04. Artificial neural networks.ipynb

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    "<div align='left' style=\"width:400px;height:120px;overflow:hidden;\">\n",
    "<a href='http://www.uff.br'>\n",
    "<img align='left' style='display: block;height: 92%' src='imgs/UFF.png' alt='UFF logo' title='UFF logo'/>\n",
    "</a>\n",
    "<a href='http://www.ic.uff.br'>\n",
    "<img align='left' style='display: block;height: 100%' src='imgs/logo-ic.png' alt='IC logo' title='IC logo'/>\n",
    "</a>\n",
    "</div>"
   ]
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   "cell_type": "markdown",
   "metadata": {
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     "align_type": "Left",
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   "source": [
    "### Machine Learning\n",
    "# 4. Artificial Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Luis Martí](http://lmarti.com)\n",
    "#### [Instituto de Computação](http://www.ic.uff)\n",
    "#### [Universidade Federal Fluminense](http://www.uff.br)\n",
    "$\\newcommand{\\vec}[1]{\\boldsymbol{#1}}$"
   ]
  },
  {
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   "execution_count": 1,
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   "outputs": [],
   "source": [
    "import random, itertools\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "plt.rc('font', family='serif')\n",
    "\n",
    "import seaborn\n",
    "seaborn.set(style='whitegrid'); seaborn.set_context('talk')\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "source": [
    "random.seed(a=42)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   },
   "outputs": [],
   "source": [
    "from ipywidgets import interact, interactive, fixed\n",
    "import ipywidgets as widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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     "slide_type": "skip"
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   "outputs": [],
   "source": [
    "# tikzmagic extesion for figures - https://github.com/mkrphys/ipython-tikzmagic\n",
    "%load_ext tikzmagic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why to study bio-inspired methods\n",
    "\n",
    "* Nature is one of the best problem-solvers we know.\n",
    "* Evolutionary optimization.\n",
    "* Natural intelligence and artificial intelligence\n",
    "    * Cellular automata\n",
    "    * **Neural computation**\n",
    "    * Evolutionary computation\n",
    "    * Swarm intelligence\n",
    "    * Artificial immune systems\n",
    "    * Membrane computing\n",
    "    * Amorphous computing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "## Pigeons as art connoisseurs (Watanabe et al., 1995)\n",
    "* Pigeons were put in a Skinner box, and\n",
    "* presented with photos of paintings by Monet and Picasso. \n",
    "* They were rewarded if they recognized correctly the painter they were presented with.\n",
    "<hr/>\n",
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-4\" align='center'><div class='well well-sm'>\n",
    "      [Skinner box](https://en.wikipedia.org/wiki/Operant_conditioning_chamber)\n",
    "      <img class='img-thumbnail' width='96%' src='imgs/05/pigeon.png'/>\n",
    "      </div></div>\n",
    "      <div class=\"col-md-4\" align='center'><div class='well well-sm'>\n",
    "      [Claude Monet](https://en.wikipedia.org/wiki/Claude_Monet)\n",
    "      <img class='img-thumbnail' src='imgs/05/monet.jpg'/>\n",
    "      </div></div>\n",
    "      <div class=\"col-md-4\" align='center'><div class='well well-sm'>\n",
    "      [Pablo Picasso](https://en.wikipedia.org/wiki/Pablo_Picasso)\n",
    "      <img class='img-thumbnail' width='83%' src='imgs/05/picasso.jpg'/>\n",
    "      </div></div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
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   },
   "source": [
    "<small>Watanabe, S., Sakamoto, J., &amp; Wakita, M. (1995). Pigeons’ discrimination of paintings by Monet and Picasso. Journal of the Experimental Analysis of Behavior, 63(2), 165–174. http://doi.org/10.1901/jeab.1995.63-165</small>"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "## Results\n",
    "\n",
    "* Pigeons were capable of discriminate between painters with an accuracy of **95%** when confronted with paintings on the **training set**.\n",
    "* Surprinsingly, they scored a **85%** on paintings they had never seen during training (**validation set**).\n",
    "* They were not just learning exhaustively which painting belonged to each painter.\n",
    "* They were able to recognize **styles** or **patterns** and\n",
    "* to **generalize** from what they had seen before.\n",
    "\n",
    "> In AI, we have been trying to replicate this capacity (and many others) in a computer for about 60 years."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# Artificial neural networks\n",
    "\n",
    "* Inspired (at different degrees) on the brain and the nervous system.\n",
    "* Massive parallelization of relatively simple processing units.\n",
    "* Simple principles lead to complex behaviours.\n",
    "* Capable of learn form data."
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "## Creating [artificial neurons](https://en.wikipedia.org/wiki/Artificial_neuron) \n",
    "\n",
    "Artificial neurons are designed to mimic aspects of their biological counterparts.\n",
    "<hr/>\n",
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-4\" align='center'><div class='well well-sm'>\n",
    "      <img class='img-thumbnail' src='imgs/05/Complete_neuron_cell_diagram_en.svg'/>\n",
    "      </div></div>\n",
    "      <div class=\"col-md-8\">\n",
    "<ul>\n",
    "<li>**Dendrites** – act as the input receptor, allowing the cell to receive signals from a large (>1000) number of neighboring neurons. Each dendrite is able to perform a \"multiplication\" by that dendrite's \"weight value.\"\n",
    "\n",
    "<li>**Soma** – acts as a summation function. As positive and negative signals (exciting and inhibiting, respectively) arrive in the soma from the dendrites they are added together.\n",
    "\n",
    "<li>**Axon** – gets its signal from the summation behavior which occurs inside the soma. The opening to the axon  samples the electrical potential inside the soma. Once the soma reaches a certain potential, the axon will transmit an all-in signal pulse down its length. \n",
    "<li>In this regard, the axon behaves as the ability for us to connect our artificial neuron to other artificial neurons.\n",
    "</ul>\n",
    "</div>\n",
    "</div>\n",
    "</div>\n",
    "\n"
   ]
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   "source": [
    "#### Note:\n",
    "\n",
    "* Unlike most artificial neurons, biological neurons fire in discrete pulses. \n",
    "* Each time the electrical potential inside the soma reaches a certain threshold, a pulse is transmitted down the axon. \n",
    "* This pulsing can be translated into continuous values. The rate (activations per second, etc.) at which an axon fires converts directly into the rate at which neighboring cells get signal ions introduced into them. \n",
    "* The faster a biological neuron fires, the faster nearby neurons accumulate electrical potential (or lose electrical potential, depending on the \"weighting\" of the dendrite that connects to the neuron that fired). \n",
    "* It is this conversion that allows computer scientists and mathematicians to simulate biological neural networks using artificial neurons which can output distinct values (often from −1 to 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "The first artificial neuron was the **Threshold Logic Unit (TLU)**, proposed by McCulloch and Pitts (1943). \n",
    "* The model was specifically targeted as a computational model of the \"nerve net\" in the brain.\n",
    "* As a transfer function, it employed a threshold, equivalent to using the Heaviside step function. \n",
    "* A simple model was considered, with binary inputs and outputs, and \n",
    "* restrictions on the possible weights, and a more flexible threshold value.\n",
    "\n",
    "* Any Boolean function could be implemented by networks of such devices, what is easily seen from the fact that one can implement the `AND` and `OR` functions, and use them in the disjunctive or the conjunctive normal form. \n",
    "* Cyclic TLU networks, with feedbacks through neurons, could define dynamical systems with memory, but\n",
    "* most research concentrated (and still does) on strictly feed-forward networks because of the smaller difficulty they pose."
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "<small>McCulloch, W. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5:115–133. http://link.springer.com/article/10.1007%2FBF02478259</small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "## Artificial neuron as a neuron abstraction"
   ]
  },
  {
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    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "pdf2svg terminated with signal -127\n",
      "No image generated.\n"
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   "source": [
    "%tikz -s 700,200 -sc 1.0 -l shapes,calc,shapes,arrows -f svg \\input{imgs/05/neuron.tikz}"
   ]
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   "source": [
    "In general terms, an input $\\vec{x}\\in\\mathbb{R}^n$ is multiplied by a weight vector $\\vec{w}$ and added a bias $b$ producing the net activation, $\\text{net}$. $\\text{net}$ is passed to the *activation function* $f()$ that computed the neuron's output $\\hat{y}$.\n",
    "$$\n",
    "\\hat{y} = f\\left(\\text{net}\\right)= f\\left(\\vec{w}\\cdot\\vec{x}+b\\right) = f\\left(\\sum_{i=1}^{n}{w_i x_i + b}\\right).\n",
    "$$"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "**Note:** This is a rather simplistic approximation of natural neurons. See [Spiking Neural Networks](https://en.wikipedia.org/wiki/Spiking_neural_network) for a more biologically plausible representation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "# The Perceptron\n",
    "\n",
    "The [Perceptron](https://en.wikipedia.org/wiki/Perceptron) and its learning algorithm pioneered the research in neurocomputing.\n",
    "\n",
    "* The perceptron is an algorithm for learning a linear binary classifier. \n",
    "* That is a function that maps its input $\\vec{x}\\in\\mathbb{R}^n$ (a real-valued vector) to an output value $f(\\vec{x})$ (a single binary value) as,\n",
    "\n",
    "$$\n",
    "f(\\vec{x}) = \\begin{cases}\n",
    "                1 & \\text{if }\\vec{w} \\cdot \\vec{x} + b > 0\\,,\\\\\n",
    "                0 & \\text{otherwise};\n",
    "             \\end{cases}\n",
    "$$\n",
    "\n",
    "where $\\vec{w}$ is a vector of real-valued *weights*, $\\vec{w} \\cdot \\vec{x}$ is the *dot product* $\\sum_{i=1}^n w_i x_i$, and $b$ is known as the *bias*. "
   ]
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   "source": [
    "## Perceptron learning\n",
    "\n",
    "Learning goes by calculating the prediction of the perceptron, $\\hat{y}$, as\n",
    "\n",
    "$$\\hat{y} = f\\left(\\vec{w}\\cdot\\vec{x} + b) = f( w_{1}x_{1} + w_2x_{2} + \\cdots + w_nx_{n}+b\\right)\\,.$$\n",
    "\n",
    "After that, we update the weights and the bias using the perceptron rule:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "w_i & = w_i + \\alpha (y - \\hat{y}) x_{i} \\,,\\  i=1,\\ldots,n\\,;\\\\\n",
    "b & = b + \\alpha (y - \\hat{y})\\,.\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Here $\\alpha\\in\\left(0,1\\right]$ is known as the *learning rate*."
   ]
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   "source": [
    "## Mark I: The Perceptron implementation\n",
    "\n",
    "<hr/>\n",
    "<div class=\"container-fluid\">\n",
    "   <div class=\"col-md-1\">&nbsp;</div>\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-4\">\n",
    "      <div class='well well-sm'>\n",
    "              <img src='imgs/04/mark1.png'/>\n",
    "      </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-6\">\n",
    "      <ul><li>An array of cadmium sulfide photocells was used for capturing 20x20 (400) pixel images that were used as inputs.\n",
    "      <li>A switchboard was used for manually selecting which input elements (pixels) were passed to the perceptrons.\n",
    "      <li>They used potentiometers as variable weights.\n",
    "      <li>Electric motors automatically modified the weights.</ul>\n",
    "      </div>\n",
    "      <div class=\"col-md-1\">&nbsp;</div>\n",
    "  </div>\n",
    "</div>"
   ]
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   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "# Implementing the Perceptron\n",
    "\n",
    "We are going to start implementing a perceptron as a class. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Perceptron:\n",
    "    'A simple Perceptron implementation.'\n",
    "    def __init__(self, weights, bias, alpha=0.1):\n",
    "        self.weights = weights\n",
    "        self.bias = bias\n",
    "        self.alpha = alpha\n",
    "    \n",
    "    def propagate(self, x):\n",
    "        return self.activation(self.net(x)) \n",
    "        \n",
    "    def activation(self, net):\n",
    "        if net > 0:\n",
    "            return 1\n",
    "        return 0\n",
    "    \n",
    "    def net(self, x):\n",
    "        return np.dot(self.weights, x) + self.bias\n",
    "    \n",
    "    def learn(self, x, y):\n",
    "        y_hat = self.propagate(x)\n",
    "        self.weights = [ w_i + self.alpha*x_i*(y-y_hat) for (w_i, x_i) in zip(self.weights, x)]\n",
    "        self.bias = self.bias + self.alpha*(y-y_hat)\n",
    "        return np.abs(y_hat - y)"
   ]
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     "slide_type": "skip"
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   "source": [
    "**Note**: Bear in mind that I have made the implementation as clear and easy to follow as possible and, therefore, I have sacrificed performance in the sake of clarity. There are many points where it can be improved."
   ]
  },
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   "source": [
    "### Testing our `Perceptron` class.\n",
    "\n",
    "After having the perceptron implementation ready we need an example data set.\n",
    "\n",
    "We are going to create a dataset containing random points in $\\left[0,1\\right]^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "size = 50 # size of data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(columns=('$x_1$', '$x_2$'),\n",
    "                    data=np.random.uniform(size=(size,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "So far, our data set looks like this (we are showning only the first ten elements):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "      <th>4</th>\n",
       "      <td>0.786634</td>\n",
       "      <td>0.900275</td>\n",
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       "      <td>0.271016</td>\n",
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       "      <th>7</th>\n",
       "      <td>0.990957</td>\n",
       "      <td>0.878344</td>\n",
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       "      <th>8</th>\n",
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       "      <td>0.383407</td>\n",
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       "      $x_1$     $x_2$\n",
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     "execution_count": 10,
     "metadata": {},
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   "source": [
    "data.head(10)"
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  },
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   "cell_type": "markdown",
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   "source": [
    "We need to add a *target* or *classification* attribute. In this example, we are going to make this target to be equal to one if the point lies in the upper-right triangle of the $\\left[0,1\\right]\\times\\left[0,1\\right]$ square and zero otherwise:\n",
    "\n",
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-4\">&nbsp;</div>\n",
    "      <div class=\"col-md-4\">\n",
    "      <div class='well well-sm'>\n",
    "              <img src='imgs/04/dataset.jpeg' alt='description of the data set' title='description of the data set'/>\n",
    "      </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-4\">&nbsp;</div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
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   },
   "source": [
    "We can formalize this condition as:\n",
    "\n",
    "$$\n",
    "y = \\begin{cases}\n",
    "    1 & \\ \\text{if}\\ x_1 + x_2 > 1\\,,\\\\\n",
    "    0 & \\ \\text{otherwise}\\,.\n",
    "    \\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Lets code it..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def condition(x):\n",
    "    return int(np.sum(x) > 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "...and apply it to the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['y'] = data.apply(condition, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The resulting data set looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$x_1$</th>\n",
       "      <th>$x_2$</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.939672</td>\n",
       "      <td>0.304112</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.748428</td>\n",
       "      <td>0.754524</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.990574</td>\n",
       "      <td>0.641591</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.426878</td>\n",
       "      <td>0.825523</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.786634</td>\n",
       "      <td>0.900275</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.625920</td>\n",
       "      <td>0.180962</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.568821</td>\n",
       "      <td>0.271016</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.990957</td>\n",
       "      <td>0.878344</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.223451</td>\n",
       "      <td>0.383407</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.570892</td>\n",
       "      <td>0.631924</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      $x_1$     $x_2$  y\n",
       "0  0.939672  0.304112  1\n",
       "1  0.748428  0.754524  1\n",
       "2  0.990574  0.641591  1\n",
       "3  0.426878  0.825523  1\n",
       "4  0.786634  0.900275  1\n",
       "5  0.625920  0.180962  0\n",
       "6  0.568821  0.271016  0\n",
       "7  0.990957  0.878344  1\n",
       "8  0.223451  0.383407  0\n",
       "9  0.570892  0.631924  1"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can now take a better look at the data set in graphical form. Elements with $y=1$ are shown in green ($\\color{green}{\\bullet}$) and those with $y=0$ are shown in red ($\\color{red}{\\bullet}$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(data, ax):\n",
    "    data[data.y==1].plot(kind='scatter', \n",
    "                         x='$x_1$', y='$x_2$', \n",
    "                         color='green', ax=ax)\n",
    "    data[data.y==0].plot(kind='scatter', \n",
    "                         x='$x_1$', y='$x_2$', \n",
    "                         color='red', ax=ax)\n",
    "    ax.set_xlim(-0.1,1.1); ax.set_ylim(-0.1,1.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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P2/p4SUlvk3Rc0mFJVUm2ecy7rbVrbSodQERsDLqZnp/ecrATg24AwBXZd0FjzKykT0p6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\nKJUkSVLjDEolSZLUOINSSZIkNe7/AZZxLS/cTwPxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bcdf128>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 325,
       "width": 338
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "plot_data(data, fig.gca())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Iterating the data set\n",
    "\n",
    "Having the data set we can now code how the perceptron learns it by iterating throu it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def learn_data(perceptron, data):\n",
    "    'Returns the number of errors made.'\n",
    "    count = 0 \n",
    "    for i, row in data.iterrows():\n",
    "        count += perceptron.learn(row[0:2], row[2])\n",
    "    return count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Visualizing learning\n",
    "\n",
    "We need now to plot the decision boundary or threshold of the perceptron.\n",
    "\n",
    "To calculate it we start with the equation that describes the boundary,\n",
    "$$w_1x_1+w_2x_2 + b =0.$$\n",
    "\n",
    "From it we can obtain $x_2$ from a given $x_1$ applying a fairy simple math,\n",
    "$$x_2 = \\frac{-w_1x_1-b}{w_2}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def threshold(perceptron, x_1):\n",
    "    return (-perceptron.weights[0] * x_1 - perceptron.bias) / perceptron.weights[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_perceptron_threshold(perceptron, ax):\n",
    "    xlim = ax.get_xlim(); ylim = ax.get_ylim()\n",
    "    \n",
    "    x2s = [threshold(perceptron, x1) for x1 in xlim]\n",
    "    ax.plot(xlim, x2s)\n",
    "    \n",
    "    ax.set_xlim(-0.1,1.1); ax.set_ylim(-0.1,1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "A function that plots a perceptron as the threshold and the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def plot_all(perceptron, data, t, ax=None):\n",
    "    if ax==None:\n",
    "        fig = plt.figure(figsize=(5,4))\n",
    "        ax = fig.gca()\n",
    "    plot_data(data, ax)\n",
    "    plot_perceptron_threshold(perceptron, ax)\n",
    "    \n",
    "    ax.set_title('$t='+str(t+1)+'$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Our perceptron in action\n",
    "\n",
    "All set now! Let's create a perceptron and train it. \n",
    "\n",
    "**Note**: Normally the initial weights and the bias should be set to *small* random values. I am setting them by hand to a value that I know that looks good in the examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "perceptron = Perceptron([0.1,-0.1], 0.02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WHn/W5FSz/2Lg0bpOvvjvr7NiUR733lLFykX5YW6tiMyWioAiMuccOtnO136wm/5B54Rt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BJAhlU9jskk+RpmwS21I+hU35pHySGFM+hc2N+ZR3cg4Hkizu+dta+h0b325ZEr2YfPQmBh+b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\nbX7UfFpaW1j03aIua0J0V/Fa0fO83Z2YFzeIaMWe1KxaDhyvQq0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OLE1Yyvyo+RbzGKKz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\nOCUgAAAAABT3Dr6AqUjc6nmGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11e3d36a0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 494,
       "width": 640
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axarr = plt.subplots(3, 4, sharex=True, sharey=True, figsize=(9,7))\n",
    "axs = list(itertools.chain.from_iterable(axarr))\n",
    "for t in range(12):\n",
    "    plot_all(perceptron, data, t, ax=axs[t])\n",
    "    learn_data(perceptron, data)\n",
    "f.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is clear how the Perceptron threshold is progresively adjusted according to the data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Animating the Perceptron\n",
    "\n",
    "This results are better understood in animated from."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def animate(frame_index, perceptron, data, ax):\n",
    "    ax.clear()\n",
    "    plot_data(data, ax=ax)\n",
    "    ax.set_title('$t='+str(frame_index)+'$')\n",
    "    \n",
    "    if not frame_index:\n",
    "        return None\n",
    "    plot_perceptron_threshold(perceptron, ax=ax)\n",
    "    learn_data(perceptron, data)\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(4,4))\n",
    "ax = fig.gca()\n",
    "perceptron = Perceptron([0.1,-0.1], 0.02)\n",
    "anim = animation.FuncAnimation(fig, lambda i: animate(i, perceptron, data, ax), frames=30, interval=600, \n",
    "                               blit=False)\n",
    "plt.tight_layout()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(anim.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Self-study\n",
    "\n",
    "* Experiment with the learning rate ($\\alpha$). How it impacts learning? Do you remember if we have seen another similar parameter in previous classes?\n",
    "* Create a new data set with a non-linear boundary. What happens now with our perceptron? How would you fix it?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Suggested reading\n",
    "\n",
    "* Minsky M. L. and Papert S. A. (1969). *Perceptrons*. Cambridge, MA: MIT Press.\n",
    "* Gallant, S. I. (1990). *Perceptron-based learning algorithms*. IEEE Transactions on Neural Networks, vol. 1, no. 2, pp. 179–191.\n",
    "* Mikel Olazaran (1996). *A Sociological Study of the Official History of the Perceptrons Controversy*. Social Studies of Science 26 (3): 611–659. doi:10.1177/030631296026003005."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The XOR issue \n",
    "\n",
    "Take a dataset that contains all the possible value combination of the logical XOR function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.array([[0, 1], [1, 0], [0, 0], [1, 1]])\n",
    "Y = np.array([1, 1, 0, 0])\n",
    "N = Y.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data set has ones (represented in black) when $x_1 = 1$ and $x_2 = 0$ or when $x_1 = 0$ and $x_2 = 1$, as defined for the XOR function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+k3s9bxQ8eu6GfQnwKuAfIuJXwxteno6OjtF424a6urro7u6mra2N9vb20R6O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\nL7LhWrhwIccff/yIfgblW7J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hoD4vm0hx7XL4n8d09jga2A54E/Adipvv9NxsB+Bb5Xup\nSaqc15TSm4Hdy8UJwE0pJRp4KCJ2Hd4n0No06TurUdakeT0Y+D6wN8XG5Tkppc5eNRdTXKGtu7IP\nov+h6nmNiB+V57KdT3HY08KU0vMUfyDuuTrQ/cB+rbjRqfpuP7mHQkTEEcAHKP6y0UnxH+4y4HRg\nt4h4aoj1llP8D+w4Xtk9uwZYCHwC/wc2Iiqc17f0ej6Z/k/e7f3YuIrxa+2q/s6qNTThd/EKYB7F\n5UNvo7ji0zjgXuBzwO4R8dDaK6gKTZjXbwA7AhcCv6P4Q8//b++OQeSqwjAMf6sb2cJoJQp2Ifpb\niAlY2IRYBlFIkIBNRCIGEWyMoiJGECtFsRNRCYIELKwMgmKRQhGx0EJQD4EQCxsRFNKoSRyLubLL\nsom7h83MTuZ5YNl7z9yBf7t9OXfuXEzyXcaPld3VWvtx0/4AJmaW/39aGI225FwAAMAMsEMBAAB0\nExQAAEA3QQEAAHQTFAAAQDdBAQAAdBMUAABAN0EBAAB0ExQAAEA3QQEAAHQTFAAAQDdBAQAAdBMU\nAABAN0EBAAB0ExQAAEA3QQEAAHQTFAAAQDdBAQAAdFuc9gAA8H+qajHJD0luS/Jnkp2ttV8uce1j\nSd4dTk8mebC1dmEigwLMITsUAGx5QxC8MJwuJTm21nVVtT/J28Ppl0keEhMAV9bCaDSa9gwAsC5V\n9XWSe5KcT3JHa+3Mitf2JPk84+D4Psne1tofUxkUYI7YoQBgljw7/N6W5OX/Fqvqzoxvb1pKcjbJ\nPjEBMBl2KACYKVV1MskDSf5JcleSc0m+SnJrkl+T7GmtnZ7ehADzxQ4FALPm+Yxj4pokbyT5LOOY\nOJfkPjEBMFl2KACYOVV1PMnhFUt/ZRwTpy7znoNJ7k2yO8muJNuTnGitHbqSswJc7exQADCL3lp1\nfuhyMTF4McmTGQfFmo+cBWDjBAUAM6Wqbkzy3qrl69bx1qeS3J7khiRPbPZcAPNKUAAwM6pqKcnH\nGd+ydCHJ78NLr1TVZaOitXaqtXa6teZeX4BNJCgAmAlVdW2SD5PsHZaOJHlpON6R5PFpzAUw7wQF\nALPinST7h+PnWmvvD2tnh7VjVbV9CnMBzDVBAcCWV1WvJnl0OH2ztfZakrTW/s7yF9zdlOSZKYwH\nMNcEBQBbWlUdzfI3ZJ9I8vSqSz5I8tNwfLSqbp7UbAAICgC2sKp6OMnrw+mnSQ6v/lB1a+1ilj9L\ncf2KYwAmQFAAsCVV1f1JjidZSPJNkoOttfOXuPyjJN8Ox0eqaucERgQgyeK0BwCAtbTWPkmybZ3X\njpLcfWUnAmAtdigAAIBuC6OR7/cB4OpXVQeSHBhOb0myL8mZJF8Ma7+11jwlCmCD3PIEwLzYneSR\nVWs7hp8k+TkeOwuwYXYoAACAbj5DAQAAdBMUAABAN0EBAAB0ExQAAEA3QQEAAHQTFAAAQDdBAQAA\ndBMUAABAN0EBAAB0ExQAAEA3QQEAAHQTFAAAQDdBAQAAdBMUAABAN0EBAAB0ExQAAEC3fwEUbOqs\nr7p5pgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1205cd828>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 394
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=Y, edgecolor='k', cmap=cm.gray_r, s=100)\n",
    "plt.xlabel('$x_1$');plt.ylabel('$x_2$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is evident that a perceptron is unable to solve this simple problem as it is only able to separate the space by a hyperplane."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "To solve the XOR problem we need to stack perceptrons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "pdf2svg terminated with signal -127\n",
      "No image generated.\n"
     ]
    }
   ],
   "source": [
    "%tikz -s 500,250 -sc 1.0 -l positioning -f svg \\input{imgs/05/xor-nn.tikz}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "But, how can we train the weights from neurons 1 and 2?\n",
    "* This is known as a credit assignment problem.\n",
    "* Our current method for Perceptron learning determine how the weights of neurons 1 and 2 influence the error.\n",
    "* Let's visualize it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### A \"handcoded\" XOR neural network\n",
    "\n",
    "Forward propagation for 2 inputs $(x_1, x_2)$, 2 hidden nodes, 1 output.\n",
    "* We will be extending the Perceptron activation as the logistic (*logit*) function\n",
    "$$\\hat{y} = f(\\text{net}) = \\frac{1}{1+\\exp{\\left(-\\text{net}\\right)}}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logit(a): \n",
    "    return 1.0 / (1+np.exp(-a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def fprop(x1, x2,\n",
    "          w1= 0.1, w2= 0.2,  b1= 0.1, \n",
    "          w3=-0.2, w4= 0.2,  b2=-0.1,\n",
    "          w5=-0.3, w6=-0.25, b3=0.2):\n",
    "    y_hat_1 = logit(b2 + w3*x1 + w4*x2) # N1\n",
    "    y_hat_2 = logit(b3 + w5*x1 + w6*x2) # N2\n",
    "    return logit(b1 + w1*y_hat_1 + w2*y_hat_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Error Surface of the XOR Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "99a433183df64a06ad60e75e6f212dc2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=5, description='i', max=6, min=1), IntSlider(value=6, description='j', max=6, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(i=(1,6), j=(1,6)) \n",
    "def error_plot(i=5, j=6):\n",
    "    W1, W2 = np.meshgrid(np.arange(-10, 10, 0.5), np.arange(-10, 10, 0.5))\n",
    "    E = np.sum([(fprop(X[n, 0], X[n, 1],\n",
    "                       **{\"w%d\"%(i) : W1, \"w%d\"%(j) : W2})-Y[n])**2\n",
    "                 for n in range(N)], axis=0)\n",
    "    ax = plt.figure(figsize=(7, 4.5)).add_subplot(111, projection=\"3d\")\n",
    "    surf = ax.plot_surface(W1, W2, E, rstride=1, cstride=1, cmap=cm.viridis, lw=0.11, alpha=0.74)\n",
    "    plt.setp(ax, xlabel=\"$w_%d$\" % (i), ylabel=\"$w_%d$\" % (j), zlabel=\"$E()$\");\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Local Minima "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3ff757b986a0469896e6970204d507e4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='i', max=5), IntSlider(value=1, description='j', max=5), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(i=(0,5), j=(0,5)) \n",
    "def errors_plot(i=0, j=1):\n",
    "    plt.figure(figsize=(12, 3))\n",
    "    W = np.arange(-10, 10, 0.25)\n",
    "    errors = [(fprop(X[n, 0], X[n, 1], **{\"w%d\"%(i+1) : W, \"w%d\"%(j+1) : W+2})-Y[n])**2 for n in range(N)]\n",
    "    plt.subplot(1, 2, 1)\n",
    "    for n in range(N): \n",
    "        plt.plot(W, errors[n], label=\"$E^{(%d)}$\" % (n+1))\n",
    "    plt.setp(plt.gca(), xlabel=\"$w$\", ylabel=\"$E$\", title='Split errors');plt.legend(loc=\"best\", frameon=True)\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(W, np.sum(errors, axis=0), label=\"$E(\\cdot)$\")\n",
    "    plt.setp(plt.gca(), xlabel=\"$w$\", ylabel=\"$E$\", title='Total error');plt.legend(loc=\"best\", frameon=True);\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Multilayer Perceptron (MLP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The composition of layers of perceptrons can capture complex relations between inputs and outputs in a hierarchical way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "pdf2svg terminated with signal -127\n",
      "No image generated.\n"
     ]
    }
   ],
   "source": [
    "%tikz -s 600,400 -sc 1.0 -l positioning -f svg \\input{imgs/05/neural-network.tikz}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...but how can we adapt the weights of the neurons in the hidden layers?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Improving the notation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to proceed we need to improve the notation we have been using. That for, for each layer $1\\geq l\\geq L$, the activations and outputs are calculated as:\n",
    "\n",
    "$$\\text{net}^l_j = \\sum_i w^l_{ji} x^l_i\\,,$$\n",
    "$$y^l_j = f^l(\\text{net}^l_j)\\,,$$\n",
    "\n",
    "where:\n",
    "\n",
    "* $y^l_j$ is the $j$th output of layer $l$,\n",
    "* $x^l_i$ is the $i$th input to layer $l$,\n",
    "* $w^l_{ji}$ is the weight of the $j$-th neuron connected to input $i$,\n",
    "* $\\text{net}^l_{j}$ is called net activation, and\n",
    "* $f^l(\\cdot)$ is the activation function of layer $l$, e.g. $\\tanh()$, in the hidden layers and the identity in the last layer (for regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Error function (SSE)\n",
    "\n",
    "* For $\\Psi=\\left\\{\\left<\\vec{x}^{(1)},\\vec{y}^{(1)}\\right>,\\ldots,\\left<\\vec{x}^{(k)},\\vec{y}^{(k)}\\right>,\\ldots\\left<\\vec{x}^{(K)},\\vec{y}^{(K)}\\right>\\right\\}$:\n",
    "\n",
    "$$\n",
    "E = \n",
    "\\frac{1}{2} \\sum_{k=1}^{K}{\\ell(\\hat{\\vec{y}}_j^{L}(\\vec{x}^{(k)}), \\vec{y}^{(k)})} =\n",
    "\\frac{1}{2} \\sum_{k=1}^{K} \\sum_{j=1}^{m} \\left( \\hat{y}_j^{L}(\\vec{x}^{(k)}) - y_j^{(k)} \\right)^2\\,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Training MLPs with Backpropagation\n",
    "\n",
    "* Backpropagation of errors is a procedure to compute the **gradient of the error function with respect to the weights** of a neural network.\n",
    "* We can use the gradient from backpropagation to apply **gradient descent**!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### A math flashback\n",
    "\n",
    "The **chain rule** can be applied in composite functions as,\n",
    "$$\n",
    "\\left( f \\circ g\\right)'(x) = \\left(f\\left(g\\left(x\\right)\\right)\\right)'= f'\\left(g(x)\\right)g'(x).\n",
    "$$\n",
    "or, in Leibniz notation,\n",
    "$$\n",
    "\\frac{\\partial f\\left(g\\left(x\\right)\\right)}{\\partial x} =\n",
    "\\frac{\\partial f\\left(g\\left(x\\right)\\right)}{\\partial g\\left(x\\right)} \\cdot\n",
    "\\frac{\\partial g\\left(x\\right)}{\\partial x}\n",
    "$$\n",
    "\n",
    "The **total derivative** of $f(x_1,x_2,...x_n)$ on $x_i$ is\n",
    "$$\n",
    "\\frac{\\partial f}{\\partial x_i}=  \n",
    "\\sum_{j=1}^n{\\frac{\\partial f}{\\partial x_j}\\cdot\\frac{\\partial x_j}{\\partial x_i}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### To apply gradient descent we need... to calculate the gradients\n",
    "\n",
    "Applying the chain rule,\n",
    "$$\n",
    "\\frac{\\partial \\ell}{\\partial w^l_{ji}}=\n",
    "\\color{blue}{\\overbrace{\\frac{\\partial \\ell}{\\partial \\text{net}^l_j}}^{\\delta^l_j}}\n",
    "\\color{forestgreen}{\\underbrace{\\frac{\\partial{\\text{net}^l_j}}{\\partial w^l_{ji}}}_{\\frac{\\partial\\left(\\sum_{i}w^l_{ji}x^l_i\\right)}{\\partial w^l_{ji}}=x^l_i}}\n",
    "$$\n",
    "hence we can write\n",
    "$$\n",
    "\\frac{\\partial \\ell}{\\partial w^l_{ji}}=\n",
    "\\color{blue}{\\delta^l_j}\n",
    "\\color{forestgreen}{x^l_i}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### For the output layer ($l=L$)\n",
    "$$\n",
    "\\delta^L_j = \\frac{\\partial \\ell}{\\partial \\text{net}^L_j} =\n",
    "\\color{red}{\n",
    "  \\overbrace{\n",
    "    \\frac{\\partial \\ell}{\\partial\\hat{y}^L_j}}^{\\frac{\\partial\\left(\\frac{1}{2}\\sum_j{\\left(y_j-\\hat{y}^L_j\\right)^2} \\right)}\n",
    "    {\\partial\\hat{y}^L_j}=\\left(y_j-\\hat{y}^L_j\\right)}}\n",
    "\\cdot\n",
    "\\color{magenta}{\n",
    "\\underbrace{\\frac{\\partial\\hat{y}^L_j}{\\text{net}^l_j}}_{f'(\\text{net}_j^L)}}\n",
    "=\\color{red}{\\left(y_j-\\hat{y}^L_j\\right)}\\color{magenta}{f'(\\text{net}_j^L)}.\n",
    "$$\n",
    "therefore\n",
    "$$\n",
    "\\frac{\\partial \\ell}{\\partial w^L_{ji}}=\n",
    "\\color{red}{\\left(y_j-\\hat{y}^L_j\\right)}\\color{magenta}{f'(\\text{net}_j^L)}\n",
    "\\color{forestgreen}{x^L_i}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### What about the hidden layers ($1\\leq l<L$)?\n",
    "\n",
    "We can express the loss $\\ell$ as a function of the activations of the subsequent layer,\n",
    "\n",
    "$$\n",
    "\\ell = \\ell\\left(\\text{net}^{l+1}_1,\\ldots,\\text{net}^{l+1}_K\\right)\\,,\n",
    "$$\n",
    "\n",
    "therefore, applying total derivatives,\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\ell}{\\partial\\hat{y}^l_j} = \n",
    "\\frac{\\partial \\ell\\left(\\text{net}^{l+1}_1,\\ldots,\\text{net}^{l+1}_K\\right)}{\\partial\\hat{y}^l_j}\\,.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Applying total derivatives we get\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\ell}{\\partial\\hat{y}^l_j} = \n",
    "\\sum_{k}{\n",
    "\\color{orange}{\n",
    "\\overbrace{\n",
    "\\frac{\\partial \\ell}{\\partial\\text{net}^{l+1}_k}}^{\\delta^{l+1}_k}}\n",
    "\\color{purple}{\n",
    "\\underbrace{\\frac{\\partial \\text{net}^{l+1}_{k}}{\\partial\\hat{y}^l_j}\n",
    "}_{\\frac{\\partial{\\sum_{j}{w^{l+1}_{kj}\\hat{y}^l_j}}}{\\partial\\hat{y}^l_j}=w^{l+1}_{kj}}}\n",
    "} =\n",
    "\\sum_{k}{\\color{orange}{\\delta^{l+1}_k}\\color{purple}{w^{l+1}_{kj}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Back-propagating the errors to the hidden layer\n",
    "\n",
    "The $\\delta$s of the subsequent layers are used to calculate the $\\delta$s of the more internal ones.\n",
    "\n",
    "$$\n",
    "\\delta^{l}_j =\n",
    "\\frac{\\partial\\ell}{\\partial\\text{net}^l_j} =\n",
    "\\overbrace{\\frac{\\partial\\ell}{\\partial\\hat{y}^l_j}}^\n",
    "{\\sum_{k}{\n",
    "  \\color{orange}{\\delta^{l+1}_k}\n",
    "  \\color{purple}{w^{l+1}_{kj}}}}\n",
    "\\color{forestgreen}{\\underbrace{\\frac{\\partial\\hat{y}^l_j}{\\partial\\text{net}^l_j}}_\n",
    "{f'(\\text{net}^l_j)}}=\n",
    "\\sum_{k}{\\left(\n",
    "  \\color{orange}{\\delta^{l+1}_k}\n",
    "  \\color{purple}{w^{l+1}_{kj}}\n",
    "  \\right)}\\color{forestgreen}{f'(\\text{net}^l_j)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "## Backpropagation in brief"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "In each layer (we will omit the sample index $k$ and layer $l$)\n",
    "\n",
    "$$\n",
    "\\delta_j = \n",
    "   \\begin{cases}\n",
    "   \\hat{y}_j - y_j & \\text{in the output layer,}\\\\\n",
    "   \\\\ f'(\\text{net}_j) \\sum_k \\frac{\\partial \\ell}{\\partial \\hat{y}_k} & \\text{otherwise.}\n",
    "   \\end{cases}\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial \\ell}{\\partial w_{ji}} = \\delta_j x_i\\,;\\quad \\frac{\\partial \\ell}{\\partial x_i} = \\delta_j w_{ji}\\,.$$\n",
    "\n",
    "where\n",
    "\n",
    "* all nodes $k$ are in the layer after $j$;\n",
    "* $\\text{net}_j$ is known from propagation: $\\sum_i w_{ji} x_i$;\n",
    "* actually you do not have to save $a_j$ because $g'(a_j)$ usually can be computed from $y_j$, e.g.\n",
    "    * identity function: $f'(\\text{net}_j) = 1$,\n",
    "    * $\\tanh$: $f'(\\text{net}_j) = 1 - y_j^2$;\n",
    "* $\\frac{\\partial \\ell}{\\partial w_{ji}}$ will be used to update the weight $w_{ji}$ in gradient descent;\n",
    "* $\\frac{\\partial \\ell}{\\partial x_i}$ will be passed to the previous layer to compute the deltas;\n",
    "\n",
    "**Do not forget to sum up the gradient with respect to the weights for each training example!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "## Efficient Implementation for Fully Connected Layers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Make sure that you have an efficient **linear algebra library**.\n",
    "* Organize your data in matrices, i.e.\n",
    "    * The matrix $\\boldsymbol{X}$ contains an input vector in each row. Note that you must expand each row by the bias 1.\n",
    "    * The matrix $\\boldsymbol{T}$ contains an output (of the network) in each row.\n",
    "* Each layer should have the functions\n",
    "    * `fprop(W, X, f) -> Y`\n",
    "    * `backprop(W, X, f_derivative, Y, d_loss/dY) -> d_loss/dX, d_lossdW`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-3\" align='center'>\n",
    "      </div>\n",
    "      <div class=\"col-md-6\">\n",
    "      <div class='well well-sm'>\n",
    "              <img src='imgs/05/backprop.svg'/>\n",
    "      </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-3\" align='center'>\n",
    "      </div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "## Efficient forward propagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "-"
    }
   },
   "source": [
    "In each layer\n",
    "\n",
    "$$\\boldsymbol{NET} = \\boldsymbol{X} \\boldsymbol{W}^\\intercal$$\n",
    "$$\\boldsymbol{\\hat{Y}} = f(\\boldsymbol{NET})$$\n",
    "\n",
    "where\n",
    "\n",
    "* $\\boldsymbol{Y} \\in \\mathbb{R}^{N \\times J}$ contains an output vector in each row, i.e. $\\boldsymbol{Y}_{kj} = y^{(k)}_j$\n",
    "* $\\boldsymbol{X} \\in \\mathbb{R}^{N \\times I}$ contains an input vector (the output of the previous layer) in each row, i.e. $\\boldsymbol{X}_{ki} = x^{(k)}_i$\n",
    "* $\\boldsymbol{W} \\in \\mathbb{R}^{J \\times I}$ is the weight matrix of the layer, i.e. $\\boldsymbol{W}_{ji}$ is the weight between input $i$ and output $j$.\n",
    "* $f$ is the activation function (implemented to work with matrices)\n",
    "* $I$ is the number of inputs, i.e. the number of outputs of the previous layer plus 1 (for the bias)\n",
    "* $J$ is the number of outputs\n",
    "\n",
    "**Make sure that you add the bias entry in each row before you pass $Y$ as input to the next layer!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Error function (SSE)\n",
    "\n",
    "$$E = \\frac{1}{2} ||\\boldsymbol{Y} - \\boldsymbol{T}||_2^2$$\n",
    "\n",
    "where\n",
    "\n",
    "* $||\\cdot||_2$ is the [Frobenius norm](http://en.wikipedia.org/wiki/Matrix_norm#Frobenius_norm)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "# Efficient Backpropagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "-"
    }
   },
   "source": [
    "In each layer:\n",
    "\n",
    "$$\\Delta = f'(\\boldsymbol{NET}) \\ast \\frac{\\partial \\ell}{\\partial \\boldsymbol{Y}}\\,,$$\n",
    "$$\\frac{\\partial \\ell}{\\partial \\boldsymbol{W}} = \\Delta^T \\cdot \\boldsymbol{X}\\,,$$\n",
    "$$\\frac{\\partial \\ell}{\\partial \\boldsymbol{X}} = \\Delta \\cdot \\boldsymbol{W}\\,.$$\n",
    "\n",
    "where:\n",
    "\n",
    "* $*$ is the [Hadamard product](http://en.wikipedia.org/wiki/Hadamard_product_%28matrices%29) or Schur product or entrywise product\n",
    "* $\\frac{\\partial \\ell}{\\partial \\boldsymbol{Y}}$ contains derivatives of the error function with respect to the outputs ($\\boldsymbol{Y} - \\boldsymbol{T} = \\frac{\\partial \\ell}{\\partial \\boldsymbol{Y}}$ in the last layer)\n",
    "* $\\frac{\\partial \\ell}{\\partial \\boldsymbol{X}} \\in \\mathbb{R}^{N \\times I}$ contains derivatives of the error function with respect to the inputs and will be passed to the previous layer\n",
    "* $\\Delta \\in \\mathbb{R}^{N \\times J}$ contains deltas: $\\delta_j^{(n)} = \\Delta_{jn}$\n",
    "* $g'$ is the derivative of $g$ and can be computed based only on $\\boldsymbol{Y}$\n",
    "* $\\frac{\\partial \\ell}{\\partial \\boldsymbol{W}} \\in \\mathbb{R}^{J \\times I}$ contains the derivatives of the error function with respect to $\\boldsymbol{W}$ and will be used to optimize the weights of the ANN\n",
    "\n",
    "**Make sure that you remove the bias entry in each row before you pass $\\frac{\\partial \\ell}{\\partial \\boldsymbol{X}}$ to the previous layer!**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Pseudocode of backpropagation\n",
    "\n",
    "```pseudo\n",
    "initialize network weights (often small random values)\n",
    "  do\n",
    "     foreach training example, x\n",
    "        prediction = neural-net-output(network, x)                 // forward pass\n",
    "        actual = teacher-output(x)\n",
    "        compute error (prediction - actual) at the output units\n",
    "        compute deltas for all weights from hidden layer to output layer  // backward pass\n",
    "        compute deltas for all weights from input layer to hidden layer   // backward pass continued\n",
    "        update network weights                                            // input layer not modified by error estimate\n",
    "  until all examples classified correctly or another stopping criterion satisfied\n",
    "  return the network\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "## Tips for Your Implementations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Depending on the problem type you have to select different activation functions for the output layer.\n",
    "* Check your gradients with finite differences:\n",
    "$$\\frac{\\partial f}{\\partial x} = \\frac{f(x + \\varepsilon) - f(x - \\varepsilon)}{2 \\varepsilon} + \\mathcal{O}(\\varepsilon^2)\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "### How to initialize weights $\\boldsymbol{w}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.05466522,  0.04519595, -0.12944682, -0.05341159, -0.00769046,\n",
       "       -0.04324446, -0.07862767,  0.01952648,  0.04378596,  0.06973566])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(10) * 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Draw components of $\\boldsymbol{w}$ iid (independend and identically distributed) from a Gaussian distrubition with **small** standard deviation, e.g. 0.05.\n",
    "* Initialization with 0 will prevent the gradient from flowing back to the lower layers as\n",
    "\n",
    "$$\\frac{\\partial \\ell}{\\partial x_i} = \\delta_j w_{ji}\\,.$$\n",
    "\n",
    "* It has been shown that initialization of weights is a key to have good results. See:\n",
    "    - <small>Glorot, X., &amp; Bengio, Y. (2010).*Understanding the difficulty of training deep feedforward neural networks*. Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS), 9, 249–256. http://doi.org/10.1.1.207.2059</small>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_afun(x, y, sp_idx, label=None):\n",
    "    \"\"\"Plot activation function.\"\"\"\n",
    "    ax = plt.subplot(2, 4, sp_idx)\n",
    "    if label is not None: \n",
    "        plt.title(label)\n",
    "    plt.setp(ax, xlim=(np.min(x), np.max(x)), ylim=(np.min(y)-0.5, np.max(y)+0.5))\n",
    "    plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/R/hu7kDq+/kOYXCMXOSrPiqH7ggixRI/d1idw/rxdZLf43i3mFzOY9pt4ZVN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AitkZL+aIz5nKRtCvfj7pb0A0keSW8oPF0IAPoS/SL0GV9zUI0Bv06fb0h1KMhAJLgAoAvW2l2S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\nNxtjbrLWvtFVm8aYS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1209cb400>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 604
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "x = np.linspace(-5, 5, 100)\n",
    "plot_afun(x, x, 1, label=\"Identity\")\n",
    "plot_afun(x, np.tanh(x), 2, label=\"tanh\")\n",
    "plot_afun(x, logit(x), 3, label=\"Logistic (logit)\")\n",
    "plot_afun(x, np.max((x, np.zeros_like(x)), axis=0), 4, label=\"Rectified \\nLinear Unit (ReLU)\")\n",
    "plot_afun(x, np.ones_like(x), 5)\n",
    "plot_afun(x, 1-np.tanh(x)**2, 6)\n",
    "plot_afun(x, logit(x)*(1-logit(x)), 7)\n",
    "plot_afun(x, np.max((np.sign(x), np.zeros_like(x)), axis=0), 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "slide"
    }
   },
   "source": [
    "## Derivatives of Activation Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Identity\n",
    "\n",
    "$$\\hat{y} = f(\\text{net}) = a;\\quad f'(\\text{net}) = 1\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Hyperbolic tangent\n",
    "\n",
    "$$\\hat{y} = f(\\text{net}) = \\tanh(\\text{net});\\quad f'(\\text{net}) = 1 - \\tanh^2(\\text{net}) = 1-\\hat{y}^2\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "align_type": "Left",
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Logistic function\n",
    "\n",
    "$$y = f(\\text{net}) = \\frac{1}{1+\\exp{\\left(-\\text{net}\\right)}}\\,,$$\n",
    "$$f'(\\text{net}) = f(\\text{net}) (1 - f(\\text{net})) = \\hat{y} (1-\\hat{y})\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Summarizing\n",
    "\n",
    "* We now know how to compute the $\\frac{\\partial\\ell}{\\partial w^l_{ji}}$ for all neurons.\n",
    "* For the neurons on the hidden layers we use the $\\delta$s of the next layer.\n",
    "* We know how to updates the weights as:\n",
    "$$\n",
    "\\Delta w^l_{ji}=-\\eta\\frac{\\partial\\ell}{w^l_{ji}}=-\\eta\\delta^l_j x^l_i. \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Difficulties\n",
    "\n",
    "* There are many **local minima**.\n",
    "* The optimization problem is **ill-conditioned**.\n",
    "* There are many **flat regions** (saddle points).\n",
    "* There is **no guarantee** to reach the global minimum.\n",
    "* Deep architectures suffer from the **vanishing gradient** problem.\n",
    "* Neural networks are *usually* considered to be the **blackest box** of all learning algorithms.\n",
    "* There are sooo many **hyperparameters** (number of layers/nodes, activation function, connectivity, weight initialization, loss function, regularization, ...).\n",
    "* Training neural networks has been regarded as **black magic** by many researchers.\n",
    "* And here is the grimoire: [Neural Networks: Tricks of the Trade](http://link.springer.com/book/10.1007%2F978-3-642-35289-8) (1st edition: 1998; 2nd edition: 2012).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Theoretical features\n",
    "\n",
    "**Universal approximation theorem**:\n",
    "\n",
    "> A feed-forward network with **a single hidden** layer containing a finite number of neurons can approximate any continuous functions on compact subsets of $\\mathbb{R}^n$, under mild assumptions on the activation function. \n",
    "\n",
    "Hornik showed in 1991 that it is not the specific choice of the activation function, but rather the multilayer feedforward architecture itself which gives neural networks the potential of being universal approximators. \n",
    "\n",
    "<small>Kurt Hornik (1991) Approximation Capabilities of Multilayer Feedforward Networks, Neural Networks, 4(2), 251–257</small>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There have been three hypes around ANNs:\n",
    "\n",
    "* Perceptron (50s-XOR problem)\n",
    "* Backpropagation (80s-SVM)\n",
    "* Deep Learning (2006-now)\n",
    "\n",
    "And they work incredibly well in practice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### But... why do neural nets work well in practice?\n",
    "* Universal function approximation property.\n",
    "* Stochastic gradient descent finds **sufficiently good** local minima.\n",
    "* We don't want to find the global minimum $\\implies$ ** fights overfitting!**\n",
    "* Neural nets learn **feature hierarchies** to represent functions *efficiently*.\n",
    "    * **features will be learned** automatically\n",
    "    * allows learning of **hierarchical features** which is much more efficient than just one layer of abstraction\n",
    "* **multiclass classification** can be integrated with linear complexity (softmax activation function, cross-entropy error function)\n",
    "* it is a **parametric** model, it does not store any training data directly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Drawbacks\n",
    "\n",
    "* input has to be a **vector of real numbers**, e.g. text must be converted before classification\n",
    "* in general, the **optimization problem** is very difficult because it is **ill-conditioned** and **non-separable**\n",
    "* objective function is **not convex**, there are many local minima and flat regions\n",
    "* **black box**: in most cases it is very difficult to interpret the weights of a neural network although it is possible!\n",
    "* **catastrophic forgetting**: learning one instance can change the whole network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<hr/>\n",
    "<div class=\"container-fluid\">\n",
    "  <div class='well'>\n",
    "      <div class=\"row\">\n",
    "          <div class=\"col-md-3\" align='center'>\n",
    "              <img align='center'alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\"/>\n",
    "          </div>\n",
    "          <div class=\"col-md-9\">\n",
    "              This work is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n",
    "          </div>\n",
    "      </div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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         "module": "IPython",
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         "version": "1.0.0"
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        {
         "module": "sklearn",
         "version": "0.19.1"
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      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)]</td></tr><tr><td>IPython</td><td>6.2.1</td></tr><tr><td>OS</td><td>Darwin 17.3.0 x86_64 i386 64bit</td></tr><tr><td>scipy</td><td>1.0.0</td></tr><tr><td>numpy</td><td>1.13.3</td></tr><tr><td>matplotlib</td><td>2.1.0</td></tr><tr><td>sklearn</td><td>0.19.1</td></tr><tr><td colspan='2'>Thu Nov 23 08:19:13 2017 -02</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)] \\\\ \\hline\n",
       "IPython & 6.2.1 \\\\ \\hline\n",
       "OS & Darwin 17.3.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "scipy & 1.0.0 \\\\ \\hline\n",
       "numpy & 1.13.3 \\\\ \\hline\n",
       "matplotlib & 2.1.0 \\\\ \\hline\n",
       "sklearn & 0.19.1 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Thu Nov 23 08:19:13 2017 -02} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.3 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)]\n",
       "IPython 6.2.1\n",
       "OS Darwin 17.3.0 x86_64 i386 64bit\n",
       "scipy 1.0.0\n",
       "numpy 1.13.3\n",
       "matplotlib 2.1.0\n",
       "sklearn 0.19.1\n",
       "Thu Nov 23 08:19:13 2017 -02"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext version_information\n",
    "%version_information scipy, numpy, matplotlib, sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href=\"https://fonts.googleapis.com/css?family=Fira+Sans:300,300i,600,600i\" rel=\"stylesheet\">\n",
       "<link href=\"https://fonts.googleapis.com/css?family=Inconsolata\" rel=\"stylesheet\">\n",
       "<link href=\"https://fonts.googleapis.com/css?family=Titillium+Web:400,400i,700,700i\" rel=\"stylesheet\">\n",
       "<style>\n",
       ".text_cell_render {\n",
       "font-style: regular;\n",
       "font-family: 'Fira Sans', sans-serif;\n",
       "display: block;\n",
       "}\n",
       "/*font-weight: 200;*/\n",
       "/*text-align: left;\n",
       "line-height: 100%;\n",
       "display: block;\n",
       "}*/\n",
       ".text_cell_render h1 {\n",
       "/*font-size: 24pt;*/\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#4a4a4a;\n",
       "}\n",
       "\n",
       ".reveal h1 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#4a4a4a;\n",
       "}\n",
       ".text_cell_render h2 {\n",
       "/*font-size: 21pt;*/\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h3 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 19pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h4 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 17pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h5 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 15pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       "div.text_cell_render{\n",
       "line-height: 120%;\n",
       "font-size: 100%;\n",
       "font-weight: 400;\n",
       "text-align: justify;\n",
       "margin-left:0em;\n",
       "margin-right:0em;\n",
       "}\n",
       ".reveal div.text_cell_render{\n",
       "line-height: 120%;\n",
       "font-size: 74%;\n",
       "font-weight: 400;\n",
       "text-align: justify;\n",
       "margin-left:0em;\n",
       "margin-right:0em;\n",
       "}\n",
       "\n",
       ".reveal h2 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal h3 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal h4 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal .code_cell {\n",
       "    font-size: 92%;\n",
       "}\n",
       ".reveal code {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       ".reveal pre {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       "code {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       "pre {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       ".CodeMirror{\n",
       "font-family: \"Inconsolata\", monospace;\n",
       "}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this code is here for cosmetic reasons\n",
    "from IPython.core.display import HTML\n",
    "from urllib.request import urlopen\n",
    "HTML(urlopen('https://raw.githubusercontent.com/lmarti/jupyter_custom/master/custom.include').read().decode('utf-8'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.3"
  },
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 },
 "nbformat": 4,
 "nbformat_minor": 2
}