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data.
    • +
    • Low Bias: A low bias model has fewer assumptions about the form of the function of dataset.
    • +
    +linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias. +

    + +

    Machine learning algorithm with low bias:

    +
      +
    • Decision Trees
    • +
    • k-Nearest Neighbours
    • +
    + +

    Machine learning algorithm with high bias:

    +
      +
    • Linear Regression
    • +
    • Logistic Regression
    • +
    + + +

    What is variance?

    + +

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    + +

    low varince means that we have small variation in the changes of training data with prediction in target function! +high variance means there is a high variation in the prediction of the target function with changes in the training dataset

    + +

    a model that has high variance is well-performed with training data but can not generalize unseen dataset as well. +high variance leads to overfitting and increases model complexities! +

    + +

    machine learning algorithms with low variance:

    +
      +
    • Linear Regression
    • +
    • Logistic Regression
    • +
    + +

    machine learning algorithms with high variance:

    +
      +
    • decision tree
    • +
    • K-nearest neighbours
    • +
    + +in general variance shows us how much our model is dependent to our dataset! + +

    in the following image you can see the impact of bias and variance in machine learning model:

    + + + +

    Bias and Variance Trade-Off

    +

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! +low-bias and high-variance leads to overfitting, high-bias and low-variance leads to unferfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. +in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    + + + + + +

    OverFitting and Underfitting

    +

    Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

    + +

    An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

    +
      +
    • Generalization: It shows how well a model is trained to predict unseen data.

    • +
    • Noise: Noise is meaningless or irrelevant data present in the dataset. It affects the performance of the model if it is not removed.
    • +
    + +

    The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

    + +

    There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

    + +

    Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

    + + +

    So what is overfitting?

    +

    when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
    +This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize. +An overfitted model is said to have low bias and high variance. +

    +

    To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

    + + +

    What is underfiting?

    +

    Underfitting refers to a model that can neither model the training data nor generalize to new data. +An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

    + + +

    and how to prevent overfitting?

    +
      +
    • cross validation: In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds.
    • +
    • regularization: in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function
    • +
    • ...
    • +
    + + + + + + + + +

    Parameter Estiamtion

    + + +

    What is MLE?

    + +

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    + +

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    +

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    +L(x1,x2,⋯,xn;θ) = P(X1=x1,X2=x2,⋯,Xn=xn;θ) + +

      +
    1. If Xi's are discrete, then the likelihood function is defined as +L(x1,x2,⋯,xn;θ) = PX1X2⋯Xn(x1,x2,⋯,xn;θ).
    2. + +
    3. If Xi's are jointly continuous, then the likelihood function is defined as +L(x1,x2,⋯,xn;θ)=fX1X2⋯Xn(x1,x2,⋯,xn;θ).
    4. +
    +

    + +

    In some problems, it is easier to work with the log likelihood function given by +ln L(x1,x2,⋯,xn;θ).

    + +

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1, X2=x2, ⋯, Xn=xn. The maximum likelihood estimate of θ, shown by θ^ML is the value that maximizes the likelihood function +L(x1,x2,⋯,xn;θ). +

    + +

    Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

    + + +

    Waht is MAP?

    + +

    we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

    + +

    in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution.
    +After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y, +we use bayes formula for calculating posterior distribution. +

    + + +

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we explained it later!

    + +

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    + +

    Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes: +
    fY|X(y|x)fX(x)
    +

    + +


    in many cases we choose alpha-beta distribution for prior distribution

    + + +

    Handle unseen events

    + +

    One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example. +

    + +
    + +

    + +Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset.

    + +
    + +| data | label | +| :-----------: | :-----------: | +|[1, 1, 1, 0, 1]| a | +|[1, 0, 1, 0, 0]| a | +|[0, 0, 1, 0, 1]| a | +|[0, 1, 1, 0, 0]| a | +|[0, 0, 1, 0, 0]| a | +|[0, 0, 0, 0, 1]| b | +|[0, 1, 1, 0, 1]| b | +|[0, 1, 0, 1, 1]| b | +|[0, 1, 1, 1, 1]| b | +|[0, 0, 0, 1, 1]| b | + +

    + +We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset.

    + + + +

    Now, we calculate the probability of each label based on the created naïve Bayes model.

    + +
    + +$P\left(label=a\right)\propto\frac{2}{5}\times\frac{2}{5}\times0\times1\times\frac{2}{5}=0$ + +
    + +$P\left(label=b\right)\propto0\times\frac{3}{5}\times\frac{3}{5}\times\frac{2}{5}\times1=0$ + +

    + +If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b.

    + +
    + +So, what would we do to handle this situation? + + +

    Laplace Smoothing

    +

    One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is: +

    + + +$P\left(color=green\right)=1$ + +
    + +$P\left(color=yellow\right)=0$ +

    Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows:

    + + +$P\left(color=green\right)=\frac{4}{5}$ + +
    + +$P\left(color=yellow\right)=\frac{1}{5}$ + +

    In general:

    + +$P_{LAP,k}\left(x\right)=\frac{c\left(x\right)+k}{N+k\left|X\right|}$ + +
    + +

    And for conditional probabilities:

    + +$P_{LAP,k}\left(x|y\right)=\frac{c\left(x,y\right)+k}{c\left(y\right)+k\left|X\right|}$ + +Using Laplace smoothing with large k is not appropriate as it ignores the prior belief. + + +  + +

    + +Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data:

    + +| data | label | +| :-----------: | :-----------: | +|[1, 1, 1, 1, 1]| a | +|[1, 1, 1, 1, 1]| b | +|[0, 0, 0, 0, 0]| a | +|[0, 0, 0, 0, 0]| b | + + + +$P\left(label=a\right)\propto\frac{3}{7}\times\frac{3}{7}\times\frac{1}{7}\times\frac{6}{7}\times\frac{3}{7}=\frac{162}{16807}$ + +
    + +$P\left(label=b\right)\propto\frac{1}{7}\times\frac{4}{7}\times\frac{4}{7}\times\frac{3}{7}\times\frac{6}{7}=\frac{288}{16807}$ + + + +

    Linear interpolation

    + + +

    + +In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large. + +

    + + + +

    + +Another useful method is linear interpolation. Linear interpolation (also known as Lerp) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line.

    + +

    + +In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$ + +

    + +
    +

    In general:

    + +$P_{LIN}\left(x\middle|\ y\right)=\alpha P\left(x\middle|\ y\right)+\left(1-\alpha\right)P\left(x\right),\ 0<\alpha<1$ + +

    By choosing an appropriate value for $\alpha$, we can handle unseen events.

    + + + +

    More about dataset

    + +

    + +In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\alpha$ and k?

    + +
    + +

    We introduce three datasets:

    + + +

    Training Dataset

    +The sample of data used to fit the model. +

    The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data.

    + + +

    Validation Dataset

    +The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration. +

    The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\alpha$ and $k$.

    + +
    + + + +
    + + +

    Test Dataset

    +The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset. +

    The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world.

    + + +

    About the dataset split ratio

    +

    Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets.


    +

    This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training.


    +

    Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too!

    + + + + + +

    Conclusion

    +

    so in this chapter, we introduced key concepts of machine learning. +we learned about the applications of ML, supervised and unsupervised in ML, and some algorithms like naive Bayes. +after these primary concepts, we learned about some problems like bias and variance and their relations to overfitting and underfitting. +for parameter estimation, we learned two statistical approaches like Bayesian and frequentist approach and after that, we used these two frameworks and some formulas like Laplace and linear interpolation which are based on MLE and MAP. +we also learned about how to work with datasets in machine learning

    + + +

    References

    + +[Gentle Introduction to the Bias-Variance Trade-Off in Machine Learning](https://machinelearningmastery.com/gentle-introduction-to-the-bias-variance-trade-off-in-machine-learning/). + +
    + +[Understanding the Bias-Variance Tradeoff](https://towardsdatascience.com/understanding-the-bias-variance-tradeoff-165e6942b229). + +
    + +[Underfitting and Overfitting](https://www.geeksforgeeks.org/underfitting-and-overfitting-in-machine-learning/). + +
    + +[Probability concepts explained: Maximum likelihood estimation](https://towardsdatascience.com/probability-concepts-explained-maximum-likelihood-estimation-c7b4342fdbb1). + +
    + +[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). + From b336ec90e551fa8694e2ec92c10bca62d325c4f0 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 18:55:04 +0330 Subject: [PATCH 04/21] some comments resolved --- .../images/bayes_net.png | Bin 0 -> 20047 bytes .../images/intro_pic_3.png | Bin 0 -> 162158 bytes .../images/intro_pic_4.png | Bin 0 -> 197639 bytes .../images/intro_pic_5.png | Bin 0 -> 14596 bytes .../images/intro_pic_6.png | Bin 0 -> 1077354 bytes .../images/intro_pic_7.png | Bin 0 -> 286613 bytes .../images/naive_bayes_inference.png | Bin 0 -> 78923 bytes .../12_Intro_to_machine_learning/index.md | 442 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    Introduction

    -

    Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations?

    - -

    Machine learning technics allow computers to automatically learn from a historical dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our past dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm:

    - - -

    History

    -

    The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief:

    -
  • 1834: Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure.
  • -
  • 1936: Alan Turing gave a theory about how machines can execute a set of instructions.
  • -
  • 1940: First manually operated computer named "ENIAC" was invented.
  • -
  • 1943: The first model of human neural network was modeled with electronic circuits.
  • -
  • 1950: "Computer Machinery and Intelligence," was published by Alan Turing on the topic of AI with this question, "Can machines think?".
  • -
  • 1952: Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more.
  • -
  • 1959: Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter.
  • -
  • 1974 to 1980: These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced.
  • -
  • 1985: A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week.
  • -
  • 1997: The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov.
  • -
  • 2006: Geoffrey Hinton has first used name of "deep learning" instead of neural net research.
  • -
  • 2012: Google developed a deep neural network system to distinguish cat and human images in a YouTube video.
  • -
  • 2016: AlphaGo won a Go game against number one and number second player of Go.
  • - -

    ML Applications

    -

    The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are:

    -
  • Image recognition:

    One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms.

  • -
  • Speech Recognition:

    This project converts your voice to text and is also known as "Computer speech recognition." Some examples of this technology are Google assistant, Siri, Cortana, and Alexa.

  • -
  • Traffic prediction:

    Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users.

  • -
  • Product recommendations:

    Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its last searches or other features that are used in dataset.

  • - -

    Types of Machine Learning

    -

    There are three major recognized categories for ML:

    - - -

    Supervised Learning

    -

    In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless. -The supervised algorithms are grouped in two main categories: -

    -
      -
    • Classification
    • -
    • Regression
    • -
    - -

    Classification

    -

    In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that the output of classification algorithm is a label or category, but the output of a regression algorithm is a value. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem:

    -
  • Lazy Learners:

      These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are:

      -
    • K-NN algorithm
    • -
    • b. Case-based reasoning
    • -
    -
  • -
  • Eager Learners:

      In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are:

      -
    • Decision Trees
    • -
    • Naïve Bayes
    • -
    • ANN
    • -
    -
  • - -

    Naïve Bayes Classifier Algorithm

    -

    Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem.

    -
      -

      Advantages of Naïve Bayes Classifier

      -
        -
      • It is fast and not that much complicated.
      • -
      • It can be used for Binary as well as Multi-class Classifications.
      • -
      • It is the most popular choice for text classification problems.
      • -
      -

      Disadvantages of Naïve Bayes Classifier

      -
        -
      • Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact.
      • -
      -
    - -

    Unsupervised Learning

    -

    In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format. -The supervised algorithms are grouped in two main categories: -

    -
      -
    • Clustering
    • -
    • Association
    • -
    +1. [Introduction](#introduction) + 1. [History](#history) + 2. [ML Applications](#ml-applications) +2. [Types of Machine Learning](#types-of-machine-learning) + 1. [Supervised Learning](#supervised-learning) + 1. [Classification](#classification) + 2. [Naïve Bayes Classifier Algorithm](#naïve-bayes-Classifier-algorithm) + 2. [Unsupervised Learning](#unsupervised-learning) +3. [Bias and Variance](#bias-and-variance) + 1. [What is Bias?](#what-is-Bbas?) + 2. [What is variance?](#what-is-variance?) + 3. [Bias and Variance Trade-Off](#bias-and-variance-trade-off) +4. [OverFitting and Underfitting](#overFitting-and-underfitting) + 1. [So what is overfitting?](#so-what-is-overfitting?) + 2. [What is underfiting?](#what-is-underfiting?) + 3. [and how to prevent overfitting?](#and-how-to-prevent-overfitting?) +5. [Parameter Estiamtion](#parameter-estiamtion) + 1. [What is MLE?](#what-is-mle?) + 2. [Waht is MAP?](#waht-is-map?) +6. [Handle unseen events](#handle-unseen-events) + 1. [Laplace Smoothing](#laplace-smoothing) + 2. [Linear interpolation](#linear-interpolation) +7. [More about dataset](#more-about-dataset) + 1. [Training Dataset](#training-dataset) + 2. [Validation Dataset](#validation-dataset) + 3. [Test Dataset](#test-Dataset) + 4. [About the dataset split ratio](#about-the-dataset-split-ratio) +8. [Conclusion](#conclusion) +9. [References](#references) + +# Introduction +Humans are capable of learning by experiencing, but how about computers? Can they learn from past data and make correct decisions for future situations? + +![](./images/intro_pic_1.png) + +Machine learning techniques allow computers to automatically learn from a dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm: + +![](./images/intro_pic_2.png) + +## History +The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief: + +* **1834:** Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure. +* **1936:** Alan Turing gave a theory about how machines can execute a set of instructions. +* **1940:** First manually operated computer named "ENIAC" was invented. +* **1943:** The first model of human neural network was modeled with electronic circuits. +* **1950:** "Computer Machinery and Intelligence," was published by Alan Turing on the topic of AI with this question, "Can machines think?". +* **1952:** Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more. +* **1959:** Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter. +* **1974 to 1980:** These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced. +* **1985:** A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week. +* **1997:** The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov. +* **2006:** Geoffrey Hinton has first used name of "deep learning" instead of neural net research. +* **2012:** Google developed a deep neural network system to distinguish cat and human images in a YouTube video. +* **2016:** AlphaGo won a Go game against number one and number second player of Go. + +## ML Applications + + +![](./images/intro_pic_3.png) + +The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are: + +* **Image recognition:** + + One example can be Facebook friends tagging suggestion that when we upload a photo with our Facebook friends, then we can see some labels suggestions with their names. This project is called Deep Face which uses face detection and recognition algorithms. + +![](./images/intro_pic_4.png) +* **Speech Recognition:** + + This project converts your voice to text and is also known as "Computer speech recognition." Some examples of this technology are Google assistant, Siri, Cortana, and Alexa. + +![](./images/intro_pic_5.png) +* **Traffic prediction:** + + Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users. + +![](./images/intro_pic_6.png) +* **Product recommendations:** + + Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its previous searches or other features that are used in dataset. + +![](./images/intro_pic_7.png) + +# Types of Machine Learning + + +There are three major recognized categories for ML: + +![](./images/types_learning_1.png) + +## Supervised Learning + + +In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished, the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless. The supervised algorithms are grouped in two main categories: + +* **Classification** +* **Regression** + +### Classification + +In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that classification is a process of finding a function which helps in dividing the dataset into classes based on different parameters, but regression is a process of finding the correlations between dependent and independent variables. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem: + +* **Lazy Learners:** + + Lazy learning methods simply store the data and generalizing beyond these data is postponed until an explicit request is made. In this case we just store dataset without learning from it and start classifying data when test data is received. These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are: + + * K-Nearest Neighbours algorithm + * Case-based reasoning +* **Eager Learners:** + + Eager learning methods construct general (one-fits-all), explicit (input independent) description of the target function based on the provided training examples. In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are: + + * Decision Trees + * Naïve Bayes + * ANN + +### Naïve Bayes Classifier Algorithm + +Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem. + +A general naïve bayes model has the form below that Y is our label variable and F is our feature set: + +![](./images/bayes_net.png) + +As a result of bayes net above and bayes theorem we can say that: +$P\\left(Y, F\_1, F\_2, ..., F\_n\\right) = P\\left(Y\\right)\\prod\_{i}P(F\_i|Y)$ +As we can use this equation for computing posterior distribution over label variable Y first by calculating joint probibility of evidence and label for each label using equation above second sum to get probability of evidence and then divide the first by second to calculate $P\\left(Y| F\_1, F\_2, ..., F\_n\\right)$ . +The process can be seen in figure below: + +![](./images/naive_bayes_inference.png) + +#### Advantages of Naïve Bayes Classifier + +* It is fast and not that much complicated. +* It can be used for Binary as well as Multi-class Classifications. +* It is the most popular choice for text classification problems. + +#### Disadvantages of Naïve Bayes Classifier + +* Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact. + +## Unsupervised Learning +In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format. The unsupervised algorithms are grouped in two main categories: + +* **Clustering** +* **Association**

    Bias and Variance

    -if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors shows small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    +if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors causes small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    @@ -275,19 +312,21 @@ we use bayes formula for calculating posterior distribution.


    in many cases we choose alpha-beta distribution for prior distribution

    - -

    Handle unseen events

    -

    One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example. -

    -
    -

    -Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset.

    -
    + + + + +# Handle unseen events + +One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example. + +Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset. + | data | label | | :-----------: | :-----------: | @@ -302,68 +341,55 @@ Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training |[0, 1, 1, 1, 1]| b | |[0, 0, 0, 1, 1]| b | -

    - -We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset.

    +We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes model. First, we create a naïve Bayes model based on the training dataset. - +![](./images/naive_model_1.png) -

    Now, we calculate the probability of each label based on the created naïve Bayes model.

    +Now, we calculate the probability of each label based on the created naïve Bayes model. -
    -$P\left(label=a\right)\propto\frac{2}{5}\times\frac{2}{5}\times0\times1\times\frac{2}{5}=0$ +$P(label=a)\propto\frac{2}{5}\times\frac{2}{5} \times0\times1\times\frac{2}{5}=0$ -
    -$P\left(label=b\right)\propto0\times\frac{3}{5}\times\frac{3}{5}\times\frac{2}{5}\times1=0$ +$P(label=b)\propto0\times\frac{3}{5}\times\frac{3}{5}\times\frac{2}{5}\times1=0$ -

    -If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b.

    +If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b. -
    -So, what would we do to handle this situation? +**So, what would we do to handle this situation?** - -

    Laplace Smoothing

    -

    One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is: -

    - +## Laplace Smoothing -$P\left(color=green\right)=1$ +One of the most common methods to solve the above problem is using Laplace smoothing. Consider a bag of green and yellow balls. Suppose there are three green balls and no yellow balls in the bag. So, the probability of each color is: -
    +![](./images/balls_1.png) -$P\left(color=yellow\right)=0$ -

    Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows:

    - +$P(color=green)=1$ -$P\left(color=green\right)=\frac{4}{5}$ +$P(color=yellow)=0$ -
    +Using Laplace smoothing, we pretend that we saw every outcome extra time. For the above example, by using Laplace smoothing with, the probabilities for each color are as follows: -$P\left(color=yellow\right)=\frac{1}{5}$ +![](./images/balls_2.png) -

    In general:

    +$P(color=green)=\frac{4}{5}$ -$P_{LAP,k}\left(x\right)=\frac{c\left(x\right)+k}{N+k\left|X\right|}$ -
    +$P(color=yellow)=\frac{1}{5}$ -

    And for conditional probabilities:

    +In general: -$P_{LAP,k}\left(x|y\right)=\frac{c\left(x,y\right)+k}{c\left(y\right)+k\left|X\right|}$ +$P_{LAP,k}(x)=\frac{c(x)+k}{N+k|X|}$ -Using Laplace smoothing with large k is not appropriate as it ignores the prior belief. +And for conditional probabilities: +$P_{LAP,k}(x|y)=\frac{c(x,y)+k}{c(y)+k|X|}$ -  +**Using Laplace smoothing with large k is not appropriate as it ignores the prior belief.** -

    -Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data:

    +Now, back to the label prediction example. We use Laplace smoothing with $k=1$ and calculate label probabilities again. We consider the following extra data: | data | label | | :-----------: | :-----------: | @@ -372,112 +398,78 @@ Now, back to the label prediction example. We use Laplace smoothing with $k=1$ a |[0, 0, 0, 0, 0]| a | |[0, 0, 0, 0, 0]| b | - - -$P\left(label=a\right)\propto\frac{3}{7}\times\frac{3}{7}\times\frac{1}{7}\times\frac{6}{7}\times\frac{3}{7}=\frac{162}{16807}$ +![](./images/naive_model_2.png) -
    +$P(label=a)\propto\frac{3}{7}\times\frac{3}{7}\times\frac{1}{7}\times\frac{6}{7}\times\frac{3}{7}=\frac{162}{16807}$ -$P\left(label=b\right)\propto\frac{1}{7}\times\frac{4}{7}\times\frac{4}{7}\times\frac{3}{7}\times\frac{6}{7}=\frac{288}{16807}$ +$P(label=b)\propto\frac{1}{7}\times\frac{4}{7}\times\frac{4}{7}\times\frac{3}{7}\times\frac{6}{7}=\frac{288}{16807}$ - -

    Linear interpolation

    +## Linear interpolation -

    - -In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large. +In practice, Laplace smoothing often performs poorly for $P(X|Y)$ When $X$ or $Y$ is very large. -

    +Another useful method is **linear interpolation**. Linear interpolation (also known as **Lerp**) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line. -

    -Another useful method is linear interpolation. Linear interpolation (also known as Lerp) is a method to find unknown values between two known points. The unknown values are approximated through Linear interpolation by connecting these two known points with a straight line.

    +In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$ -

    +In general: -In this method, we consider both $p(x|y)$ and $p(x)$ to calculate the $p(x|y)$ +$P_{LIN}(x|y)=\alpha P(x|y)+(1-\alpha)P(x), 0<\alpha<1$ -

    +By choosing an appropriate value for $\alpha$, we can handle unseen events. -
    -

    In general:

    -$P_{LIN}\left(x\middle|\ y\right)=\alpha P\left(x\middle|\ y\right)+\left(1-\alpha\right)P\left(x\right),\ 0<\alpha<1$ +# More about dataset -

    By choosing an appropriate value for $\alpha$, we can handle unseen events.

    +In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\alpha$ and k? +We introduce three datasets: - -

    More about dataset

    +## Training Dataset -

    +**The sample of data used to fit the model.** +The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data. -In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\alpha$ and k?

    +## Validation Dataset +**The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.** +The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\alpha$ and $k$. -
    +![](./images/diagram.png) -

    We introduce three datasets:

    +## Test Dataset - -

    Training Dataset

    -The sample of data used to fit the model. -

    The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data.

    +**The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset.** - -

    Validation Dataset

    -The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration. -

    The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\alpha$ and $k$.

    +The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world. -
    +## About the dataset split ratio +Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets. +This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training. +Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too! - +![](./images/ratio.png) -
    - -

    Test Dataset

    -The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset. -

    The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world.

    - - -

    About the dataset split ratio

    -

    Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets.


    -

    This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training.


    -

    Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too!

    - - - - - -

    Conclusion

    -

    so in this chapter, we introduced key concepts of machine learning. +# Conclusion +so in this chapter, we introduced key concepts of machine learning. we learned about the applications of ML, supervised and unsupervised in ML, and some algorithms like naive Bayes. after these primary concepts, we learned about some problems like bias and variance and their relations to overfitting and underfitting. for parameter estimation, we learned two statistical approaches like Bayesian and frequentist approach and after that, we used these two frameworks and some formulas like Laplace and linear interpolation which are based on MLE and MAP. -we also learned about how to work with datasets in machine learning

    - - -

    References

    - -[Gentle Introduction to the Bias-Variance Trade-Off in Machine Learning](https://machinelearningmastery.com/gentle-introduction-to-the-bias-variance-trade-off-in-machine-learning/). - -
    - -[Understanding the Bias-Variance Tradeoff](https://towardsdatascience.com/understanding-the-bias-variance-tradeoff-165e6942b229). - -
    +we also learned about how to work with datasets in machine learning. -[Underfitting and Overfitting](https://www.geeksforgeeks.org/underfitting-and-overfitting-in-machine-learning/). +# References -
    +[Gentle Introduction to the Bias-Variance Trade-Off in Machine Learning](https://machinelearningmastery.com/gentle-introduction-to-the-bias-variance-trade-off-in-machine-learning/). -[Probability concepts explained: Maximum likelihood estimation](https://towardsdatascience.com/probability-concepts-explained-maximum-likelihood-estimation-c7b4342fdbb1). +[Understanding the Bias-Variance Tradeoff](https://towardsdatascience.com/understanding-the-bias-variance-tradeoff-165e6942b229). -
    +[Underfitting and Overfitting](https://www.geeksforgeeks.org/underfitting-and-overfitting-in-machine-learning/). -[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). +[Probability concepts explained: Maximum likelihood estimation](https://towardsdatascience.com/probability-concepts-explained-maximum-likelihood-estimation-c7b4342fdbb1). +[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). \ No newline at end of file From a8ccfeab9aeea2c63477c2b08bdf250ef984df0b Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 19:28:47 +0330 Subject: [PATCH 05/21] small changes --- .../12_Intro_to_machine_learning/index.md | 21 ++++++++++--------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index 1828bcb9..a5b98b35 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -158,12 +158,12 @@ if the model in machine learning is not accurate, it will make errors and these

    What is Bias?

    -In general, a machine learning model analyses the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. -While the model in making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors -It can be defined as an inability of ml algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ml has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either: +In general, a machine learning model analyzes the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. +While the model is making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors +It can be defined as an inability of ML algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ML has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either:

    • High Bias: A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data.
    • -
    • Low Bias: A low bias model has fewer assumptions about the form of the function of dataset.
    • +
    • Low Bias: A low bias model will make fewer assumptions about the form of the target function.
    linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias.

    @@ -185,10 +185,10 @@ linear algorithms have a high bias, as they learn fast. The simpler the algorith

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    -

    low varince means that we have small variation in the changes of training data with prediction in target function! +

    low varince means that we have small variation in the changes of training data with prediction in target function! high variance means there is a high variation in the prediction of the target function with changes in the training dataset

    -

    a model that has high variance is well-performed with training data but can not generalize unseen dataset as well. +

    a model that has high variance performs well on training data but can not generalize unseen dataset as well. high variance leads to overfitting and increases model complexities!

    @@ -212,7 +212,7 @@ in general variance shows us how much our model is dependent to our dataset!

    Bias and Variance Trade-Off

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! -low-bias and high-variance leads to overfitting, high-bias and low-variance leads to unferfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. +low-bias and high-variance leads to overfitting, high-bias and low-variance leads to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    @@ -267,7 +267,7 @@ An underfit machine learning model is not a suitable model and will be obvious a

    What is MLE?

    -

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data. From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    +

    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    @@ -300,9 +300,10 @@ L(x1,x2,⋯,xn;θ). After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y, we use bayes formula for calculating posterior distribution.

    - -

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we explained it later!

    +![](./images/formula.PNG) + +

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we will explain it later!

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    From 7ebe84f0c41717abbe605239d1d6c145b3088893 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 31 Dec 2021 19:49:18 +0330 Subject: [PATCH 06/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index a5b98b35..eaf5e247 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -8,7 +8,7 @@ 2. [Naïve Bayes Classifier Algorithm](#naïve-bayes-Classifier-algorithm) 2. [Unsupervised Learning](#unsupervised-learning) 3. [Bias and Variance](#bias-and-variance) - 1. [What is Bias?](#what-is-Bbas?) + 1. [What is Bias?](#what-is-bias?) 2. [What is variance?](#what-is-variance?) 3. [Bias and Variance Trade-Off](#bias-and-variance-trade-off) 4. [OverFitting and Underfitting](#overFitting-and-underfitting) @@ -473,4 +473,4 @@ we also learned about how to work with datasets in machine learning. [Probability concepts explained: Maximum likelihood estimation](https://towardsdatascience.com/probability-concepts-explained-maximum-likelihood-estimation-c7b4342fdbb1). -[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). \ No newline at end of file +[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). From 835c0c57ccf527179c1d22b3e7f7e9872e036634 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 31 Dec 2021 20:06:04 +0330 Subject: [PATCH 07/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index eaf5e247..6efb41b3 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -326,7 +326,7 @@ we use bayes formula for calculating posterior distribution. One of the most important concepts in machine learning is to handle unseen events. To clarify, consider the following example. -Consider the vector $X=[x_1,x_2,x_3,x_4,x_5]$ and the following data as training dataset. +Consider the vector $ X=[x_1,x_2,x_3,x_4,x_5] $ and the following data as training dataset. | data | label | @@ -349,10 +349,10 @@ We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes mo Now, we calculate the probability of each label based on the created naïve Bayes model. -$P(label=a)\propto\frac{2}{5}\times\frac{2}{5} \times0\times1\times\frac{2}{5}=0$ +$P(label=a)\propto \frac{2}{5}\times \frac{2}{5}\times 0\times 1\times \frac{2}{5}=0$ -$P(label=b)\propto0\times\frac{3}{5}\times\frac{3}{5}\times\frac{2}{5}\times1=0$ +$P(label=b)\propto \times \frac{3}{5}\times \frac{3}{5}\times \frac{2}{5}\times 1=0$ If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b. From b013b3d177d225b41498184871d2a167d879f432 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 31 Dec 2021 20:12:42 +0330 Subject: [PATCH 08/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index 6efb41b3..f6fe0431 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -349,10 +349,10 @@ We want to predict the label of $[1, 1, 0, 0, 1]$ using a simple naïve Bayes mo Now, we calculate the probability of each label based on the created naïve Bayes model. -$P(label=a)\propto \frac{2}{5}\times \frac{2}{5}\times 0\times 1\times \frac{2}{5}=0$ +$P(label=a)\propto \frac{2}{5} \times \frac{2}{5} \times 0 \times 1 \times \frac{2}{5} = 0$ -$P(label=b)\propto \times \frac{3}{5}\times \frac{3}{5}\times \frac{2}{5}\times 1=0$ +$P(label=b)\propto 0 \times \frac{3}{5} \times \frac{3}{5} \times \frac{2}{5} \times 1 = 0$ If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b. @@ -401,10 +401,10 @@ Now, back to the label prediction example. We use Laplace smoothing with $k=1$ a ![](./images/naive_model_2.png) -$P(label=a)\propto\frac{3}{7}\times\frac{3}{7}\times\frac{1}{7}\times\frac{6}{7}\times\frac{3}{7}=\frac{162}{16807}$ +$P(label=a)\propto \frac{3}{7} \times \frac{3}{7} \times \frac{1}{7} \times \frac{6}{7} \times \frac{3}{7} = \frac{162}{16807}$ -$P(label=b)\propto\frac{1}{7}\times\frac{4}{7}\times\frac{4}{7}\times\frac{3}{7}\times\frac{6}{7}=\frac{288}{16807}$ +$P(label=b)\propto \frac{1}{7} \times \frac{4}{7} \times \frac{4}{7} \times \frac{3}{7} \times \frac{6}{7} = \frac{288}{16807}$ ## Linear interpolation From 4d20064c1b9ac1604ee05cd543e4773a3a648ff7 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 31 Dec 2021 20:25:34 +0330 Subject: [PATCH 09/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index f6fe0431..d2f9c402 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -437,14 +437,14 @@ We introduce three datasets: The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data. ## Validation Dataset -**The sample of data used to provide an unbiased evaluation of a model fit on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.** +**The sample of data used to provide an unbiased evaluation of a trained model on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.** The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\alpha$ and $k$. ![](./images/diagram.png) ## Test Dataset -**The sample of data used to provide an unbiased evaluation of a final model fit on the training dataset.** +**The sample of data used to provide an unbiased evaluation of final trained model on the training dataset.** The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world. 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    The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

    We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

    -

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ=(θ1,θ2,⋯,θk).) Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    -L(x1,x2,⋯,xn;θ) = P(X1=x1,X2=x2,⋯,Xn=xn;θ) +

    Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, + + θ + + = + ( + + θ + 1 + + , + + θ + 2 + + , + + , + + θ + k + + ) +. Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
    + + + + + L + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + + + + = + P + ( + + X + 1 + + = + + x + 1 + + , + + X + 2 + + = + + x + 2 + + , + + , + + X + n + + = + + x + n + + ; + θ + ) + + + + + + + = + + P + + + X + 1 + + + X + 2 + + + + X + n + + + + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + . + + + +

    1. If Xi's are discrete, then the likelihood function is defined as -L(x1,x2,⋯,xn;θ) = PX1X2⋯Xn(x1,x2,⋯,xn;θ).
    2. + + + + + L + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + = + + P + + + X + 1 + + + X + 2 + + + + X + n + + + + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + . + + + +.
    3. If Xi's are jointly continuous, then the likelihood function is defined as -L(x1,x2,⋯,xn;θ)=fX1X2⋯Xn(x1,x2,⋯,xn;θ).
    4. + + + + + L + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + = + + f + + + X + 1 + + + X + 2 + + + + X + n + + + + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + . + + + +.

    In some problems, it is easier to work with the log likelihood function given by -ln L(x1,x2,⋯,xn;θ).

    - -

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1, X2=x2, ⋯, Xn=xn. The maximum likelihood estimate of θ, shown by θ^ML is the value that maximizes the likelihood function -L(x1,x2,⋯,xn;θ). + + + + + ln + + L + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + . + + + +.

    + +

    Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1 , X2=x2 , ⋯ , Xn=xn . The maximum likelihood estimate of θ is the value that maximizes the likelihood function: + + + + + L + ( + + x + 1 + + , + + x + 2 + + , + + , + + x + n + + ; + θ + ) + . + + + +.

    Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

    @@ -303,12 +636,91 @@ we use bayes formula for calculating posterior distribution. ![](./images/formula.PNG) -

    in the above image we have Fx|y(x|y) as postrior distribution and fx(X) as priror distribution. in many problems Fy|x(y|x) is MLE function that we will explain it later!

    - -

    The posterior distribution, fX|Y(x|y), contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    - -

    Note that fY(y) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes: -
    fY|X(y|x)fX(x)
    +

    in the above image we have + + + f + + X + + | + + Y + + + ( + x + + | + + y + ) + as postrior distribution and + + + f + + X + + + ( + x + ) + as priror distribution. in many problems + + + f + + Y + + | + + X + + + ( + y + + | + + x + ) + is MLE function that we explained it!

    + +

    The posterior distribution, + + + f + + X + + | + + Y + + + ( + x + + | + + y + ) +, contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

    + +

    Note that + + f + + Y + + + ( + y + ) + + does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:
    +


    in many cases we choose alpha-beta distribution for prior distribution

    From 33603412a7d45a5dd3cfaf5d1fe8163180f9b313 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 20:55:18 +0330 Subject: [PATCH 11/21] index --- .../12_Intro_to_machine_learning/index.md | 33 +++++++------------ 1 file changed, 11 insertions(+), 22 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index cb9cae8e..fcc7d02b 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -148,15 +148,13 @@ In this method our training dataset doesn’t contain labels and they have not b * **Clustering** * **Association** - -

    Bias and Variance

    +# Bias and Variance

    if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors causes small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

    On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

    - -

    What is Bias?

    +## What is Bias?

    In general, a machine learning model analyzes the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. While the model is making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors @@ -180,8 +178,7 @@ linear algorithms have a high bias, as they learn fast. The simpler the algorith

  • Logistic Regression
  • - -

    What is variance?

    +## What is variance?

    The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

    @@ -209,8 +206,7 @@ in general variance shows us how much our model is dependent to our dataset!

    in the following image you can see the impact of bias and variance in machine learning model:

    - -

    Bias and Variance Trade-Off

    +## Bias and Variance Trade-Off

    the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! low-bias and high-variance leads to overfitting, high-bias and low-variance leads to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

    @@ -218,8 +214,7 @@ in simple words bias and variance are related to each other and we can not reduc - -

    OverFitting and Underfitting

    +# OverFitting and Underfitting

    Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

    An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

    @@ -234,21 +229,18 @@ in simple words bias and variance are related to each other and we can not reduc

    Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

    - -

    So what is overfitting?

    +## So what is overfitting?

    when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
    This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize. An overfitted model is said to have low bias and high variance.

    To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

    - -

    What is underfiting?

    +## What is underfiting?

    Underfitting refers to a model that can neither model the training data nor generalize to new data. An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

    - -

    and how to prevent overfitting?

    +## and how to prevent overfitting?

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    • cross validation: In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds.
    • regularization: in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function
    • @@ -261,11 +253,9 @@ An underfit machine learning model is not a suitable model and will be obvious a - -

      Parameter Estiamtion

      +# Parameter Estiamtion - -

      What is MLE?

      +## What is MLE?

      The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

      @@ -624,8 +614,7 @@ An underfit machine learning model is not a suitable model and will be obvious a

      Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

      - -

      Waht is MAP?

      +## Waht is MAP?

      we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

      From db6f5e570f2c0ad9a455caab901fe01625c13980 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 21:33:41 +0330 Subject: [PATCH 12/21] some html to md --- .../12_Intro_to_machine_learning/index.md | 202 +++++++++--------- 1 file changed, 100 insertions(+), 102 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index fcc7d02b..d79098fa 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -150,102 +150,100 @@ In this method our training dataset doesn’t contain labels and they have not b * **Association** # Bias and Variance -

      -if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors causes small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions

      -

      On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset.

      + +if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors causes small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions. +On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset. ## What is Bias? -

      + In general, a machine learning model analyzes the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. -While the model is making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors -It can be defined as an inability of ML algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ML has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either: -

        -
      • High Bias: A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data.
      • -
      • Low Bias: A low bias model will make fewer assumptions about the form of the target function.
      • -
      +**While the model is making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors** +It can be defined as an inability of ML algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ML has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either: + +- **High Bias:** A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data. +- **Low Bias:** A low bias model will make fewer assumptions about the form of the target function. + linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias. -

      -

      Machine learning algorithm with low bias:

      -
        -
      • Decision Trees
      • -
      • k-Nearest Neighbours
      • -
      -

      Machine learning algorithm with high bias:

      -
        -
      • Linear Regression
      • -
      • Logistic Regression
      • -
      +#### Machine learning algorithm with low bias:#### + +- Decision Trees +- k-Nearest Neighbours + + +#### Machine learning algorithm with high bias: +- Linear Regression +- Logistic Regression + -## What is variance? +## What is variance? + +The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has **low variance** but some of them has **high variance.** -

      The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has low variance but some of them has high variance.

      +**low varince** means that we have small variation in the changes of training data with prediction in target function! +**high variance means there is a high variation in the prediction of the target function with changes in the training dataset** -

      low varince means that we have small variation in the changes of training data with prediction in target function! -high variance means there is a high variation in the prediction of the target function with changes in the training dataset

      +a model that has high variance performs well on training data but can not generalize unseen dataset as well. +high variance leads to overfitting and increases model complexities! -

      a model that has high variance performs well on training data but can not generalize unseen dataset as well. -high variance leads to overfitting and increases model complexities! -

      -

      machine learning algorithms with low variance:

      -
        -
      • Linear Regression
      • -
      • Logistic Regression
      • -
      +#### machine learning algorithms with low variance: +- Linear Regression +- Logistic Regression + + +#### machine learning algorithms with high variance: + +- decision tree +- K-nearest neighbours -

      machine learning algorithms with high variance:

      -
        -
      • decision tree
      • -
      • K-nearest neighbours
      • -
      in general variance shows us how much our model is dependent to our dataset! -

      in the following image you can see the impact of bias and variance in machine learning model:

      +in the following image you can see the impact of bias and variance in machine learning model: ## Bias and Variance Trade-Off -

      the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! +the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! low-bias and high-variance leads to overfitting, high-bias and low-variance leads to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. -in simple words bias and variance are related to each other and we can not reduce both of them simultanously!

      +in simple words bias and variance are related to each other and we can not reduce both of them simultanously! # OverFitting and Underfitting -

      Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y

      +Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y). f(X) = Y + +An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy -

      An important consideration in learning the target function from the training data is how well the model generalizes to new data. Generalization is important because the data we collect is only a sample, it is incomplete and noisy

      -
        -
      • Generalization: It shows how well a model is trained to predict unseen data.

      • -
      • Noise: Noise is meaningless or irrelevant data present in the dataset. It affects the performance of the model if it is not removed.
      • -
      +- **Generalization:** It shows how well a model is trained to predict unseen data. +- **Noise:**
      Noise is meaningless or irrelevant data present in the dataset. It affects the performance of the model if it is not removed. -

      The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen.

      -

      There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

      +The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen. -

      Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms.

      +There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting. + +Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms. ## So what is overfitting? -

      when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm!
      -This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize. -An overfitted model is said to have low bias and high variance. -

      -

      To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting

      +when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm! +This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize. +***An overfitted model is said to have low bias and high variance.*** + +To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting ## What is underfiting? -

      Underfitting refers to a model that can neither model the training data nor generalize to new data. -An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data.

      +Underfitting refers to a model that can neither model the training data nor generalize to new data. +An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data. ## and how to prevent overfitting? -
        -
      • cross validation: In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds.
      • -
      • regularization: in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function
      • -
      • ...
      • -
      + +- **cross validation:** In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds. +- **regularization:** in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function +- ... + @@ -257,10 +255,10 @@ An underfit machine learning model is not a suitable model and will be obvious a ## What is MLE? -

      The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data.

      +The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data. -

      We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE)

      -

      Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, +We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE) +Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, θ @@ -283,8 +281,9 @@ An underfit machine learning model is not a suitable model and will be obvious a k ) -. Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ:
      - + Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ: + +** @@ -394,15 +393,14 @@ An underfit machine learning model is not a suitable model and will be obvious a ; θ ) - . - +** -

        -
      1. If Xi's are discrete, then the likelihood function is defined as - + +- If Xi's are discrete, then the likelihood function is defined as +** @@ -470,10 +468,10 @@ An underfit machine learning model is not a suitable model and will be obvious a -.
      2. +**. -
      3. If Xi's are jointly continuous, then the likelihood function is defined as - +- If Xi's are jointly continuous, then the likelihood function is defined as +** @@ -541,12 +539,13 @@ An underfit machine learning model is not a suitable model and will be obvious a -.
      4. -
      -

      +** + + -

      In some problems, it is easier to work with the log likelihood function given by - +In some problems, it is easier to work with the log likelihood function given by + +** @@ -577,10 +576,10 @@ An underfit machine learning model is not a suitable model and will be obvious a -.

      +.** -

      Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1 , X2=x2 , ⋯ , Xn=xn . The maximum likelihood estimate of θ is the value that maximizes the likelihood function: - +Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1 , X2=x2 , ⋯ , Xn=xn . The maximum likelihood estimate of θ is the value that maximizes the likelihood function: +** @@ -605,27 +604,26 @@ An underfit machine learning model is not a suitable model and will be obvious a ; θ ) - . -. -

      +** -

      Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable

      + +Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable ## Waht is MAP? -

      we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach.

      +we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. -

      in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution.
      +in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution. After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y, -we use bayes formula for calculating posterior distribution. -

      +we use bayes formula for calculating posterior distribution. + ![](./images/formula.PNG) -

      in the above image we have +in the above image we have f @@ -655,8 +653,8 @@ we use bayes formula for calculating posterior distribution. ( x ) - as priror distribution. in many problems - + as priror distribution. in many problems +** f @@ -674,10 +672,10 @@ we use bayes formula for calculating posterior distribution. x ) - is MLE function that we explained it!

      +** is MLE function that we explained it! -

      The posterior distribution, - +The posterior distribution, +** f @@ -695,9 +693,9 @@ we use bayes formula for calculating posterior distribution. y ) -, contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation

      +**, contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation -

      Note that +Note that f @@ -709,10 +707,10 @@ we use bayes formula for calculating posterior distribution. ) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:
      - -

      + + -


      in many cases we choose alpha-beta distribution for prior distribution

      +***in many cases we choose alpha-beta distribution for prior distribution*** From 7d363304a744d017ed78336d051d9e740cc68c37 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 21:38:06 +0330 Subject: [PATCH 13/21] change image tag --- notebooks/12_Intro_to_machine_learning/index.md | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index d79098fa..adddf9cd 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -202,14 +202,14 @@ high variance leads to overfitting and increases model complexities! in general variance shows us how much our model is dependent to our dataset! in the following image you can see the impact of bias and variance in machine learning model: - - + +![](./images/bias-and-variance-in-machine-learning4.png) ## Bias and Variance Trade-Off the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! low-bias and high-variance leads to overfitting, high-bias and low-variance leads to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. in simple words bias and variance are related to each other and we can not reduce both of them simultanously! - - + +![](./images/bias-and-variance-in-machine-learning6.png) # OverFitting and Underfitting @@ -246,8 +246,8 @@ An underfit machine learning model is not a suitable model and will be obvious a - - + +![](./images/overfitting-in-machine-learning.png) @@ -707,8 +707,8 @@ Note that ) does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:
      - - + +![](./images/formula1.png) ***in many cases we choose alpha-beta distribution for prior distribution*** From 2879bf576281983ff78289f8c751ad0ee73e0178 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 22:14:58 +0330 Subject: [PATCH 14/21] tex formulas --- .../12_Intro_to_machine_learning/index.md | 461 ++---------------- 1 file changed, 36 insertions(+), 425 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index adddf9cd..9b3672c9 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -255,460 +255,71 @@ An underfit machine learning model is not a suitable model and will be obvious a ## What is MLE? -The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity θ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data. +The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity $ \theta $ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data. We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE) -Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ (In general, θ might be a vector, - - θ - - = - ( - - θ - 1 - - , - - θ - 2 - - , - - , - - θ - k - - ) - Suppose that x1, x2, x3, ..., xn are the observed values of X1, X2, X3, ..., Xn. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of θ: - -** - - - - L - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - - - - = - P - ( - - X - 1 - - = - - x - 1 - - , - - X - 2 - - = - - x - 2 - - , - - , - - X - n - - = - - x - n - - ; - θ - ) - - - - - - - = - - P - - - X - 1 - - - X - 2 - - - - X - n - - - - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - - - -** +Let $ X_1,X_2,X_3, ... ,X_n $ be a random sample from a distribution with a parameter $ \theta $ (In general, θ might be a vector, ${\theta}=(\theta_1, \theta_2, \cdots, \theta_k)$ Suppose that $ x_1,x_2,x_3, ... ,x_n $ are the observed values of $ X_1,X_2,X_3, ... ,X_n $. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of $ \theta $: + +$\begin{align} + L(x_1, x_2, \cdots, x_n; \theta)&=P(X_1=x_1, X_2=x_2, \cdots, X_n=x_n; \theta) +&=P_{X_1 X_2 \cdots X_n}(x_1, x_2, \cdots, x_n; \theta). +\end{align}$ - If Xi's are discrete, then the likelihood function is defined as -** - - - - L - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - = - - P - - - X - 1 - - - X - 2 - - - - X - n - - - - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - . - - - -**. +$\begin{align} + L(x_1, x_2, \cdots, x_n; \theta)=P_{X_1 X_2 \cdots X_n}(x_1, x_2, \cdots, x_n; \theta). +\end{align}$ - If Xi's are jointly continuous, then the likelihood function is defined as -** - - - - L - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - = - - f - - - X - 1 - - - X - 2 - - - - X - n - - - - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - . - - - -** +$\begin{align} +L(x_1, x_2, \cdots, x_n; \theta)=f_{X_1 X_2 \cdots X_n}(x_1, x_2, \cdots, x_n; \theta). +\end{align}$ In some problems, it is easier to work with the log likelihood function given by +$\begin{align} + \ln L(x_1, x_2, \cdots, x_n; \theta). +\end{align}$ -** - - - - ln - - L - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - . - - - -.** - -Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter θ. Suppose that we have observed X1=x1 , X2=x2 , ⋯ , Xn=xn . The maximum likelihood estimate of θ is the value that maximizes the likelihood function: -** - - - - L - ( - - x - 1 - - , - - x - 2 - - , - - , - - x - n - - ; - θ - ) - - - -** +Now that we have defined the likelihood function, we are ready to define maximum likelihood estimation. Let X1, X2, X3, ..., Xn be a random sample from a distribution with a parameter $ \theta $. Suppose that we have observed X1=x1 , X2=x2 , ⋯ , Xn=xn . The maximum likelihood estimate of $ \theta $ is the value that maximizes the likelihood function: +$\begin{align} + L(x_1, x_2, \cdots, x_n; \theta). +\end{align}$ Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable ## Waht is MAP? -we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, Θ, as a random variable. we assume that we have some initial guess about the distribution of Θ. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. +we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, $ \theta $, as a random variable. we assume that we have some initial guess about the distribution of $ \theta $. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution. After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y, we use bayes formula for calculating posterior distribution. +$\begin{align} +f_{X|Y}(x|y)=\frac{f_{Y|X}(y|x)f_{X}(x)}{f_{Y}(y)}. +\end{align}$ -![](./images/formula.PNG) + in the above image we have - - - f - - X - - | - - Y - - - ( - x - - | - - y - ) - as postrior distribution and - - - f - - X - - - ( - x - ) - as priror distribution. in many problems -** - - f - - Y - - | - - X - - - ( - y - - | - - x - ) -** is MLE function that we explained it! +$f_{X|Y}(x|y)$ as postrior distribution and +$f_{X}(x)$ as priror distribution. in many problems +$f_{Y|X}(y|x)$ is MLE function that we explained it! The posterior distribution, -** - - f - - X - - | - - Y - - - ( - x - - | - - y - ) -**, contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posteriori (MAP) estimation - -Note that - - f - - Y - - - ( - y - ) - - does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes:
      +$f_{X|Y}(x|y)$ , contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posterior (MAP) estimation . + +Note that +$f_{Y}(y)$ does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes: +$\begin{align} +f_{Y|X}(y|x)f_{X}(x). +\end{align}$ -![](./images/formula1.png) + ***in many cases we choose alpha-beta distribution for prior distribution*** From 673aa7e1efaa9f0adaef84406c78bc7014b502a9 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 31 Dec 2021 22:36:04 +0330 Subject: [PATCH 15/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index 9b3672c9..d3c2bde6 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -8,16 +8,16 @@ 2. [Naïve Bayes Classifier Algorithm](#naïve-bayes-Classifier-algorithm) 2. [Unsupervised Learning](#unsupervised-learning) 3. [Bias and Variance](#bias-and-variance) - 1. [What is Bias?](#what-is-bias?) - 2. [What is variance?](#what-is-variance?) + 1. [What is Bias?](#what-is-bias) + 2. [What is variance?](#what-is-variance) 3. [Bias and Variance Trade-Off](#bias-and-variance-trade-off) 4. [OverFitting and Underfitting](#overFitting-and-underfitting) - 1. [So what is overfitting?](#so-what-is-overfitting?) - 2. [What is underfiting?](#what-is-underfiting?) - 3. [and how to prevent overfitting?](#and-how-to-prevent-overfitting?) + 1. [So what is overfitting?](#so-what-is-overfitting) + 2. [What is underfiting?](#what-is-underfiting) + 3. [and how to prevent overfitting?](#and-how-to-prevent-overfitting) 5. [Parameter Estiamtion](#parameter-estiamtion) - 1. [What is MLE?](#what-is-mle?) - 2. [Waht is MAP?](#waht-is-map?) + 1. [What is MLE?](#what-is-mle) + 2. [Waht is MAP?](#waht-is-map) 6. [Handle unseen events](#handle-unseen-events) 1. [Laplace Smoothing](#laplace-smoothing) 2. [Linear interpolation](#linear-interpolation) From e11560ede7527b4d5029c95b528f8acdf5c9e8e3 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 31 Dec 2021 22:36:31 +0330 Subject: [PATCH 16/21] comments omitted --- notebooks/12_Intro_to_machine_learning/index.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index 9b3672c9..5e42acbd 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -202,13 +202,13 @@ high variance leads to overfitting and increases model complexities! in general variance shows us how much our model is dependent to our dataset! in the following image you can see the impact of bias and variance in machine learning model: - + ![](./images/bias-and-variance-in-machine-learning4.png) ## Bias and Variance Trade-Off the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! low-bias and high-variance leads to overfitting, high-bias and low-variance leads to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. in simple words bias and variance are related to each other and we can not reduce both of them simultanously! - + ![](./images/bias-and-variance-in-machine-learning6.png) @@ -246,7 +246,7 @@ An underfit machine learning model is not a suitable model and will be obvious a - + ![](./images/overfitting-in-machine-learning.png) @@ -303,7 +303,7 @@ $\begin{align} f_{X|Y}(x|y)=\frac{f_{Y|X}(y|x)f_{X}(x)}{f_{Y}(y)}. \end{align}$ - + in the above image we have $f_{X|Y}(x|y)$ as postrior distribution and @@ -318,8 +318,7 @@ $f_{Y}(y)$ does not depend on the value of x. Therefore, we can equivalently fin $\begin{align} f_{Y|X}(y|x)f_{X}(x). \end{align}$ - - + ***in many cases we choose alpha-beta distribution for prior distribution*** From 9b4b1ee4277ff9030097e90f6cedc86c9c64aa23 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 7 Jan 2022 16:14:24 +0330 Subject: [PATCH 17/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index ccd3fb47..5d68033b 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -17,7 +17,7 @@ 3. [and how to prevent overfitting?](#and-how-to-prevent-overfitting) 5. [Parameter Estiamtion](#parameter-estiamtion) 1. [What is MLE?](#what-is-mle) - 2. [Waht is MAP?](#waht-is-map) + 2. [What is MAP?](#what-is-map) 6. [Handle unseen events](#handle-unseen-events) 1. [Laplace Smoothing](#laplace-smoothing) 2. [Linear interpolation](#linear-interpolation) @@ -74,7 +74,7 @@ The machine learning concepts are growing every day and we can see its usages ev ![](./images/intro_pic_5.png) * **Traffic prediction:** - Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and technics to provide the shortest routes with the least traffic to its users. + Google Maps gathers data from all its users and sends them to its database and uses ML algorithms and techniques to provide the shortest routes with the least traffic to its users. ![](./images/intro_pic_6.png) * **Product recommendations:** @@ -126,9 +126,9 @@ A general naïve bayes model has the form below that Y is our label variable and As a result of bayes net above and bayes theorem we can say that: -$P\\left(Y, F\_1, F\_2, ..., F\_n\\right) = P\\left(Y\\right)\\prod\_{i}P(F\_i|Y)$ +$P(Y, F_1, F_2, ..., F_n) = P(Y)\prod_{i}P(F_i|Y)$ -As we can use this equation for computing posterior distribution over label variable Y first by calculating joint probibility of evidence and label for each label using equation above second sum to get probability of evidence and then divide the first by second to calculate $P\\left(Y| F\_1, F\_2, ..., F\_n\\right)$ . +As we can use this equation for computing posterior distribution over label variable Y first by calculating joint probibility of evidence and label for each label using equation above second sum to get probability of evidence and then divide the first by second to calculate $P(Y| F_1, F_2, ..., F_n)$ . The process can be seen in figure below: ![](./images/naive_bayes_inference.png) @@ -151,7 +151,7 @@ In this method our training dataset doesn’t contain labels and they have not b # Bias and Variance -if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors causes small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions. +if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two error cause small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions. On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset. ## What is Bias? @@ -291,7 +291,7 @@ $\begin{align} Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable -## Waht is MAP? +## What is MAP? we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, $ \theta $, as a random variable. we assume that we have some initial guess about the distribution of $ \theta $. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. @@ -482,4 +482,4 @@ we also learned about how to work with datasets in machine learning. [Probability concepts explained: Maximum likelihood estimation](https://towardsdatascience.com/probability-concepts-explained-maximum-likelihood-estimation-c7b4342fdbb1). -[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). +[A Gentle Introduction to Maximum Likelihood Estimation and Maximum A Posteriori Estimation](https://towardsdatascience.com/a-gentle-introduction-to-maximum-likelihood-estimation-and-maximum-a-posteriori-estimation-d7c318f9d22d#:~:text=estimated%20with%20MLE.-,Maximum%20A%20Posteriori%20Estimation,when%20you%20have%20enough%20data.&text=For%20example%2C%20if%20Liverpool%20only,is%202%2F2%20%3D%201). From 1b57e2212fa857cff0f71333d81fe44543708a04 Mon Sep 17 00:00:00 2001 From: Alireza Eiji Date: Fri, 7 Jan 2022 16:44:33 +0330 Subject: [PATCH 18/21] Update index.md small sentence was removed --- notebooks/12_Intro_to_machine_learning/index.md | 1 - 1 file changed, 1 deletion(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index 5d68033b..f3eab53b 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -181,7 +181,6 @@ linear algorithms have a high bias, as they learn fast. The simpler the algorith The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has **low variance** but some of them has **high variance.** -**low varince** means that we have small variation in the changes of training data with prediction in target function! **high variance means there is a high variation in the prediction of the target function with changes in the training dataset** a model that has high variance performs well on training data but can not generalize unseen dataset as well. From fd3cde34405e5e005466d7bfc1595b6cf3e3dbad Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 4 Feb 2022 22:55:23 +0330 Subject: [PATCH 19/21] Update index.md --- notebooks/12_Intro_to_machine_learning/index.md | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index f3eab53b..dccd3a2d 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -1,3 +1,5 @@ +#### Introduction to machine learning key concepts + # Table of contents 1. [Introduction](#introduction) 1. [History](#history) @@ -128,8 +130,8 @@ As a result of bayes net above and bayes theorem we can say that: $P(Y, F_1, F_2, ..., F_n) = P(Y)\prod_{i}P(F_i|Y)$ -As we can use this equation for computing posterior distribution over label variable Y first by calculating joint probibility of evidence and label for each label using equation above second sum to get probability of evidence and then divide the first by second to calculate $P(Y| F_1, F_2, ..., F_n)$ . -The process can be seen in figure below: +As we can use this equation for computing posterior distribution over label variable Y first by calculating the joint probability of evidence and label for each label using the equation above the second sum to get the probability of evidence and then divide the first by second to calculate $P(Y| F_1, F_2, ..., F_n)$ . +The process can be seen in the figure below: ![](./images/naive_bayes_inference.png) @@ -144,14 +146,14 @@ The process can be seen in figure below: * Naive Bayes assumes that all features are independent or unrelated, so it cannot learn the relationship between features. It can be helpful in some cases to consider features independent, but sometimes the results are not exact. ## Unsupervised Learning -In this method our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case machine learns to group, cluster the data such that a human (or other intelligent algorithm) can come in and make sense of the newly organized data. In another word the goal of unsupervised learning is to find the underlying structure of dataset, group that data according to similarities, and represent that dataset in a compressed format. The unsupervised algorithms are grouped in two main categories: +In this method, our training dataset doesn’t contain labels and they have not been categorized. Instead, our algorithm would be fed a lot of data and given the tools to understand the properties of the data. In this case, the machine learns to group, cluster the data such that a human (or other intelligent algorithms) can come in and make sense of the newly organized data. In another word, the goal of unsupervised learning is to find the underlying structure of the dataset, group that data according to similarities, and represent that dataset in a compressed format. The unsupervised algorithms are grouped into two main categories: * **Clustering** * **Association** # Bias and Variance -if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two error cause small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions. +if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two error cause small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions. On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset. ## What is Bias? @@ -166,13 +168,13 @@ It can be defined as an inability of ML algorithms such as polynomial Regression linear algorithms have a high bias, as they learn fast. The simpler the algorithm, the higher the bias it has! but a nonlinear algorithm often has low bias. -#### Machine learning algorithm with low bias:#### +#### Machine learning algorithms with low bias: - Decision Trees - k-Nearest Neighbours -#### Machine learning algorithm with high bias: +#### Machine learning algorithms with high bias: - Linear Regression - Logistic Regression From ce27f8b14119ea650002a078fcc551566f80e516 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 4 Feb 2022 22:57:17 +0330 Subject: [PATCH 20/21] Update index.md --- .../12_Intro_to_machine_learning/index.md | 30 +++++++++---------- 1 file changed, 15 insertions(+), 15 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index dccd3a2d..2748a7a7 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -1,4 +1,4 @@ -#### Introduction to machine learning key concepts +# Introduction to machine learning key concepts # Table of contents 1. [Introduction](#introduction) @@ -36,12 +36,12 @@ Humans are capable of learning by experiencing, but how about computers? Can the ![](./images/intro_pic_1.png) -Machine learning techniques allow computers to automatically learn from a dataset and improve its performance from experiences and enables them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our dataset that is known as training data and use these models for future decision. The diagram below shows the ML algorithm: +Machine learning techniques allow computers to automatically learn from a dataset and improve their performance from experiences and enable them to predict things in a new situation without being explicitly programmed. Machine learning algorithms bring computer science and statistics together to build mathematical models from our dataset that is known as training data and use these models for future decisions. The diagram below shows the ML algorithm: ![](./images/intro_pic_2.png) ## History -The base idea behind machine learning has a long history, But the term of machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief: +The base idea behind machine learning has a long history, But the term machine learning was first used by Arthur Samuel in 1959. Below we can see a timeline of ML in brief: * **1834:** Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure. * **1936:** Alan Turing gave a theory about how machines can execute a set of instructions. @@ -49,11 +49,11 @@ The base idea behind machine learning has a long history, But the term of machin * **1943:** The first model of human neural network was modeled with electronic circuits. * **1950:** "Computer Machinery and Intelligence," was published by Alan Turing on the topic of AI with this question, "Can machines think?". * **1952:** Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more. -* **1959:** Arthur Samuel first used the term of “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter. +* **1959:** Arthur Samuel first used the term “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter. * **1974 to 1980:** These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced. * **1985:** A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week. -* **1997:** The IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov. -* **2006:** Geoffrey Hinton has first used name of "deep learning" instead of neural net research. +* **1997:** IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov. +* **2006:** Geoffrey Hinton has first used the name "deep learning" instead of neural net research. * **2012:** Google developed a deep neural network system to distinguish cat and human images in a YouTube video. * **2016:** AlphaGo won a Go game against number one and number second player of Go. @@ -62,7 +62,7 @@ The base idea behind machine learning has a long history, But the term of machin ![](./images/intro_pic_3.png) -The machine learning concepts are growing every day and we can see its usages everywhere. Some of the real-world applications of ML are: +Machine learning concepts are growing every day and we can see their usages everywhere. Some of the real-world applications of ML are: * **Image recognition:** @@ -102,7 +102,7 @@ In this method computer is provided by a set of labeled (tagged) data which is c ### Classification -In this algorithm machine learns from given training data and identifies the category of input data and classifies it into number of groups or classes. The main difference of this method and regression is that classification is a process of finding a function which helps in dividing the dataset into classes based on different parameters, but regression is a process of finding the correlations between dependent and independent variables. The classifiers can be binary that means we have only two possible outcomes, or multi-class that means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem: +In this algorithm, the machine learns from given training data and identifies the category of input data, and classifies it into some groups or classes. The main difference of this method and regression is that classification is a process of finding a function that helps in dividing the dataset into classes based on different parameters, but regression is a process of finding the correlations between dependent and independent variables. The classifiers can be binary which means we have only two possible outcomes or multi-class which means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem: * **Lazy Learners:** @@ -112,7 +112,7 @@ In this algorithm machine learns from given training data and identifies the cat * Case-based reasoning * **Eager Learners:** - Eager learning methods construct general (one-fits-all), explicit (input independent) description of the target function based on the provided training examples. In this method the learner creates a model according to the training dataset, so the training time is more than lazy learners but prediction is faster. Some algorithms of this method are: + Eager learning methods construct a general (one-fits-all), explicit (input independent) description of the target function based on the provided training examples. In this method, the learner creates a model according to the training dataset, so the training time is more than lazy learners but the prediction is faster. Some algorithms of this method are: * Decision Trees * Naïve Bayes @@ -120,7 +120,7 @@ In this algorithm machine learns from given training data and identifies the cat ### Naïve Bayes Classifier Algorithm -Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem. +Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that the occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem. A general naïve bayes model has the form below that Y is our label variable and F is our feature set: @@ -181,7 +181,7 @@ linear algorithms have a high bias, as they learn fast. The simpler the algorith ## What is variance? -The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models has **low variance** but some of them has **high variance.** +The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models have **low variance** but some of them have **high variance.** **high variance means there is a high variation in the prediction of the target function with changes in the training dataset** @@ -233,7 +233,7 @@ when the ml model predicts training data very well but it can not predict unseen This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize. ***An overfitted model is said to have low bias and high variance.*** -To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested!Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting +To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested! Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting ## What is underfiting? Underfitting refers to a model that can neither model the training data nor generalize to new data. @@ -294,9 +294,9 @@ Note that the value of the maximum likelihood estimate is a function of the obse ## What is MAP? -we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, $ \theta $, as a random variable. we assume that we have some initial guess about the distribution of $ \theta $. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inference about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. +we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, $ \theta $, as a random variable. we assume that we have some initial guess about the distribution of $ \theta $. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inferences about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. -in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with prior distribution. +in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with a prior distribution. After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y, we use bayes formula for calculating posterior distribution. @@ -447,7 +447,7 @@ We introduce three datasets: The actual dataset that we use to train the model (weights and biases in the case of a Neural Network). The model sees and learns from this data. ## Validation Dataset -**The sample of data used to provide an unbiased evaluation of a trained model on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as skill on the validation dataset is incorporated into the model configuration.** +**The sample of data used to provide an unbiased evaluation of a trained model on the training dataset while tuning model hyperparameters. The evaluation becomes more biased as a skill on the validation dataset is incorporated into the model configuration.** The validation set is used to evaluate a given model, but this is for frequent evaluation. We, as machine learning engineers, use this data to fine-tune the model hyperparameters. Hence the model occasionally sees this data but never does it “Learn” from this. We use the validation set results and update higher-level hyperparameters. So, the validation set affects a model, but only indirectly. The validation set is also known as the Dev set or the Development set. This makes sense since this dataset helps during the “development” stage of the model. We use this dataset to calculate $\alpha$ and $k$. ![](./images/diagram.png) From 6b1312f0cdb24ad50d381110dad43d37f5671075 Mon Sep 17 00:00:00 2001 From: MohammadAli-Khodabandelou <62250783+MohammadAli-Khodabandelou@users.noreply.github.com> Date: Fri, 4 Feb 2022 23:04:49 +0330 Subject: [PATCH 21/21] Update index.md --- .../12_Intro_to_machine_learning/index.md | 84 +++++++++---------- 1 file changed, 42 insertions(+), 42 deletions(-) diff --git a/notebooks/12_Intro_to_machine_learning/index.md b/notebooks/12_Intro_to_machine_learning/index.md index 2748a7a7..b33a0907 100644 --- a/notebooks/12_Intro_to_machine_learning/index.md +++ b/notebooks/12_Intro_to_machine_learning/index.md @@ -45,12 +45,12 @@ The base idea behind machine learning has a long history, But the term machine l * **1834:** Charles Babbage made the first computer that could be programmed by punched cards and all modern computers followed its logical structure. * **1936:** Alan Turing gave a theory about how machines can execute a set of instructions. -* **1940:** First manually operated computer named "ENIAC" was invented. +* **1940:** First manually operated the computer named "ENIAC" was invented. * **1943:** The first model of human neural network was modeled with electronic circuits. * **1950:** "Computer Machinery and Intelligence," was published by Alan Turing on the topic of AI with this question, "Can machines think?". * **1952:** Arthur Samuel created a program to play checkers for an IBM computer that could play better by playing more. * **1959:** Arthur Samuel first used the term “Machine Learning” and popularized it. In this year, the first neural network was used to solve a real-world problem to remove echoes over phone lines using an adaptive filter. -* **1974 to 1980:** These years are known as AI winter that lots of people lost their interest from AI and governmental funding reduced. +* **1974 to 1980:** These years are known as AI winter that lots of people lost their interest in AI and governmental funding reduced. * **1985:** A neural network was developed named NETtalk that was able to correctly pronounce 20000 words in a week. * **1997:** IBM’s computer named Deep Blue won a chess game against human chess expert Garry Kasparov. * **2006:** Geoffrey Hinton has first used the name "deep learning" instead of neural net research. @@ -81,7 +81,7 @@ Machine learning concepts are growing every day and we can see their usages ever ![](./images/intro_pic_6.png) * **Product recommendations:** - Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page is able to see most relevant suggestion according to its previous searches or other features that are used in dataset. + Amazon and Netflix use ML for their product recommendation systems. Every time a user opens an amazon page can see the most relevant suggestion according to its previous searches or other features that are used in the dataset. ![](./images/intro_pic_7.png) @@ -95,18 +95,18 @@ There are three major recognized categories for ML: ## Supervised Learning -In this method computer is provided by a set of labeled (tagged) data which is called training data and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training finished, the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who that is in the photo (suggesting a tag) is a supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless. The supervised algorithms are grouped in two main categories: +In this method, the computer is provided by a set of labeled (tagged) data which is called training data, and tries to create a mathematical model according to it and learn to approximate the exact nature of the relationship between examples and their labels. By the time this process of training is finished, the supervised learning algorithm will be able to observe a new, never-before-seen example and predict a good label for it. Then we provide another set of data called sample data to test if the predictions are exact or not. One example of supervised learning is Face Recognition that we have a system that takes a photo, finds faces, and guesses who is in the photo (suggesting a tag) is supervised process. It has multiple layers to it, finding faces and then identifying them, but is still supervised nonetheless. The supervised algorithms are grouped into two main categories: * **Classification** * **Regression** ### Classification -In this algorithm, the machine learns from given training data and identifies the category of input data, and classifies it into some groups or classes. The main difference of this method and regression is that classification is a process of finding a function that helps in dividing the dataset into classes based on different parameters, but regression is a process of finding the correlations between dependent and independent variables. The classifiers can be binary which means we have only two possible outcomes or multi-class which means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem: +In this algorithm, the machine learns from given training data and identifies the category of input data, and classifies it into some groups or classes. The main difference between this method and regression is that classification is a process of finding a function that helps in dividing the dataset into classes based on different parameters, but regression is a process of finding the correlations between dependent and independent variables. The classifiers can be binary which means we have only two possible outcomes or multi-class which means we can have more than two labels or classes. In another hand we have two types of learners in a classification problem: * **Lazy Learners:** - Lazy learning methods simply store the data and generalizing beyond these data is postponed until an explicit request is made. In this case we just store dataset without learning from it and start classifying data when test data is received. These learners find the most related data that is stored in our training dataset. First they store the training data and start the next phase when the test dataset arrives. In this method we reduce the training time but prediction time increases. Some algorithms of this method are: + Lazy learning methods simply store the data and generalizing beyond these data is postponed until an explicit request is made. In this case, we just store the dataset without learning from it and start classifying data when test data is received. These learners find the most related data that is stored in our training dataset. First, they store the training data and start the next phase when the test dataset arrives. In this method, we reduce the training time but prediction time increases. Some algorithms of this method are: * K-Nearest Neighbours algorithm * Case-based reasoning @@ -122,7 +122,7 @@ In this algorithm, the machine learns from given training data and identifies th Naïve Bayes algorithm is a probabilistic classifier based on Bayes theorem and is used to solve classification problems. It is called naïve because it assumes that the occurrence of a certain feature is independent of the occurrence of other features. It is also called Bayes because it depends on the principle of Bayes' Theorem. -A general naïve bayes model has the form below that Y is our label variable and F is our feature set: +A general naïve Bayes model has the form below that Y is our label variable and F is our feature set: ![](./images/bayes_net.png) @@ -153,13 +153,13 @@ In this method, our training dataset doesn’t contain labels and they have not # Bias and Variance -if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two error cause small difference between predicted and actual value! In machine learning we want to reduce these errors to get more accurate predictions. -On the basis of these errors, the machine learning model is selected that can perform best on the particular dataset. +if the model in machine learning is not accurate, it will make errors and these errors are known as Bias and Variance. these two errors cause a small difference between predicted and actual values! In machine learning, we want to reduce these errors to get more accurate predictions. +Based on these errors, the machine learning model is selected that can perform best on the particular dataset. ## What is Bias? -In general, a machine learning model analyzes the data, find patterns in it and make predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. -**While the model is making prediction about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors** +In general, a machine learning model analyzes the data, finds patterns in it, and makes predictions. While training, the model learns these patterns in the dataset and applies them to test data for prediction. +**While the model is making predictions about data, a difference occurs between prediction values made by the machine learning model and actual values is known as bias errors** It can be defined as an inability of ML algorithms such as polynomial Regression to capture the true relationship between the data points. Each algorithm in ML has some amount of bias because bias occurs from assumptions in the model, which makes the target function simple to learn. A model has either: - **High Bias:** A model with a high bias has more assumptions, and the model can not capture the important features of our dataset. the model with high biased has good performance on training data but not test data. @@ -179,13 +179,13 @@ linear algorithms have a high bias, as they learn fast. The simpler the algorith - Logistic Regression -## What is variance? +## What is a variance? -The variance of model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models have **low variance** but some of them have **high variance.** +The variance of the model tells us the amount of variation in the prediction if the different data is used. a model should not vary too much from one training dataset to another, which means the algorithm should be good in understanding the mapping between inputs and outputs. some models have **low variance** but some of them have **high variance.** **high variance means there is a high variation in the prediction of the target function with changes in the training dataset** -a model that has high variance performs well on training data but can not generalize unseen dataset as well. +a model that has high variance performs well on training data but can not generalize unseen datasets as well. high variance leads to overfitting and increases model complexities! @@ -197,18 +197,18 @@ high variance leads to overfitting and increases model complexities! #### machine learning algorithms with high variance: - decision tree -- K-nearest neighbours +- K-nearest neighbors -in general variance shows us how much our model is dependent to our dataset! +in general, variance shows us how much our model is dependent on our dataset! -in the following image you can see the impact of bias and variance in machine learning model: +in the following image you can see the impact of bias and variance in the machine learning model: ![](./images/bias-and-variance-in-machine-learning4.png) ## Bias and Variance Trade-Off -the best and ideal model has low bias and low variance but it can not be acheived and is not possible practically! -low-bias and high-variance leads to overfitting, high-bias and low-variance leads to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. -in simple words bias and variance are related to each other and we can not reduce both of them simultanously! +the best and ideal model has low bias and low variance but it can not be achieved and is not possible practically! +low-bias and high-variance lead to overfitting, high-bias, and low-variance lead to underfitting! so it is required to make a balance between bias and variance errors, and this balance between the bias error and variance error is known as the Bias-Variance trade-off. +in simple words, bias and variance are related to each other and we can not reduce both of them simultaneously! ![](./images/bias-and-variance-in-machine-learning6.png) @@ -224,25 +224,25 @@ An important consideration in learning the target function from the training dat The goal of a good machine learning model is to generalize well from the training data to any data from the problem domain. This allows us to make predictions in the future on data the model has never seen. -There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting. +There is terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting. -Overfitting and underfitting are the two biggest causes for poor performance of machine learning algorithms. +Overfitting and underfitting are the two biggest causes for the poor performance of machine learning algorithms. ## So what is overfitting? -when the ml model predicts training data very well but it can not predict unseen data as well as training data we face overfitting in our ml algorithm! -This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the models ability to generalize. +when the ml model predicts training data very well but can not predict unseen data as well as training data we face overfitting in our ml algorithm! +This means that the noise or random fluctuations in the training data is picked up and learned as concepts by the model. The problem is that these concepts do not apply to new data and negatively impact the model's ability to generalize. ***An overfitted model is said to have low bias and high variance.*** -To detect overfitting we must split our dataset.about 80% of our data set is goinig to be trained and 20% of dataset is going to be tested! Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example if the error is 2.5% in training data and 20% in test data we have overfitting +To detect overfitting we must split our dataset. about 80% of our data set is going to be trained and 20% of the dataset is going to be tested! Now, if the model performs well with the training dataset but not with the test dataset, then it is likely to have an overfitting issue. for example, if the error is 2.5% in training data and 20% in test data we have overfitting -## What is underfiting? -Underfitting refers to a model that can neither model the training data nor generalize to new data. +## What is underfitting? +Underfitting refers to a model that can neither model the training data nor generalizes to new data. An underfit machine learning model is not a suitable model and will be obvious as it will have poor performance on the training data. ## and how to prevent overfitting? -- **cross validation:** In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds. -- **regularization:** in this technique we reduce our model features and simplify it with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing term to our objective function. as an example in linear regression we use l2 regularization and add sum penalizing term to the MSE function +- **cross-validation:** In the general k-fold cross-validation technique, we divided the dataset into k-equal-sized subsets of data; these subsets are known as folds. +- **regularization:** in this technique we reduce our model features and simplify them with our tools! it may increase bias but reduce the variance of the model. in many cases we add penalizing terms to our objective function. as an example, in linear regression, we use l2 regularization and add sum penalizing term to the MSE function - ... @@ -252,11 +252,11 @@ An underfit machine learning model is not a suitable model and will be obvious a -# Parameter Estiamtion +# Parameter Estimation ## What is MLE? -The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is frequentist approach to this problem. In this approach, the unknown quantity $ \theta $ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data. +The following is a general setup for a statistical inference problem: There is an unknown quantity that we would like to estimate. We get some data From the data, we estimate the desired quantity this is a frequentist approach to this problem. In this approach, the unknown quantity $ \theta $ is assumed to be a fixed (non-random) quantity that is to be estimated by the observed data. We now would like to talk about a systematic way of parameter estimation. Specifically, we would like to introduce an estimation method, called maximum likelihood estimation (MLE) Let $ X_1,X_2,X_3, ... ,X_n $ be a random sample from a distribution with a parameter $ \theta $ (In general, θ might be a vector, ${\theta}=(\theta_1, \theta_2, \cdots, \theta_k)$ Suppose that $ x_1,x_2,x_3, ... ,x_n $ are the observed values of $ X_1,X_2,X_3, ... ,X_n $. If Xi's are discrete random variables, we define the likelihood function as the probability of the observed sample as a function of $ \theta $: @@ -290,15 +290,15 @@ $\begin{align} \end{align}$ -Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, as any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable +Note that the value of the maximum likelihood estimate is a function of the observed data. Thus, like any other estimator, the maximum likelihood estimator (MLE) is indeed a random variable ## What is MAP? -we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, $ \theta $, as a random variable. we assume that we have some initial guess about the distribution of $ \theta $. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inferences about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics.That is why this approach is called the Bayesian approach. +we would like to discuss a different approach for inference, namely the Bayesian approach. In the Bayesian framework, we treat the unknown quantity, $ \theta $, as a random variable. we assume that we have some initial guess about the distribution of $ \theta $. This distribution is called the prior distribution. We observe some data. We then use Bayes' rule to make inferences about the unobserved random variable. This is generally how we approach inference problems in Bayesian statistics. That is why this approach is called the Bayesian approach. -in this approach our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with a prior distribution. +in this approach, our goal is to draw inferences about an unknown variable X by observing a related random variable Y. The unknown variable is modeled as a random variable X, with a prior distribution. After observing the value of the random variable Y, we find the posterior distribution of X. This is the conditional PDF (or PMF) of X given Y=y, -we use bayes formula for calculating posterior distribution. +we use the Bayes formula for calculating posterior distribution. $\begin{align} f_{X|Y}(x|y)=\frac{f_{Y|X}(y|x)f_{X}(x)}{f_{Y}(y)}. @@ -312,7 +312,7 @@ $f_{X}(x)$ as priror distribution. in many problems $f_{Y|X}(y|x)$ is MLE function that we explained it! The posterior distribution, -$f_{X|Y}(x|y)$ , contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posterior (MAP) estimation . +$f_{X|Y}(x|y)$ , contains all the knowledge about the unknown quantity X. Therefore, we can use the posterior distribution to find point estimation of X. One way to obtain a point estimate is to choose the value of x that maximizes the posterior PDF (or PMF). This is called the maximum a posterior (MAP) estimation. Note that $f_{Y}(y)$ does not depend on the value of x. Therefore, we can equivalently find the value of x that maximizes: @@ -321,7 +321,7 @@ f_{Y|X}(y|x)f_{X}(x). \end{align}$ -***in many cases we choose alpha-beta distribution for prior distribution*** +***in many cases we choose an alpha-beta distribution for prior distribution*** @@ -365,7 +365,7 @@ $P(label=a)\propto \frac{2}{5} \times \frac{2}{5} \times 0 \times 1 \times \frac $P(label=b)\propto 0 \times \frac{3}{5} \times \frac{3}{5} \times \frac{2}{5} \times 1 = 0$ -If you look at the naïve bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for label a, and there is no data with $x_1=1$ or $x_5=0$ for label b. +If you look at the naïve Bayes model again, you will find out that there is no data with $x_3=0$ or $x_4=1$ for the label a, and there is no data with $x_1=1$ or $x_5=0$ for label b. **So, what would we do to handle this situation?** @@ -435,7 +435,7 @@ $P_{LIN}(x|y)=\alpha P(x|y)+(1-\alpha)P(x), 0<\alpha<1$ By choosing an appropriate value for $\alpha$, we can handle unseen events. -# More about dataset +# More about the dataset In the last section, we learned about Laplace smoothing and linear interpolation. But how can we calculate appropriate values for $\alpha$ and k? @@ -454,13 +454,13 @@ The validation set is used to evaluate a given model, but this is for frequent e ## Test Dataset -**The sample of data used to provide an unbiased evaluation of final trained model on the training dataset.** +**The sample of data used to provide an unbiased evaluation of the final trained model on the training dataset.** The Test dataset provides the gold standard used to evaluate the model. It is only used once a model is completely trained(using the train and validation sets). The test set is generally what is used to evaluate competing models (For example on many Kaggle competitions, the validation set is released initially along with the training set, and the actual test set is only released when the competition is about to close, and it is the result of the model on the Test set that decides the winner). Many times the validation set is used as the test set, but it is not good practice. The test set is generally well-curated. It contains carefully sampled data that spans the various classes that the model would face when used in the real world. ## About the dataset split ratio -Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation and Test sets. -This mainly depends on 2 things. First, the total number of samples in your data and second, on the actual model you are training. +Now that you know what these datasets do, you might be looking for recommendations on how to split your dataset into Train, Validation, and Test sets. +This mainly depends on 2 things. First, the total number of samples in your data, and second, on the actual model you are training. Some models need substantial data to train upon, so in this case, you would optimize for the larger training sets. Models with very few hyperparameters will be easy to validate and tune, so you can probably reduce the size of your validation set, but if your model has many hyperparameters, you would want to have a large validation set as well(although you should also consider cross-validation). Also, if you happen to have a model with no hyperparameters or ones that cannot be easily tuned, you probably don’t need a validation set too! ![](./images/ratio.png)

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[Introduction](#Introduction)\n", + " 1. [History](#History)\n", + " 2. [ML Applications](#Applications)\n", + "2. [Types of Machine Learning](#Types)\n", + " 1. [Supervised Learning](#Supervised)\n", + " 1. [Classification](#Classification)\n", + " 2. [Naïve Bayes Classifier Algorithm](#Naïve)\n", + " 2. [Unsupervised Learning](#Unsupervised)\n", + "3. [Bias and Variance](#Bias)\n", + " 1. [What is Bias?](#What)\n", + " 2. [What is variance?](#variance)\n", + " 3. [Bias and Variance Trade-Off](#Trade)\n", + "4. [OverFitting and Underfitting](#and)\n", + " 1. [So what is overfitting?](#overfitting)\n", + " 2. [What is underfiting?](#underfiting)\n", + " 3. [and how to prevent overfitting?](#prevent)\n", + "5. [Parameter Estiamtion](#Estiamtion)\n", + " 1. [What is MLE?](#MLE)\n", + " 2. [Waht is MAP?](#MAP)\n", + "6. [Handle unseen events](#Handle)\n", + " 1. [Laplace Smoothing](#Laplace)\n", + " 2. [Linear interpolation](#Linear)\n", + "7. [More about dataset](#More)\n", + " 1. [Training Dataset](#Training)\n", + " 2. [Validation Dataset](#Validation)\n", + " 3. [Test Dataset](#Test)\n", + " 4. [About the dataset split ratio](#ratio)\n", + "8. [Conclusion](#Conclusion)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "

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