04-logistic-regression-training.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config IPCompleter.greedy=True\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sklearn.preprocessing, sklearn.datasets, sklearn.model_selection\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous chapter, I introduced logistic regression and how it makes predictions. I as well pointed out, that unlike Perceptron, logistic regression returns the probability of datapoints belonging to the specific class. However, I didn't mention the training algorithm for it. That would be the content of this chapter.\n",
    "\n",
    "I also demonstrated the gradient descent algorithm in the second half of the previous chapter. There will be no surprise, that the gradient descent is the exact algorithm we are going to use in this chapter to train logistic regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression training\n",
    "\n",
    "We now should have all the knowledge we need to train logistic regression. For a reminder, the prediction of the logistic regression is:\n",
    "\n",
    "$$\n",
    "f(\\pmb{x})=\\frac{1}{1+e^{-\\pmb{x}\\pmb{w}^T}}\n",
    "$$\n",
    "\n",
    "In able to use gradient descent, we need some function, that the algorithm is going to optimize. That's why I showed a loss function. When we plug it in, we obtain the following formula.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}=\\frac{1}{2} \\sum_{i=0}^{n} \\left( t_i - f(\\pmb{x_i}) \\right)^2 = \\frac{1}{2} \\sum_{i=0}^{n} \\left( t_i - \\frac{1}{1+e^{-\\pmb{x}\\pmb{w}^T}} \\right)^2\n",
    "$$\n",
    "\n",
    "Now we want to update the weights, so we need to compute the gradient of the loss function with respect to weight (and we need to compute it for every weight). In this case, we can use the chain rule.\n",
    "\n",
    "$$\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial w_i} = \\frac{\\partial \\mathcal{L}}{\\partial f(\\pmb{x})} \\cdot \\frac{\\partial f(\\pmb{x})}{\\partial \\pmb{x}\\pmb{w}^T} \\cdot \\frac{\\partial \\pmb{x}\\pmb{w}^T}{\\partial w_i}\n",
    "$$\n",
    "\n",
    "Then the gradient is easy to obtain (note that I mark $\\sigma(x)$ as the sigmoid function, i.e. $\\sigma(x)=\\frac{1}{1+e^{-x}}$ and $y_i$ as the prediction of the model, i.e. $y_i = \\sigma(\\pmb{x}\\pmb{w}^T)$.\n",
    "\n",
    "$$\\\n",
    "\\frac{\\partial \\mathcal{L}}{\\partial w_i} = (t_i - y_i) \\cdot -\\sigma(\\pmb{x}\\pmb{w}^T)\\left( 1 - \\sigma(\\pmb{x}\\pmb{w}^T) \\right) \\cdot x_i\n",
    "$$\n",
    "\n",
    "> Note the minus in the second multiple. Because in the loss is $t_i - f(\\pmb{x})$ (minus in front of the prediction), the whole derivative is multiplied by $-1$. We can alternatively ignore the minus sign and then add the gradient to the weights, so the final formula would be $w_i = w_i + \\alpha \\frac{\\partial \\mathcal{L}}{\\partial w_i}$. I will stick with the proper mathematical formula - the gradient will be multiplied by $-1$ and I will subtract it from the weights. I just wanted to point this out, as the minus is sometimes forgotten.\n",
    "\n",
    "Finally, let's put it all to the code."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will use the same class as in the previous chapter (`Neuron`) and I will implement the fit method. Don't forget that the gradient descent algorithm needs learning rate, I will put it in the constructor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, max_iters=100, random_state=None, learning_rate=0.001):\n",
    "        self.max_iters = max_iters\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        # Learning\n",
    "        for iteration in range(self.max_iters):\n",
    "            # shufle data randomly\n",
    "            permutation = self._rand.permutation(len(X))       \n",
    "            train_data = X[permutation]\n",
    "            train_labels = y[permutation]\n",
    "            # make gradient descent on each data point\n",
    "            for datapoint, target in zip(train_data, train_labels):\n",
    "                prediction = self.predict(datapoint)\n",
    "                # compute gradient\n",
    "                gradient = -(target - prediction) * (prediction * (1 - prediction)) * datapoint\n",
    "                # update weights\n",
    "                self._weights = self._weights - self._learning_rate * gradient\n",
    "                \n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm makes `self.max_iters` iterations and in each iteration, it randomly shuffles the data and performs gradient descent for each data point. That means the algorithm will make `self.max_iters * len(X)` gradient descent executions during training. Let's see how the algorithm behaves on some dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data, classes = sklearn.datasets.make_blobs(\n",
    "    n_samples=40,\n",
    "    n_features=2,\n",
    "    centers=[[-2, -2], [2, 2]],\n",
    "    random_state=42,\n",
    ")\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MvgF2RC0RYPIgYRCuuFuO/V5jMH83KeJVwVXn52Jl8KW9AGlTAQFcIMbuCxp1cGcsX/pMSH3qnyvbr00YhivupmJdIxSVW9MsY8w3xhgxxrQ0xrTO/yiyiKsQ0LIlLFsG48bZjSuaNbPby+novEIw+++AvE1AVv6OQFmQOhGT/fUx3ysi4CpiVyZX7eJdP2c1pL0CZNtrkwEmE7P/Toyx02VN3vb8Ip6d/5Fj/0x9GpO3teA5TQ4m80N8KffhS30e4y1su7rQpSs7VeEiImDYMDs6b9UKbr3VPhzdvNnpZKocmbxtkLsJuzzkUJmY9NeKd5L4u4DoIw7G5B8vRobMD7DF+UgC2flTZbMXYkfhR/Llv3bI+XxpmN1XYg6MgczZkD4Vs/sSTPayYuUJBVrI1dGdfDIsXgxTpsCKFdCiBUyYoE24wpXZD3Lkgpd8vuI9AJeY6yBhOEhV7A5CVSFhOK7Ya4sZIofCizT2No/9SxFfY8D4Dj+S/hp4t4LJyD+Sa0f4KfdijvjaUKWFXB2bywUDBtiFROedB/fcY3co2rDB6WTK3yJO4eCjrkN5IOq8Yp1CRHDF9UZqLUNqrUJqLcMV16vYEST6MpDYgi+YPPjnHnnUBRRevtwQfeHhh7I+xv5wOIIvFby/FztXMNNCroqvXj2YOxdmzoRff4U2beDRR+2iIhUWRKIg4X6QGOyDRoAocFVF4kq2DF1EEFdsyRfLeM6GqM6HZIgAoqHSGCS/p4lENID4QTYbEfkfURB/FxLR6IggR97m+YfvKK+FFt3qTZVOcjLcfTe8/ba93TJtmm3GpcKCyVmBSZ8O3r8h6lwk7kbbayRQ1zcGcldgsj4DiUNiuiERDQt+Xd5myMq/Xx7dBYk4qcDX+NLfgdTHgUP7Crkg4lRcNT4sp39B+Shq1ooWclU2c+bA7bfDzp0wZAg8/DDEFvJrsVIOMcaHSRkOWZ9g76vn2T8jTkUqPYh4CtTFoKV7dqryccUV9t75LbfAM8/YGS5fful0qrBj8n7FZC3C5P3udJSQI+LCVeUZiL0x/0j+4DXvJ8zemzE5ax3L5i9ayFXZVa4MU6fC55+Dz2cfiN52G6SkOJ0s5BlfBr69fTG7u2NS7sPsvgLfvtswRp9LlIQxuZD5NnDkpipZmLTxTkTyKy3kyn/OPx/WrYOhQ+GVVyAxET7+2OlUIc2kPgk5qzhscU72UkzqBIeThRjfHjBFTJnNK95q02CmhVz5V2ysvcXy3Xe2XW7XrtCrl304qkrEGGM3+S2wOCYbMt9xIFEIc1Xl4CycI7hPCGiU8qCFXJWPdu1sr5YxY+Ddd+0y/7fe0mX+JeKj0PnPAObIplTqaESiILY3EHPEK9FI/N1ORPIrLeSq/Hg88NBDtqviiSfCDTfYh6PbtzudLCSIuCGyVWGvgKd9wPOEOkkYCvG3gsQDLnAdD5WfOawRV6jSQq7KX/Pm8O238Oyz9oFoYqJ9OOoLj+XR5UkqPQwSB3jyj3hA4pFKo5yMFZJEXLji70JqrURqr0ZqLsYV08XpWH6hhVwFhttt55mvWwenn26X/HfubFeIqiJJZFOkxgKI62tXPMbditT4BIk40eloIUvEhUiM49uz+ZMWchVYJ51kR+WvvGJvubRsaUfq2oSrSOKugyvhXlzVpuFKGIy4dYctdTgt5CrwRGxb3I0bbWvce++1OxStX+90MqVCkhZy5Zy6deGjj2y/lt9/h9NOs7NcsgvrRa2UKooWcuUsEbj+ejs6v+4626vl9NPh+++dThY2jPHiS5uMb1cHfDtb4NvbB5Mb+otg1EFayFVwqFED3nwT5s2zS/s7dLAPR9PTnU4W8syB0ZA2OX9jiGzI+Q6zt4fdLk2FBS3kKrhcdpndsOK222D8ePsw9IsvnE4Vsow3GTLnUGBXe5ONSZ/mSCblf1rIVfCpVAleesl2UXS57DTFfv1g/36nk4Ue7xaQqEJeyIPcHwMeR5UPLeQqeJ17rt38efhweO01u5BozhynU4UW9wlQaKdEN0SeEvA4qnxoIVfBLSYGxo61Dz+rV4du3aBHD9i1y+lkIUHcdSCqE3ZLtEN5kLhbHUikyoMWchUakpJg5Uq7R+js2dC0qX04qk24jkmqPAMx1wLR2C3OmiDVXit0WzQVmnSrNxV6/tmRaNkyuPRSmDIF6td3OlXQM8YH5CHiOebXquCkW72p8NGsGXzzDUyYYB+IJibC5MnahOsYbI8RLeLhSAu5Ck1uNwwaZJf1t28Pd9xht5j75RenkykVcFrIVWhr1AgWLoRp02DtWjvvfNw4yMtzOplSAaOFXIU+Ebj5Znvv/OKL4b777Ch9bejvjq5UcWghV+Hj+OPhgw/s1nLbt9uZLqNHaxMuBYDxpeJLn45v/2B8aZPsqtcwoYVchRcRuOYaOzq/4QZ47DFo08ZuBq0qLOPdidl9EaQ+B1nzIW0KZvdFmNxNTkfzCy3kKjxVrw4zZsCCBbbxVseOMHgwpKU5nUw5wKSOBd9eDvacyQGThkkJjy3ztJCr8HbxxXZmyx13wPPPQ4sWsGiR06lUoGV/BRQyPTVvE8ZkBjyOv2khV+EvIQEmTYKvvwaPB7p0sQuK9u1zOpkKmKLmzwvgDmSQcqGFXFUcZ59tZ7KMGGFvuzRrZpf7q5Blspfi2zsA3+5r8aW9jPEVcess9loK9puJhKjOYbFIyi+FXEQuFpGfReRXERnhj3MqVS6io+HJJ2H5cqhTB7p3h2uvhZ07nU6mSsiXNg2z7w7IWQx5ayFtEmbPlYUWc4m/CzztgGiQOJBYiDgZqfxo4IOXgzIXchFxAy8ClwDNgJ4i0qys51WqXJ12mi3mTzwBc+fa0fnrr2sTrhBhfKmQNgE49P52Nnj/xmTMKvD1Ih5c1aYh1d9FKo1Bqk5Hqs9GXFUClLh8+WNE3g741Riz2RiTA7wNdPPDecNWZlom65Zs4vcN25yOUrFFRsL998OaNbabYp8+cMkl8McfTidTx5K7Dgq9JZIN2UXvKCWRTZCYboinNSJSfvkCzB+FvC5waEXann/sMCLSX0RWisjK5OTwmYhfUnNe+oRra9/KA5c/ycD299O/1VCSt+9xOlbFduqpsGQJvPCCbcbVvDm8+KI24QpmrqpAYW0YBFw1Ap3GcQF72GmMmWqMSTLGJNWsWTNQlw0qP369kanD3yQ7M4eMA5lkZ2Tzx8btjLz0CaejKZcLBg60UxXPPNP+/Zxz4GfdbT4oRZwKruMpWMKikLg+TiRylD8K+Q7g0GbQ9fKPqSPMnjif7IzDl4v7vD52bvmbLeu3OpRKHaZhQ/jkE5g+3a4ObdXKPhzNzXU6mTqEiCDVXoOIxkAMSDxIDCSMRDynOR0v4PxRyFcAJ4tII7HzeHoAurFiIfb9vb/Q4+4INwd2pwY2jCqaiL1fvnEjXH45jBxpm3CtXu10MnUIcR+Hq8Y8pMb7SNWpSK1luOJ6OB3LEWUu5MaYPGAg8CmwCXjHGLOhrOcNR2d0TcITHVngeF5OHieffqIDidRR1aljG3C9/z78+Se0bWuLelbWsd+rAkYiGiOeJERinI7iGL/cIzfGzDfGnGKMOckY87g/zhmOLr+9C9WOq4on5mAxj4qN4uYnehKbUHG/CYNe9+6waRPcdJO9zdK6NSxd6nQqpf6le3YGWHpKOnMnL+TbOSuoWrsKV919Ka3Pa+50LL/LSM3E5/URXyXO6Sj+tXAh9O8PW7fCnXfaeegJCU6nUhVEUXt2aiFXfpW8fQ9jb3qBDUt/wgAntmzA8OkDaZgYRpsjp6XBqFF2umL9+jB1Klx0kdOpVAWgmy+rcufN8zL4rAdYt2QTeblevLlefv1hM/ecM5r0lHSn4/lPfLztpPjNNxAbazss9ukDe/c6nUxVUFrIld8sX7Ca1H1p+LwHF9IYA7nZeXw2c4mDycrJmWfamSyjRsF//2tXh773ntOpVAWkhVz5zc4tu8jL8RY4np2RzZ+/hmlTquhouwvRihVQr55twHX11fDXX04nUxWIFnLlNyef1gh3RMFvqZj4aJq0bexAogBq3Rq+/x6eego+/tg24fq//9MmXCogtJArv0nseContW542Fz5CE8EVetU4azu7R1MFiAREXDfffDjj3Ynoptvtg9Bt2xxOpkKc1rIld+ICGMXjubqe7pS/biqVKlZiUtv7cwLy57AE1VwIVTYOuUU+PJLeOklu+lz8+YwcSJ4C952UsofdPqhUuVp61a47Ta7CXSHDjBtmn0oqlQp6PRDpZxwwgn2nvkbb9hOiq1bw+OPaxMu5VdayJUqbyLQu7dd5n/llfDAA5CUBKtWOZ1MhQkt5EoFSq1aMGuW3fA5Odl2VBwxAjIzj/1epY5CC7lSgXbllbZFbt++MHas7Xn+9ddOp1IhTAu5Uk6oUgVefRU++wzy8uDcc+GOO+DAAaeTqRCkhVwpJ3XuDOvWwT33wJQpdqri/PlOp1IhRgu5Uk6Li4PnnoNvv7UtcS+7DG68EXbvdjqZChFayJUKFmecAT/8AA8+CG+/bZf5v/OOLvNXx6SFXFVIxhhWLlzLE72e5/Ge41k2bxVOLI4rICoKHn7YTk1s0ACuvx6uuspuNadUESKcDqCUE168+zU+nb6YrPRsAJbNW8VZ3dszfPpARMThdEDLlnZ5/4QJMHq0HZ0/8wzccoudl67UIXREriqcLeu38slrX/xbxAGy0rNZ8v73/LT8VweTHSEiAu691z4Mbd0a+vWDCy6AzZudTqaCjBZyVeGs/HQt3ryCDaxyMnNYvuAHBxIdQ+PG8MUX8PLLtu958+Ywfrw24VL/0kKuKpzYhGjckQXvKkZ4IoirFOtAomJwueymzxs3wvnnw5Ah0LEjbNjgdDIVBLSQB4n9ySlMGzmT29oMY1TXJ/jh83VORwpbZ199RqHHXS6h0/VnBjhNCdWrB3Pn2q3lfvsN2rSBRx6BnBynkykHaSEPAvuTUxjQehjvj5/Hb2t/Z/n81TzYbSxzXvrE6WhhqVL1BB56/15i4qOJrRRDbKUYomOjGPHm3dSoW93peMcmAj172tH5NdfAQw/B6afb2y6qQtJ+5EHg1fvf5IPxH5Obk3fY8ei4KN7bNY2omCiHkoW37Mxs1nyxHp/P0Pr85sTERTsdqXTmzoXbb7f7hN5zjx2hxwbpLSJVJtqPvAT27Uph7859AbveigVrChRxAJfbxZZ1WwOWo6KJiomi/WWn0+HypNAt4gCXX27vlffrB88+a6cufvml06lUAGkhP8T2//3JHUn30avBbfRudAf9Wg5ly/ryL6TVjqta6PG8XC9ValUu9+urMFC5su3V8sUX9vPzzoMBAyAlxdlcKiC0kOfLycrhnrNH8+vqLeRm55Gbncfv67cy5JwHyUjN5Lu5KxnS6UFubjaYKUNnsO/v/X679jVDuhIVe/jtk4hINyef1og6DWv57TqqAjjvPLv587332u6KiYkwb57TqVQ500Keb+mHK8jOzCmwTDsvN49xfSfxxA0TWPf1Jrb9tIOPXvyEAW2GkbLbPy1HT7+wFbc+1YvouChiK8UQFeOhSbvGjPlgmF/OryqY2Fh4+mm7MrRqVXvr5YYb7GYWKixVuIedPp+PzWv/wOv10bhNQ9xuNwCzxn3E/z3wVqELRdwRLrx5vsOORUZFcu3Qy/nPYz39li0rI5vNP/5B1VqVOe7E2n47r6rAcnLgqafgscfs7ZeJE6FHD13mH6L0YSfw88rf6NXgdoac+yDDOo/h+uP6sWbxegCatD2JyOjIAu/xxHiI8BQ8npudy8qFa/2aLzo2imZnnKJFXPmPx2O7Ka5eDSedZEfmV1wB27c7nUz5UYUp5JnpWdx34SPs3rGXzLQsMlOzSNmdyugrnmLfrhRadUrkpFYN8BxSzD3RkdRpWLPQrngiULN+2eYc+3w+1n65gUVvfMW2n3eU6VxKHVViIixdavuef/65bcL18svg8x37vSroVZhCvnT2cnzegt+0Pq+Pz2d+jYgwduFoet5/FXUa1aJ2g5pcM+RyJn3/JI1bN8Qd6T7sfZ6YKK4Zcnmp8+zesYf/nDqI0Vc8xQt3vsptpw3n8Z7j8Wr/DFVe3G47z3z9emjbFm67ze5Q9GsQNQpTpVJhCnlK8gHycgvO1c7JymX/LvvQMiomit6jr+WN317kzS0v8Z/HehITH8MjH91H4plN8ERHEpNgVwPe9eItNO94aqnzPN5zAju37LK/HaRlkZOZw3dzVzHnpU9LfU6liuXEE+1eoa+8YjeyaNHCtsjNK/j/hwoNZepHLiJPA5cDOcBvwH+MMfv9kMvvWp7bDJe74M+t6PhoWp/X/KjvrVyjEs8ufpjk7XtI3ZtG/VOPJ7KQ++bFtT85hZ+X/1rgN4TsjGzmTV7IVXddWupzK1UsInDrrXDJJXbT52HD7G5E06bZwq5CSllH5IuA5saYlsD/gPvLHql8nHzaiZzRNYnouIPztaNjo2jarjGnXVC8b9ya9apzYssGZSriYNulSiE/VMDOXFEqYOrWhQ8/hFmz4Pff4bTTbO+WbP0+DCVlKuTGmIXGmH9+H1sG1Ct7pPIz8r+DGDS5Py3OaUqzDqcw4Nk+PLFgFC5XYO8w1axfg6q1C67YjPBEFNmZT6lyIwLXXQebNtmpiY88Ygv6smVOJ1PF5Ld55CIyF5hljHnzWF+rTbNg3ZJNjLz0cby5XnJz8oiOi6JKrcq8uOIpKlVLcDreUXm9Xt59Zg6zn59PWkoGiWc24bZn+3BiywZOR1P+MH++Xd6/YwcMHgyPPgpxcU6nUhQ9j/yYhVxEPgPqFPLSKGPMR/lfMwpIArqbIk4oIv2B/gAnnHDC6X/88UfJ/gVhaNe23cx/5TP+/HUnrTol0rn3OUTHBn+nwwm3vcxnby4h+5DbQDHx0UxZ/TTHn1TYt0pwyMnOxeUSIgrZVEId4cABGDECJk+GRo3sg9HOnZ1OVeGVupAX48R9gQFAZ2NMRnHeoyPyslny/jL+++QH7PlzH807NqHvoz054dS6Abn2/uQUbjjhdnKzcw877o5wcfHNnRk8pX9AcpTE1p928Fy/KWxa9j/EJZx5RRKDpwygUvXg/s0nKHz9tX0o+ssv9s+nn4YqVZxOVWGVy8pOEbkYGA5cUdwiXtF5vV6WfPA94/4ziclDpvP7hm0lev/7E+Yxts8kfv1hC/t27ueb2csZ2H4E2//3ZzklPtz2//112KKpf3jzfPy8IvjmIx/Ym8qgjqPY+O1P+Lw+vLlevpuzkiGdHip0oZc6wjnnwNq1MHw4vPaaXUj00UdOp1JHKOtTvklAArBIRNaIyBQ/ZApbebl5jOjyGOP6vMCiGV/x4QsLGNhuBJ/OWFys9+dk5TDjwVmH3dIwPkN2Rg5vPPpeecU+TJ1GtcjJyi1w3OV20bB5/YBkKImF078kNyuXQ2t2Xq6XXX8k8+NXG50LFkpiYmDsWPj+e6hZE668Eq6/Hv7+2+lkKl9ZZ600NsbUN8a0zv+4zV/BwtGXs77lp+W/kJVuC7HP6yM7M4cX7niVjNTMY75/5++Fd6/zeX1sXPqzX7MWpcbx1TizWxKeGM9hxyOjIrl++JUByVASf2zcTnZmwf0sjc+w45e/HEgUwpKSYOVK24Drww/t6PzNN0F/s3FchVnZGQy+nLX03yJ+KHekm3VLNh3z/VVrVyYvt/Al/LUb1ixzvuIaPuMuLr3lfKJiPIhLaJBYnyfmj6RhYvCNyE9JOumwtQP/EmjY4oTABwp1kZEwahSsWQNNmsCNN8Jll8FW3cnKSVrIAygmIabwF4x9WPj22A+5uekgbm46iLfHfkhO1uEjyYSq8ZxzzRkFRsNRsVHcMLJ7ecUuwBMVyZ0Tb2FO6hvMS5/Jq+ueo+U5zQJ2/ZK4oPfZxFaKxR1x8FvdEx1J4zaNaNr+ZAeThbimTWHJEnj+efjqK9uUa/JkbcLlkArXj9xJaxavZ/TlTxVYvVm5ZiXqNzmeX1Zt/vc2QFSMh5NPP5HnvnoEOaR3dE5WDs/f/gqLZy3FJUJUrIcBz/ahy02dAvlPCSm7d+xh6vA3WDZ3FRGeCLr0OZe+j/YMiameIWHLFujf3/ZvOftsuzPRKac4nSosldv0w9IoTSFf8eka5rz4CWn70zn76jO4tN8FIfk/4owx7/DOuA9xR7gRl+B2u+j7aE9eGfEmWWlZh31tTHw0Y2YP57TOBVsIZKZlkrovnerHV/13cwylHGMMTJ8OQ4ZAVhY8/LD9e4TO2fenkC7kbzz6Lu+M++jf+8tRMR7qnnwcLyx7Ak+05xjvDj67d+xhzeINxFWOJemiVrwzbg4zHppVYDqcuIQ+Y66n1wNXO5RUqRL66y+4806YPdsu83/tNWjVyulUYSNkdwjan5zC20/OPuwhYXZmDn/+tpPPZy5xMFnp1ahbnQt6n0OHy5OI9ERSvW41omIL/kCKivFQvW41BxIqVUrHHQcffADvvWeX+CclwQMP2FG6KjdBX8g3LP2ZCE/BX8+y0rP59qMVDiTyv3OvPaPQf2NEZATnXqtNtFQIuvpq2LgRevWCxx+HNm3g22+dThW2gr6QV6qeUOgKPJdLqFqnSuADlYOY+BieXfww9ZocjyfGgyfGQ70mx/Pslw8TE1/ETBelgl21ava++SefQEYGnHUWDBoEaWlOJws7Qf8kIrFjExKqxpOVln1YQY+MiuSK2y9yMJl/ndiyAa9tnMDff9hFP3Ua1nI4kVJ+ctFFdnu5kSNh4kSYMwemToULL3Q6WdgI+hG5y+Vi7KIHqXNiLaLj7TZr0XFR3D25H43bNHI6nl+JCHUa1tIirsJPQgK88IKdex4VBV26wM03w759TicLCyExawXAGMNva34n/UAGTdo2Dsmph0op7IPPRx6BceNs75YXX4TugVvQFspCdtbKP0SExm0a0ercRC3iSoWy6Gh44glYsQLq1LEPRq+5BnbudDpZyAqZQq6UCjNt2sDy5baoz5tnm3DNmKFNuEpBC7lSyjmRkXD//bYJV7Nm0LcvXHIJ6A5iJaKFPEz5fD7efWYOPer1p2tcL4Zd8DC/rf3d6VhKFe7UU+1uRJMmwdKltgnXpEnahKuYtJCHqZcG/x8zxrzDnj/3kZ2Zw5ov1nPP2aPZrj24VbByuezy/vXr7Zzzu+6yOxT99JPTyYKeFvIwdGBvKgte/fywnYTAtjaYNe5DZ0IpVVwNGsCCBfZ++caNtlfLE09AbsGdqZSlhTwMbf/fX0RGFdxX0+f18fNy5/fV3LcrhUWvf8Xit5eSfkC3elWFEIGbboJNm+CKK+xmFu3awerVTicLSkG/slOV3HFF7avpEsd38Zk75VOmDJmBO8INAj6vYfSse2h/2emO5lJBqnZtePdd24jrzjuhbVsYNgweeshOY1SAjsjDUtXaVTire/uC+2pGe+gx4iqHUsHWn3YwZejr5GTlkpmWRWZqFtkZ2Tx63XOk7tP+G+ooune3t1luugmeesrebvnmG6dTBQ0t5GHq3tfu4NJbOxMV48HlEuqfWpfH5o7gxJYNHMv0xX+X4M3NK3Dc5Xbx3ZyKt2OUKqGqVW1/84ULISfH7kY0cCCkpjqdzHF6a6UMvF4vm9f+gcvtolGLE3C5gufnoicqkjufv5nbx/clLycvKDbgyM7MwectuNjD5zOF3gpSqlAXXgjr1tk+5xMnwty58PLLcPHFTidzTPBUnhDz49cb6VFvAEM7PcTgs0fTq+Ht/LzyN6djFeByufBEe9i9Yw+PXPcsXeN70a3KTbww8FUyUjMDmqVjt7aFbqDh8/pod2mbgGZRIS4+HiZMsHPO4+LsIqI+fWDPHqeTOUILeSmk7D7AqMueZP/fKWSmZZGVlsXu7Xu578JHyEwLbHEsjsy0TO5sdz9LZy8nOyOHjAOZLJj2OcMvfKTQXu/lJbHjqXS67kyi46IQsVvZRcV6uPGha6lVv0bAcqgw0qGDncnywAPw3//a1aHvvVfhlvlrIS+FxW8txVfIijOf18c3Hyx3INHRfT7zGzIOZODzHsycm53HHxu3s2Fp4BZbiAhDXr2dx+bez2UDunDlXZcw/utH6engA1gVBqKi4NFHYeVKqF8frr3WNuL6q+IsftN75KWw9+995GTmFDiem5PL/l0pDiQ6ut/WbDlsz9N/GK+PLeu30fyspgHLIiK06pRIq06JAbumqiBatYJly+C55+z0xGbN7N/79rXz0sOYjshLoXWn5sTEF5zD6o6IoOW5zRxIdHQNm9cvtPWvy+2i3inHOZBIqXISEQHDh8PatdCypd28oksX2LLF6WTlSgt5KbQ+vzmnnnEyUYcUx+i4KNpe3JombRs7mKxwF/Q+B09MJOI6OCqJiHRTq0FNHRmr8HTKKbB4MUyeDN9/D82bw/PPg9frdLJyETI7BAWbvNw8Fkz7goUzvsQd4eKSWzpzwY3n4Ha7nY5WqB2//sWEAS/z49ebEJdw1lXtuPvFflSqnuB0NKXK17ZtMGCA7d/SoQO8+qq97RKCitohSAt5BeP1ehGRoJrzrlS5M8bOahk0yC4gGj0a7rvP9kMPISG/1ZvyD7fbrUVcVTwi0KuXXeZ/1VW2kCclwapVTifzC/0/WilVcdSqBW+/DR9+CLt3246K990HmcG3/qMktJCrf+3blcI3s79n7Vcb8IbpQyGlAOjWDTZsgFtugXHj7NTFr75yOlWp6TxyhTGG8QOmsGjGV7aPuUBc5VjGLXqQ+k3qOh1PqfJRpQpMnQo9ekC/ftCpE9x2G4wdC5UqOZ2uRHREXsHt2ppMz/q3seDVL8jL9f7bXnbPjr2MvPSJgC7hV8oR558PP/4IQ4bYwp6YCPPnO52qRPxSyEVkqIgYEdGGGSHmoaueZs+fewscNwZSkg/wyw+bHUilVIDFxcGzz8K339rR+GWXQe/e9j56CChzIReR+kAXYGvZ46hA+mvz32z7aUeRr4tLyDgQ2g+BlCqR9u3hhx/sEv9Zs+x881mzgr4Jlz9G5OOB4UBw/0tVAekHMnBFFP0t4PP6OLX9yQFMpFQQiIqCMWNsQW/Y0N5Dv/JK2FH0oMdpZSrkItIN2GGMWVuMr+0vIitFZGVycnJZLqv8pGFi/SJXoroj3Qx84ZZCe7QoVSG0aAHffQfPPAOLFtnR+SuvBOXo/JiFXEQ+E5H1hXx0A0YCDxbnQsaYqcaYJGNMUs2aNcuaW/lBRGQEQ169nahYz799WFwuF7EJMTz92YNc1Pc8hxMq5TC3G4YOtQ9DTzsN+veHzp3ht+DaRKbUS/RFpAXwOZCRf6ge8CfQzhiz82jv1SX6wWXL+q3MefETkrftoe0lrenSpxMx8TFOx1IquPh8tk/LsGGQmwuPPWaX/Aewv1K591oRkd+BJGPMMR/zaiFXSoWs7dvh9tth3jy7MnTaNNtdMQC014pSSvlDvXowZw689RZs3mxvuTz8MOQU3GwmUPxWyI0xDYszGldKqZAnYmezbNpkt5YbMwZOPx2WO7PVo47IlVKqtGrUgJkzYe5c2LfP9ju/917IyDj2e/1IC7lSSpVV1662CVe/fnaFaIsWdoeiANFCrpRS/lC5MkyZYgu4iO3hMmAApJT/huxayJVSyp86dbLzzu+99+C2cnPnlusltZArpZS/xcbC00/DsmVQvTpccQXccAOU06p2LeRKKVVe2raFlSvhkUfgvfegaVP48ku/X0YLuVJKlSePx+4Runq1naLYuLHfL6E7BCmlVCAkJsKnn5bLqXVErpRSIU4LuVJKhTgt5EopFeK0kCulVIjTQq6UUiFOC7lSSoU4LeRKKRXitJArpVSI89tWbyW6qEgy8Ef+pzWAUNuQQjMHhmYODM0cGP7I3MAYU2D3ekcK+WEBRFYWtgddMNPMgaGZA0MzB0Z5ZtZbK0opFeK0kCulVIgLhkI+1ekApaCZA0MzB4ZmDoxyy+z4PXKllFJlEwwjcqWUUmWghVwppUJcUBVyERkqIkZEajid5VhE5FER+VFE1ojIQhE53ulMxyIiT4vIT/m5Z4tIFaczHYuIXCsiG0TEJyJBO91MRC4WkZ9F5FcRGeF0nuIQkddEZJeIrHc6S3GJSH0RWSwiG/O/LwY5nelYRCRaRJaLyNr8zA/7+xpBU8hFpD7QBdjqdJZietoY09IY0xqYBzzocJ7iWAQ0N8a0BP4H3O9wnuJYD3QHvnY6SFFExA28CFwCNAN6ikgzZ1MVy3TgYqdDlFAeMNQY0ww4A7gzBP5bZwPnG2NaAa2Bi0XkDH9eIGgKOTAeGA6ExNNXY8yBQz6NIwRyG2MWGmPy8j9dBtRzMk9xGGM2GWN+djrHMbQDfjXGbDbG5ABvA90cznRMxpivgb1O5ygJY8xfxpgf8v+eCmwC6jqb6uiMlZb/aWT+h1/rRVAUchHpBuwwxqx1OktJiMjjIrIN6EVojMgPdTOwwOkQYaIusO2Qz7cT5MUlHIhIQ6AN8L3DUY5JRNwisgbYBSwyxvg1c8A2XxaRz4A6hbw0ChiJva0SVI6W2RjzkTFmFDBKRO4HBgIPBTRgIY6VOf9rRmF/RZ0ZyGxFKU5mpQ4lIvHA+8DgI347DkrGGC/QOv+51GwRaW6M8duziYAVcmPMBYUdF5EWQCNgrYiA/XX/BxFpZ4zZGah8hSkqcyFmAvMJgkJ+rMwi0hfoCnQ2QbKIoAT/nYPVDqD+IZ/Xyz+myoGIRGKL+ExjzAdO5ykJY8x+EVmMfTbht0Lu+K0VY8w6Y0wtY0xDY0xD7K+lpzldxI9FRE4+5NNuwE9OZSkuEbkY+xziCmNMhtN5wsgK4GQRaSQiHqAHMMfhTGFJ7GhvGrDJGPOc03mKQ0Rq/jNDTERigAvxc71wvJCHsKdEZL2I/Ii9LRT006CASUACsCh/2uQUpwMdi4hcJSLbgQ7AxyLyqdOZjpT/AHkg8Cn24ds7xpgNzqY6NhF5C/gOaCIi20XkFqczFUNH4Ebg/Pzv4TUicqnToY7hOGBxfq1Ygb1HPs+fF9Al+kopFeJ0RK6UUiFOC7lSSoU4LeRKKRXitJArpVSI00KulFIhTgu5UkqFOC3kSikV4v4fsB/4rm6JghoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression\n",
    "train_data = np.hstack([data, np.ones((data.shape[0],1))])  # add bias\n",
    "n = Neuron(random_state=41, max_iters=500, learning_rate=0.01)\n",
    "n.fit(train_data, classes)\n",
    "\n",
    "# Visualize results\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "slope = - n._weights[0] / n._weights[1]\n",
    "bias = n._weights[2] / n._weights[1]\n",
    "plt.plot(\n",
    "    [data.min(axis=0)[0], data.max(0)[0]], \n",
    "    [slope * data.min(axis=0)[0] - bias, slope * data.max(axis=0)[0] - bias],\n",
    "    c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it, we have working logistic regression. What we have done is called **Stochastic Gradient Descent** - it computes the gradient for every sample and updates the weights accordingly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Batch gradient descent\n",
    "\n",
    "Let's think a little bit about the previous implementation. When we treat each data point separately, the optimum is \"put the separating hyperplane as far as possible from this data point\". In other words, when we have only one point and we want to minimalize the loss, the ideal separating hyperplane is infinitely far away from the datapoint (as only in infinity is the value of sigmoid 1 or 0, depending on the class). As a result, the algorithm can start oscillating the same way we have seen in the perceptron case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, what we really want, is the separating hyperplane that is optimal for all the data points we have. Let's look once again to the loss function.\n",
    "\n",
    "$$\n",
    "\\mathcal{L}=\\frac{1}{2} \\sum_{i=0}^{n} \\left( t_i - f(\\pmb{x_i}) \\right)^2 \n",
    "$$\n",
    "\n",
    "We silently ignored the sum, or more precisely we used only one data point so the sum disappeared. Let's now fix the algorithm and instead of updating the weights based on the simple sample, we are going to update it based on all the samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, max_iters=100, random_state=None, learning_rate=0.001):\n",
    "        self.max_iters = max_iters\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        # Learning\n",
    "        for iteration in range(self.max_iters):\n",
    "            # predict the data\n",
    "            prediction = self.predict(X)\n",
    "            # table of gradient for each weights and gradient in the shape (samples,weights)\n",
    "            gradient = np.reshape(-(y - prediction) * (prediction * (1 - prediction)), newshape=(-1,1)) * X\n",
    "            # sum gradient over the samples\n",
    "            sum_gradient = np.sum(gradient, axis=0)\n",
    "            # update the weights\n",
    "            self._weights = self._weights - self._learning_rate * sum_gradient\n",
    "                \n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implementation is almost the same. We first generate all the predictions for all the data points (that mean `prediction` is a vector), then compute the gradient of loss and sigmoid (the result is still a vector) and finally multiply each value with the corresponding data point. Because `X` is a matrix, we need to reshape the gradient (of loss in respect to $\\pmb{x}\\pmb{w}^T$) to the matrix of size `(samples,features)` so we can multiply it with matrix `X` of shape `(samples,features)` (in this case the real shape is `(samples,1)`). We obtain the gradient with respect to weights for each data point (that is `gradient` variable in the shape `(samples,features)`) and we sum it over the data points. Finally, we update the weights.\n",
    "\n",
    "Note that we didn't shuffle the data this time, as it doesn't make sense. As the gradient for each data point is accounted for, the order of data points doesn't matter.\n",
    "\n",
    "Now let's train the logistic regression and see the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression\n",
    "train_data = np.hstack([data, np.ones((data.shape[0],1))])  # add bias\n",
    "n = Neuron(random_state=42, max_iters=1000, learning_rate=0.05)\n",
    "n.fit(train_data, classes)\n",
    "\n",
    "# Visualize results\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "slope = - n._weights[0] / n._weights[1]\n",
    "bias = n._weights[2] / n._weights[1]\n",
    "plt.plot(\n",
    "    [data.min(axis=0)[0], data.max(0)[0]], \n",
    "    [slope * data.min(axis=0)[0] - bias, slope * data.max(axis=0)[0] - bias],\n",
    "    c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result seems to be a bit better than in the previous case. The algorithm keeps about the same distance from the first class as from the second one. Using all the data points at once, the algorithm can find the global minimum and will not oscillate.\n",
    "\n",
    "Sometimes, this algorithm is just call **gradient descent** (instead of batch gradient descent). This makes sense as the algorithm in fact optimizes the global loss (instead of loss for individual data points). In most sources gradient descent (aka batch gradient descent) is shown first and then they start talking about its stochastic version. I decided to flip the order as from the implementation point of view, the stochastic version is easier to read (at least I believe so)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pros and cons\n",
    "\n",
    "Now, when we have seen batch gradient descent (I will refer to it as gradient descent so on) and stochastic gradient descent, we should talk about the differences and what are their pros and cons.\n",
    "\n",
    "+ Gradient descent is more stable and can result in faster convergence in some cases.\n",
    "+ Gradient descent is usually more efficient, as the operations can be vectorized (performing the same operation over multiple data at once) and thus the algorithm can be faster.\n",
    "+ Because the update is following the prediction, the algorithm can be parallelized into some level.\n",
    "+ Gradient descent can get stuck in the local optimum more easily.\n",
    "+ Gradient descent can have problems for big training sets, as the data don't need to fit into memory (nothing we would need to worry about so far). That may leads even to overflow when there are so many samples that the sum of gradients does not fit into memory (or the value would be simply too big).\n",
    "+ Stochastic gradient descent updates weights more often and thus can lead to faster convergence.\n",
    "+ Stochastic gradient descent is more computationally intensive.\n",
    "+ Stochastic gradient descent can oscillate too much and avoid the global optimum (even good local optimum).\n",
    "\n",
    "These algorithms are extremes, we update weights for every data point or for all the data points. It turns out the best approach is something between, which leads us to the following algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minibatch gradient descent\n",
    "\n",
    "Minibatch gradient descent combines the approaches above. We provide the algorithm another parameter (called batch size). Before each iteration, the algorithm shuffles the data and split them into subsets of the same size (based on the batch size parameter) called batches. The weights update is then done for each batch separately.\n",
    "\n",
    "The question you may ask is what to do with the last batch in case the number of data points is not divisible by the batch size. Well, we can ignore that batch or use it anyway. Note that the batch size should be in the order of magnitudes smaller than the data, so skipping it shouldn't have an impact on the training process. When we use it, the gradient can be noisier, but again, it shouldn't have an impact on the training process as there are plenty of batches before. I am going to use it, but if you don't want to, it is as easy as modifying the source code a little bit.\n",
    "\n",
    "Before we dig into the code, I want to point one more small change in the terminology. What we called iteration before is now called epoch - one epoch is done when the algorithm processes all the data points in the set. One iteration is then done when one batch is processed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, epochs=100, random_state=None, learning_rate=0.001, batch_size=16):\n",
    "        # use epochs instead of iterations\n",
    "        self.epochs = epochs\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        self._batch_size = batch_size\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        n_data = len(X)\n",
    "        # Learning\n",
    "        for epoch in range(self.epochs):\n",
    "            # shuffle the data\n",
    "            permutation = self._rand.permutation(n_data)\n",
    "            # for each batch\n",
    "            for batch_start in range(0, n_data, self._batch_size):\n",
    "                # get batch\n",
    "                batch_data = X[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                batch_target = y[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                # predict the data\n",
    "                prediction = self.predict(batch_data)\n",
    "                # table of gradient for each weights and gradient in the shape (samples,weights)\n",
    "                gradient = np.reshape(-(batch_target - prediction) * (prediction * (1 - prediction)), newshape=(-1,1)) * batch_data\n",
    "                # sum gradient over the samples\n",
    "                sum_gradient = np.sum(gradient, axis=0)\n",
    "                # update the weights\n",
    "                self._weights = self._weights - self._learning_rate * sum_gradient\n",
    "                \n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are not many changes. First of all, we shuffle the data as we did in the stochastic gradient descent. We then iterate over the data and use Python's slicing capability to obtain one batch (we need to index the original data by the permutations)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SkwIaXoiuORNnpkUc5y4yD+nx7+QXoTI5wwq5m1SdYZjnn0/cXXrkkc4aMdZdahLQ6FK04u/Onbl/MNLpN4ivv9uxjAvatZCLyMPAeGCVqja7IEOHK+QNWXepMaYV2ruQ7wtUAI9aIW8h6y41xiSp3YdWRKQ/8IIV8jaw7lJjzGZYQ1A2EIERI+C665yC/t13cO+9TiG/5x5nlcbeveHkk23vUmPMRmm7IxeRs4GzAYqLi0csW7YsJdftMMrLYe5c52591iyn29Tng/3223S3PmCA2ymNMe3IhlZySSzmdJBumNr42WfO8cGDNxX1PfZwxtqNATS8AK18FOKrIW8sUnAS4il0O5ZpISvkuWzp0k1F/Y03nELfp48z++XII501YTpl17rLJnXilf+G8hvZ1OqfB97eSM/nrJhnmXYdIxeRx4D5wI4iskJEzkrFeU2SbO9S0wSNV0H5TdRfryUEsVVo1XS3YpkUs4agXGbdpR2ehhega38LWtH4Td9QPL2eSn8o02o2a6UjCgScdV7uuAO++goWL4apU8HvhylTYPhw2GYbOO88mDMHQqHmzmiyjXQDjSV+z9szrVFM+7FC3lGIwC67wBVXwNtvw8qV8NBDznTHRx5xNsro1QuOPRb++U9nVozJeuLfHnzFQMNNKIJIwa/ciGTagQ2tGOsuzXEaW4mu/TXEVgA+0Ah0vhhPpzPcjmZayBbNMsmx7tKcpKoQXQLxtc7CWzZbJStZITetY3uXGpMxrJCbtrPuUmNcZYXcpJZ1lxqTdlbITfuy7lJj2p0VcpM+tnepMe3CCrlxh3WXGpMyVsiN++ruXTpzpjPGbnuXGpM0K+Qm89jepSaNNPI5WnEPRBaDrz9SeB4S2N3tWC1ihdxktupqZ/XGDXfr1l1qUkgjH6M/n4KzCuSGmpcPXW/DExznYrKWsUJusod1l5oUi/98MkQWNH7DsxVSNA/JkhsEK+QmezXVXXrYYU5Rt+5S04z4T8NAqxK840V6lyCe7Jgaa8vYmuzVrx9MmuRMZVy9Gp5+2rkznzMHTjjBGUcfNw7uumvTrBhj6vL0SHxcAiD56c3SDqyQm+zSuTNMnOgsvfvjj/Dmm3DJJc6Y+oUXwrbbwpAhMHmyMysmHnc7sckEBb8Fgg0O5kPwJEQaLvGbfWxoxeQO6y7tUFRjaOXfoepfoJUQ2BPpfBnia7zej6qilX+Fir+DeECjEJyIdLkakex51tKuY+QicghwJ87q9Q+q6o2b+7wVctPurLs058XXXw7Vs9m0H6mAFCK9ZiHeLRJ+j2oNxH4AT++sXMq33Qq5OL+XLAEOBFYAC4ATVfXTpr7HCrlJK+suzTka+wktPQAIN3jHDwWn4elymRux2l17PuzcA1iqql+rahh4HJiQgvMakxq2d2nuiS4FSdQBHIHIonSncV0qCnlfYHmd1ytqj9UjImeLSImIlJSWlqbgstmpsqyKJ25+lotGX8WUY27hw9c/cTtSx2J7l+YGbz/QhnfjAF7wbZ/2OG5LxdDKscAhqvrr2tenAnuq6vlNfU9HHVqpKq9m0m5/ZPUPawlXO/8T5hXk8esbT+ao8w91OZ2x7tLsEl9zFoTfA+r8BiVBpOezCR945oL2HFr5HuhX5/XWtcdMAzPvm1OviAOEqkI8eNm/qK6odjGZASAYdJqM/vY3WLECSkrgqqucNWAuuwx22gl22MGZ7vjaaxCNup24Q5Nud0NwPBAAvOAdiHR/KGeL+OakopAvALYXkQEiEgBOAJ5PwXlzzvyZJfWK+Aa+gI8lJV+7kMg0ScQZbrnuOme5gO++g3vvdZYJuOceGDsWeveGU06BJ56A9evdTtzhiKcAT9dpSJ9FSO+FeIpmI4FGN6sdQpsLuapGgfOBOcBnwJOqagO/CXTrnbiNPBaN0aVn9k2F6lCsuzRjifgQT4HbMVxlDUFp9OHrnzD58GmEqjaN6Xm8HvrtuBV///i2rFm4x9Rhe5eaNLJFszLEs3fP5sHLp+Pze4nF4vTZpoips6+kd3GR29FMKlh3qWlHVsgzSFV5NV8u/JouPQvpP7jY7sRz1Ybu0pkzYfbs+t2lRx4J48dbd6lpESvkJq1qqkJoPE6wsOFCRR2UdZeaFLBCbtJi9Q9ruPXMe/lg3mJQ2GHkdvzh4XMpHtSoR6zjsr1LTStZITftLhaN8asdLqB0+c/EY87ysSJCYfdO/N9X99Cpq40NJ2R7l5ok2cYSpt2VzFlE2c8VG4s4OMuHRmoi/Hf6my4my3B9+sCZZ8KMGc7Uxlmz4OSTYf58OP105/199oGbb4bPP3fu3o2pwwq5SZkfvvqJaLhxt2NNVYjvl650IVEWakl36euvW3epAayQmxTablh/vP7Gu60EC/PZYcR2LiTKcs11l44ZY92lBrBCblJoyOidGDC4H4F8/8ZjPr+Xbr27MvrYUS4myxHWXWqaYA87TUrVVIV4dMqTzH30dWLRGKOPGcWZN5xI115d3I6Wu6y7tMOwWSvGdBTWXZqzrJAb0xHV7S598UVnHN26S7OWFXJjOrpIxLlDf/556y7NUlbIjTGbWHdpVrJCboxpmnWXZgUr5MaY5NjepRnLCrkxpuVUnWakDbNgPvjAOT5w4Kaivvfe4PO5m7ODaJe1VkTkOBH5RETiItIxN8szJpdt6C6dMsW6SzNYWzsEFgMTgf+lIIsxJtNZd2lGalMhV9XPVPWLVIUxxmSRzp1h4kR45BH48Ud4801nMa8ffoALL4Rtt4UhQ2DyZGdWTDze7ClN66RkjFxEXgP+oKpNDnyLyNnA2QDFxcUjli1b1ubrGmMylHWXtotWP+wUkVeALRK8NVlVn6v9zGs0U8jrsoedxnQg1l2aMk0V8mYfNavquPaJZIy7VJVvF39HPK4MGFKMxxaVah/du8NJJzlfDbtLZ81yPmPdpW2StqGVuuyO3Ljti5KvuO6YWyhfW4EgBAvzufqpSxi89yC3o3Uc1l3aYu0yj1xEjgbuBoqAdcAiVT24ue+zQm7cVFVezUnF51C5vqre8fzCfKZ/cy9denZ2KVkHZ92lzWqXeeSqOkNVt1bVPFXtk0wRN8Ztbz7zbr19RTfQeJx5j7/lQiIDJLd36ejRtndpAjYoaDqcdavWE66JNDoeqgqz5sd16Q9kGku0d+nVV0Nlpe1dmoAVctPhDNl3Z/x5jZ/zBwvzGTpmFxcSmc2y7tJmWSHPIGtXreft5xfw2btf4sYaOB3FoD0Gstu4Xckr2PQQLa8gj0F7DGT4/oNdTGaSYt2ljdiiWRlAVXnkmsd56taZ+AM+NK703Ko7N718Nb2Li9yOl5NisRgvP/Iasx/8LxpXDj59DIf++gB8flv8KWt1gL1LbfXDDPbWs+9x46l3UVMZ2njM4/XQf3A/7v/gLy4mMyaL5WB3abvMWjGpMeOu2fWKOEA8Fuf7L1ey4suVLqUyJssNHAgXX+ysrV5aCtOnw9ixzlDMUUc5QzDjx8MDDzjrw2Qx+z0yA1Ssq0x43Ov1NprrbIxphRzvLrU78joqy6q4+4IHmdjzDI7ucTq3nf03ytaUt/t19zl6DwL5/kbHxSNsu2txu1/fmA7F74f994c77oCvvoLFi2HqVOf4lCkwfDhssw2cd57zADUUau6MrrMx8lrxeJxJIy5l+effEwk5c1J9fi99+vfmwcW34fV5+XT+EtavLmPnvXagW1HXlF27sqyK80Zexuof1hCqCuPxevAHfPzh4XMZc/zeKbuOMaYZGd5dag87m7FgziKuP+5Wqitq6h0PFuZz1rSTePr2WaxbtR7xCJFQlBMuP4rTrv1lyq5fXVHNnEde493Z71O0dU8mnHcI2w3tn7LzG2NaqKm9S3/xi01DMGneu9QKeTMev+lZHrn6cWLRWKP3uvTsTPnaCjS+6d8qv1MeVz3xe/Y8bLd0xjTGuCFD9i61WSu1VJWli75hycKviMU2Fe2+A7cgEGw8Th0I+qkur65XxAFqKkM8e/eL7Z7XGJMBMry7tEPNWlmy8CumTLyFirWVIJAXDHDV479n6JhdGHXECAq7dSJUFd64oJLHIwTy/cSjSiTceC2HpmabGGNy3Ibu0kmToLwc5s517tZfeMGZ5ujzwX77bWpEGjCgXeN0mDvy6soaLh33J0qX/0x1RQ3V5TWsW1XGVUdMY+2q9fgDfu586wZ2O2AIXp8Xr8/DkH135o43b0jYLh8IBhh9zCgX/ibGmIyyYe/Sf/zDtb1LO8wY+Sv/+h93nfv3Rg8zA/l+zpx6EsdcNH7jsXAoAqoE8gO13/s6d5zzAJGaCPG4kleQR59tenHPu9MIFgZblUdVmXHXbJ646VnWry5jwJBizrntdIbuZ4s2GZMzEnWXPvUUHHtsq07X6q3ecsX60jKikcbDI+GaCGsbLF0ayKs/Vj7ulP3ov0sxz937Emt+WMueh4/goNPHkF/Q+p1LHr3uSf7zl5nUVDlzVJd+8C2TD5/KLf+dwk57bt/q8xpjMsiG7tKLL960d+mBB6b8Mh2mkO+63854vI1HkoKF+Qwd2/yKdwOHD+CSv09KSZZQdYin/jKTUFX9RoNQVZhHpzzBtBevSsl1jDEZZEN3aTto0xi5iNwiIp+LyEciMkNEuqUoV8ptv9u2jBo/gvxO9Zcu3XH3gYw4cNe0Zlmzcl2TU0+/+Xh5WrMYY7JfW+/I5wJXqGpURG4CrgAua3us9nHF9At5dfqbzH7wFaKRGAf9agyHnDk27bund9+iW6PpjBsU79Q3rVmMMdmvTYVcVV+u8/IdoHUj+Gni9Xo58LT9OPC0/VzNkV+Qx4QLDuW5e16qN7ySVxDgtCmp6xY1xnQMqRwjPxN4oqk3ReRs4GyA4mJbCOqsqSdR2LWAJ//yPBVrK+k3aCsm3X4Gg/ce5Ha0pISqQ7wzcyHrSssYOmYX+u/Sz+1IxnRYzU4/FJFXgC0SvDVZVZ+r/cxkYCQwUZOYz5iJLfpuisfjaR/eaYuli77h0gOuIxqNE4tGEYR9j9uLPzx8blb9PYzJNq2efqiq45o58enAeOCAZIq4aSybip+qcs2EmyhfW7+r9Y2n32HkQUPZ/6TRLiXbPFXl55Vr8Qd8dO3Vxe04xqRUW2etHAJcChypqrYDQhqoKnMemccZg37HUd1/xeUHX8/SRenbYParD79tVMTBWXtm1gNz05ajJT5/70vOGHQhpw08nxP7/ZaLRl/FquWr3Y5lTMq09VbwHqAzMFdEFonI31KQKef9tKyUl/4xjzeeeZdwTbhF3/vYtGe454KHWLFkJZXrq1g49yMuHn01336SnmmLsUisyamTkXDjlSPdtvandVx64J/4/suVRGoiREJRPnvnS36/7zX1Fk0zJpu1ddbKwFQF6SgeunI6z9wxC4/Xg3g8eDzCtJeuSqqbM1Qd4rFpMxrt7xmqDvN/f3qKq5/4fXvF3mjg8AEJd5rPKwgw7pR92/36LTXnH/OIReoX7HgsTtmact5/5WN2P3iYO8GMSaHsGZzNAe+/8hHP3vUi4ZoINZUhqsurqVxfxVVHTEu4DnpDPy1bjXga3w5rXFmy4Kv2iNyI1+dl8mMXkd8pD3/tUgbBwnx2GLEdh5y1f1oytMT3S38kXBNpdFxjSunyn11IZEzqdZgW/Uww+6H/blxbpa5oOMrHb3zGsGaWCui5ZTeiTQxfbDWwT0oyJmPEgUP5xxd3MffR11izch0jDhzK7ocOw+v1pi1DsoaM3onXnnir0W8xirLj7tu5lMqY1LI78jRquLZKXYnuGhvq1LUT404ZTV4wUO94XkGAk69Kby9Wr616cOLlEznvzjMZNX5ERhZxgDHH/4IeW3bHF9h0z5IXDDD8gCG2lZ7JGVbI02js8XvXW+tlg1g0zo67b8fjNz3LmTtdyJk7XcjjNz2b8EHoBX/9NYf++gACwQA+v49efXtw2aO/Y9d9d07HXyHrBPID3PPuNCacdwhFW/dkq4FbcNqUX3Ltf/7gdjRjUqbDrEeeCWLRGJPHT+OTt7+gpqIGr8+Lz+/lovvPZtYDr/Dlwq8JVTvFOy8YYPsR23Lb639CEkwTiYSdcfbCbp0Svm+MyT1Zvx55PB7n8/eWUl1ezU6jdqCgc+s2dHCT1+dl6uwreW/2B8yfWUKXHoUcfMZYVi3/maWLvt1YxMGZifLVom/54NXF7HbAkEbn8gf8+AON9xg1xnQ8WVHIl322gisPvYHyNRV4PB6ikSiT7jidw3+T+gXa25vH42HU+BGMGj9i47HXn5xPqLLx+HlNVYjP5i9JWMiNMWaDjB8jj8ViXH7Q9ZQuX011RQ2VZVWEqsPcd/EjLFmYnil37a1n3x7kFQQaHc8LBujZt4cLiYwx2STjC/niNz+nsqyKhkP5kZoIM+97OfE3ZZn9jhtVb1bFBj6/j/2Osw2ejTGbl/GFvGJtZcKHefG4sm7VehcSpV6wMMit866j36C+BIIBAsEA/Qb15dbXrmv15s7GmI4j48fIB+8ziGi48abJ+Z3y2Gfini4kah/b7roND396Bz8tKwWgzzZFLicyxmSLjL8j79qrC6deexx5BXX32gzQb8etGHviPi4max99timyIm6MaZGMvyMHOOGyoxm0x/bMvG8O5WsrGX3MKA4+fQyBPJt+Z4wxWVHIAYaNHdzsWiTGGNMRZfzQijHGmM2zQm6MMVnOCrkxxmQ5K+TGGJPl2rr58vUi8lHtfp0vi8hWqQpm2k5V+ebjZbz/34+pWNd4w2RjTG5o66yVW1T1agAR+R1wDXBOm1OZNlv9wxomHzaVH776Ea/PSyQU4ZRrjuPEy492O5oxJsXadEeuqmV1XnYC0r+4uUno2qNu5ttPllNTGaJyfRXhmgjT//w0785+3+1oxpgUa/MYuYjcICLLgZNx7sib+tzZIlIiIiWlpaVtvazZjO+XrmTZJ8uJx+L1joeqQsy4c5ZLqYwx7aXZQi4ir4jI4gRfEwBUdbKq9gOmA+c3dR5VfUBVR6rqyKIia0FvT+VrKvD6E++hua60LOFxY0z2anaMXFXHJXmu6cBs4No2JTJttu2u26DxxqNc/jw/ex3ZaJeotFq1fDX3XPAQC15ahMfrYb9f7sW5t59BYbdOruYyJpu1ddbK9nVeTgA+b1sckwqB/ADn3XUmeQV5G5cADgT9dN+iKxMvPNy1XNWVNZy/5xW8+8JCouEo4eow8x57i0vGXIsbe8cakyvaOmvlRhHZEYgDy7AZKxnj4NPH0m9QX2bcOYvV369hz8N244hJB9Gpq3t3vvMee4vq8mridX5biIajrPz6JxbNW8zw/W1LO2Nao02FXFWPSVUQk3o7j9qBnUft4HaMjb7+6FtqEuxNGovGWPbpCivkxrSSdXaatBkwuJj8TnmNjnv9Xop32tqFRMbkBivkrbR21XqmnXoXR3Q+hQldT+PW39yX0d2T8Xicd15YyI2n3sWtv7mPT97+Iu0Z9j9pH/I75ePxbvrfzhfw0WebIoaN3SXteYzJFeLGQ6aRI0dqSUlJ2q+bKuFQhLN2uojSFT8Ti8YApyD13X5LHvjwL3g8mfXzUVX58/G3895LH1BTUYOIEAgGOP7SCZx6zXFpzfLTslLuPv9BSuY4s1b2Pe4XnHvH6XTp0TmtOYzJRiKyUFUbTT3Lmo0lMslbM95j/eqyjUUcnId2q5aVUjLnQ/Y4dLiL6Rr74L8f896L728cn1ZVQlUhHr9xBgefPobexemb199nmyL+PPMKVDXhptrGmJbLrFvHLPH1x8uorqhpdDwSivDt4u9cSLR5bz9fkvAho3iEkpc/ciERVsSNSSEr5K1QvGNfgoX5jY778/1svUPmLQBZ0Dkfr69xp6fH60n48NEYk12skLfC6GNHESys/9DO6/PStWcX9jx8NxeTJTbu1P0St+wr7HXEiPQHMsaklBXyVsgvyOOu+VPZ7YAheLwevD4Pexw2nDvf/nPCO1+3FQ/qy/l3n0kgP0BBl+DGrz89dxnBwqDb8YwxbWSzVtooFnMeeHq9mVfAG6pYV8n7r3yEP8/PiAN3JZAfcDuSMaYFbNZKO8mGAr5BYbdO7HvsXm7HMMakmA2tGGNMlrNCbowxWc4KuTHGZDkr5MYYk+XsYacBYF3pep685TneeeF9uvTszDEXj2f0xD3djmWMSYIVcsM3i7/jor2voqayZuOmD18t+oavP1rGr6b80uV0xpjm2NBKB/fBqx8zacSlVDXYuaemMsSTNz9L2ZpyF9MZY5KRkkIuIpeIiIpIr1Scz6RHLBZj6kl3EovEEr7vz/Oz9INv0xvKGNNibS7kItIPOAjIvGX/zGYt+2QFoarGqyJuEI1E6bllt/QFMsa0SiruyG8HLgVsG/Qs48/z1RtOaah4p63ZZud+aUxkjGmNNhVyEZkAfK+qHybx2bNFpERESkpLS9tyWZMiW++wFUVb9yDR0uB9t9+SG2Zdmf5QxpgWa7aQi8grIrI4wdcE4ErgmmQupKoPqOpIVR1ZVJS+HWlM00SEKTMupWtRVwo6BwkE/fjzfOx99J48/NkddO/d1e2IxpgkNDv9UFXHJTouIkOAAcCHtbu9bA28LyJ7qOqPKU1p2s02O23Nv7+7jwUvLmLtT+sYvM8gG04xJsu0eh65qn4M9N7wWkS+BUaq6uoU5DJp5A/4+cWE3d2OYYxpJZtHbowxWS5lnZ2q2j9V5zLGGJM8uyM3xpgsZ4XcGGOynBVyY4zJcq5sviwipcCy2pe9gGyb6WKZ08Myp4dlTo9UZN5GVRs14rhSyOsFEClJtCt0JrPM6WGZ08Myp0d7ZrahFWOMyXJWyI0xJstlQiF/wO0ArWCZ08Myp4dlTo92y+z6GLkxxpi2yYQ7cmOMMW1ghdwYY7JcRhXybNr7U0SuF5GPRGSRiLwsIlu5nak5InKLiHxem3uGiHRzO1NzROQ4EflEROIikrHTzUTkEBH5QkSWisjlbudJhog8LCKrRGSx21mSJSL9RGSeiHxa+//FhW5nao6I5IvIeyLyYW3m61J9jYwp5Fm49+ctqrqrqg4DXiDJDTZcNhcYrKq7AkuAK1zOk4zFwETgf24HaYqIeIG/AocCOwMnisjO7qZKyiPAIW6HaKEocImq7gyMAs7Lgn/rELC/qg4FhgGHiMioVF4gYwo5Wbb3p6qW1XnZiSzIraovq2q09uU7OJuBZDRV/UxVv3A7RzP2AJaq6teqGgYeBya4nKlZqvo/YI3bOVpCVVeq6vu1fy4HPgP6uptq89RRUfvSX/uV0nqREYW8JXt/ZhIRuUFElgMnkx135HWdCbzodogc0RdYXuf1CjK8uOQCEekPDAfedTlKs0TEKyKLgFXAXFVNaeaUrUfeHBF5BdgiwVuTcfb+PChdWZK1ucyq+pyqTgYmi8gVwPnAtWkNmEBzmWs/MxnnV9Tp6czWlGQyG1OXiBQCTwMXNfjtOCOpagwYVvtcaoaIDFbVlD2bSFshz8a9P5vKnMB0YDYZUMibyywipwPjgQM0Q5oIWvDvnKm+B+pudLp17THTDkTEj1PEp6vqM27naQlVXSci83CeTaSskLs+tKKqH6tqb1XtX7vL0ApgN7eLeHNEZPs6LycAn7uVJVkicgjOc4gjVbXK7Tw5ZAGwvYgMEJEAcALwvMuZcpI4d3sPAZ+p6m1u50mGiBRtmCEmIkHgQFJcL1wv5FnsRhFZLCIf4QwLZfw0KOAeoDMwt3ba5N/cDtQcETlaRFYAewGzRGSO25kaqn2AfD4wB+fh25Oq+om7qZonIo8B84EdRWSFiJzldqYk7A2cCuxf+//wIhE5zO1QzdgSmFdbKxbgjJG/kMoLWIu+McZkObsjN8aYLGeF3BhjspwVcmOMyXJWyI0xJstZITfGmCxnhdwYY7KcFXJjjMly/w+H2dq/Vt5hawAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Train the logistic regression\n",
    "train_data = np.hstack([data, np.ones((data.shape[0],1))])  # add bias\n",
    "n = Neuron(random_state=42, epochs=1000, learning_rate=0.01, batch_size=4)\n",
    "n.fit(train_data, classes)\n",
    "\n",
    "# Visualize results\n",
    "plt.scatter(data[:,0], data[:,1], c=classes)\n",
    "slope = - n._weights[0] / n._weights[1]\n",
    "bias = n._weights[2] / n._weights[1]\n",
    "plt.plot(\n",
    "    [data.min(axis=0)[0], data.max(0)[0]], \n",
    "    [slope * data.min(axis=0)[0] - bias, slope * data.max(axis=0)[0] - bias],\n",
    "    c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is not surprising. In fact, all the algorithms look the same so far! Let's compare them on a bit more complicated example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluation\n",
    "\n",
    "To evaluate the performance, we are going to stick with the MNIST dataset once again. However, to speed up the training process, I will make some modifications. Instead of using all the digits, I will focus on 4 and 9 as they are quite similar and our model can so far predict only two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = sklearn.datasets.fetch_openml('mnist_784', version=1, return_X_y=True, as_frame=False)\n",
    "y = y.astype(int)\n",
    "one_or_seven_indices = np.logical_or(y == 4, y == 9)\n",
    "data = X[one_or_seven_indices].reshape(-1, 784)\n",
    "data[data < 128] = 0\n",
    "data[data > 0] = 1\n",
    "data = np.hstack([data, np.ones((data.shape[0],1))])\n",
    "target = y[one_or_seven_indices].reshape(-1)\n",
    "target[target==4] = 0\n",
    "target[target==9] = 1\n",
    "train_data, test_data, train_target, test_target = sklearn.model_selection.train_test_split(data, target, test_size=0.3, random_state=47)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may notice I modified the values as well. Instead of using the whole greyscale spectrum, I am going to use only black and white pictures. You can see a few examples in the following pictures. The two last lines of the code relabel the targets so class $0$ corresponds to $4$ and class $1$ to class $9$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0bE09AKybvYP9qUcAACa0u70z9QhwbjhDCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABatqYeAM7K3sH+1COcyO72ztQjAABAizOUAAAAtAhKAAAAWo4Nyqq6u6o+V1Vfr6qvVdXbZ5e/p6qeqqr92T9vOPtxAQC7GYB1cZLXUP4syV+MMb5cVS9K8qWqemR23d+MMd53duMBAHPYzQCshWODcoxxJcmV2cc/qqrHk9x11oMBAPPZzQCsixt6DWVVvSzJq5J8YXbR26rqK1X1YFXdvuzhAICj2c0ATOnEQVlVL0zyySTvGGP8MMkHk7w8yU6u/lfS9y/4vktVdbmqLv80z55+YgAgid0MwPROFJRVdSFXF9ZHxxifSpIxxtNjjJ+PMX6R5ENJ7pn3vWOMB8YYF8cYFy/klmXNDQAbzW4GYB2c5F1eK8mHkzw+xvjAocvvPPRlb0ry2PLHAwCuZzcDsC5O8i6vr07yp0m+WlX7s8veleS+qtpJMpI8keStZzAfAPB/2c0ArIWTvMvrvyapOVd9dvnjAADHsZsBWBc39C6vAAAAcI2gBAAAoOUkr6EETmB3e2fqEQAAYKWcoQQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWramHgDOyu72ztQjAADATc0ZSgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgpcYYq7uxqv9M8p0FV78kyfdXNsz54tjM57gs5tjM57gstk7H5lfHGL809RCbwm5uc2zmc1wWc2zmc1wWW6djs3A3rzQoj1JVl8cYF6eeYx05NvM5Los5NvM5Los5NszjfrGYYzOf47KYYzOf47LYeTk2nvIKAABAi6AEAACgZZ2C8oGpB1hjjs18jstijs18jstijg3zuF8s5tjM57gs5tjM57gsdi6Ozdq8hhIAAIDzZZ3OUAIAAHCOCEoAAABa1iIoq+r1VfWNqvpWVb1z6nnWRVU9UVVfrar9qro89TxTqqoHq+qZqnrs0GUvrqpHquqbsz9vn3LGqSw4Nu+pqqdm9539qnrDlDNOoarurqrPVdXXq+prVfX22eUbfb854rhs/H2G59jLi9nNz7GbF7Ob57Ob5zvvu3ny11BW1fOS/EeSP0zyZJIvJrlvjPH1SQdbA1X1RJKLY4x1+QtNJ1NVv5fkx0n+fozxm7PL/jrJD8YY7539wnP7GOMvp5xzCguOzXuS/HiM8b4pZ5tSVd2Z5M4xxper6kVJvpTkjUn+LBt8vzniuLw5G36f4Sp7+Wh283Ps5sXs5vns5vnO+25ehzOU9yT51hjj22OMnyT5RJJ7J56JNTPG+HySH1x38b1JHpp9/FCu/h9v4yw4NhtvjHFljPHl2cc/SvJ4kruy4febI44LXGMvcyJ282J283x283znfTevQ1DeleS7hz5/MufoAJ6xkeSfq+pLVXVp6mHW0B1jjCuzj7+X5I4ph1lDb6uqr8yedrNRTx25XlW9LMmrknwh7jf/47rjkrjPcJW9fDS7+WgeY4/mcXbGbp7vPO7mdQhKFnvNGOO3k/xxkj+fPX2COcbV5277O3Ce88EkL0+yk+RKkvdPOs2EquqFST6Z5B1jjB8evm6T7zdzjov7DJyM3XxCm/wYu4DH2Rm7eb7zupvXISifSnL3oc9fOrts440xnpr9+UyST+fq05B4ztOz55xfe+75MxPPszbGGE+PMX4+xvhFkg9lQ+87VXUhVx+YPzrG+NTs4o2/38w7Lu4zHGIvH8FuPtbGP8Yu4nH2Krt5vvO8m9chKL+Y5BVV9WtV9fwkf5Lk4YlnmlxV3TZ7UW6q6rYkf5TksaO/a+M8nOT+2cf3J/nMhLOslWsPyjNvygbed6qqknw4yeNjjA8cumqj7zeLjov7DIfYywvYzSey0Y+xR/E4azcvct538+Tv8poks7fA/dskz0vy4Bjjr6adaHpV9eu5+l8+k2Qrycc2+bhU1ceTvDbJS5I8neTdSf4xyT8k+ZUk30ny5jHGxr0AfsGxeW2uPj1iJHkiyVsPvTZhI1TVa5L8S5KvJvnF7OJ35eprEjb2fnPEcbkvG36f4Tn28nx28/9mNy9mN89nN8933nfzWgQlAAAA5886POUVAACAc0hQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtW6u8sefXLePW3LbKmwTgnPnv/Fd+Mp6tqefYFHYzAMc5ajevNChvzW35nXrdKm8SgHPmC+PRqUfYKHYzAMc5ajd7yisAAAAtghIAAICWUwVlVb2+qr5RVd+qqncuaygAoMduBmCV2kFZVc9L8ndJ/jjJK5PcV1WvXNZgAMCNsZsBWLXTnKG8J8m3xhjfHmP8JMknkty7nLEAgAa7GYCVOk1Q3pXku4c+f3J2GQAwDbsZgJU68782pKouJbmUJLfmBWd9cwDAMexmAJblNGcon0py96HPXzq77H8ZYzwwxrg4xrh4Ibec4uYAgGPYzQCs1GmC8otJXlFVv1ZVz0/yJ0keXs5YAECD3QzASrWf8jrG+FlVvS3JXpLnJXlwjPG1pU0GANwQuxmAVTvVayjHGJ9N8tklzQIAnJLdDMAqneYprwAAAGwwQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQMvW1AMAnHd7B/srvb3d7Z2V3h4AwCLOUAIAANAiKAEAAGg51VNeq+qJJD9K8vMkPxtjXFzGUABAj90MwCot4zWUvz/G+P4S/j0AwHLYzQCshKe8AgAA0HLaoBxJ/rmqvlRVl5YxEABwKnYzACtz2qe8vmaM8VRV/XKSR6rq38cYnz/8BbNldilJbs0LTnlzAMAx7GYAVuZUZyjHGE/N/nwmyaeT3DPnax4YY1wcY1y8kFtOc3MAwDHsZgBWqR2UVXVbVb3o2sdJ/ijJY8saDAC4MXYzAKt2mqe83pHk01V17d/zsTHGPy1lKgCgw24GYKXaQTnG+HaS31riLADAKdjNAKyavzYEAACAFkEJAABAy2n/2hBgZu9gf6W3t7u9s9Lb2wSr/hkCnEeb8Fhpx8LJOUMJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALRsTT0ArJu9g/2pRwCAM2ffLbYJx2Z3e2fqEbhJOEMJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALRsTT0AnJW9g/2pRziR3e2dqUe46fjZA5vkvDzmsV5Wfb+x825ezlACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC1bUw8AR9k72J96BABYiU3YebvbO1OPcCKb8LNYte4xPS/3mU3mDCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0LI19QBshr2D/alHOHO72ztTj3DTOS/3Gz97YJNswmNe93/jqvfWaX4W52XHdufchPvpunCGEgAAgBZBCQAAQIugBAAAoOXYoKyqB6vqmap67NBlL66qR6rqm7M/bz/bMQGAa+xmANbFSc5QfiTJ66+77J1JHh1jvCLJo7PPAYDV+EjsZgDWwLFBOcb4fJIfXHfxvUkemn38UJI3LncsAGARuxmAddF9DeUdY4wrs4+/l+SOJc0DAPTYzQCs3KnflGeMMZKMRddX1aWqulxVl3+aZ097cwDAMexmAFalG5RPV9WdSTL785lFXzjGeGCMcXGMcfFCbmneHABwDLsZgJXrBuXDSe6ffXx/ks8sZxwAoMluBmDlTvLXhnw8yb8l+Y2qerKq3pLkvUn+sKq+meQPZp8DACtgNwOwLraO+4Ixxn0LrnrdkmcBAE7AbgZgXZz6TXkAAADYTIISAACAlmOf8srNae9gf+oR1tbu9s7UI9x03N+ATXJeHvPsu8XOy8/wNLo//004NtwYZygBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgJatqQfgdPYO9qceYW3tbu9MPQIAwLHO0+8s3Vn9znrzcoYSAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGjZmnoAOCt7B/ut79vd3lnqHDeL7vE8T/zsAQBujDOUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAEDL1tQDwLrZO9ifegQAYAlWvdN3t3dWenuwDpyhBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABatqYegNPZ3d6ZeoQT2TvYn3oENsh5+f8FACfj94j14WfB9ZyhBAAAoEVQAgAA0HJsUFbVg1X1TFU9duiy91TVU1W1P/vnDWc7JgBwjd0MwLo4yRnKjyR5/ZzL/2aMsTP757PLHQsAOMJHYjcDsAaODcoxxueT/GAFswAAJ2A3A7AuTvMayrdV1VdmT7u5fWkTAQBddjMAK9UNyg8meXmSnSRXkrx/0RdW1aWqulxVl3+aZ5s3BwAcw24GYOVaQTnGeHqM8fMxxi+SfCjJPUd87QNjjItjjIsXckt3TgDgCHYzAFNoBWVV3Xno0zcleWzR1wIAZ89uBmAKW8d9QVV9PMlrk7ykqp5M8u4kr62qnSQjyRNJ3np2IwIAh9nNAKyLY4NyjHHfnIs/fAazAAAnYDcDsC5O8y6vAAAAbDBBCQAAQMuxT3mFZdjd3ln5be4d7K/8NlmuKe43AJvCnlzM/oGTc4YSAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGjZmnoAOCu72zsrvb29g/2V3t55suqfBcCUuo959sjy2T9w9pyhBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtW1MPAJwPu9s7U48AwIayg5Zv72B/6hFOxM9+/TlDCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0bE09AKybvYP9qUc4U7vbO1OPAMAcHp+B88gZSgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgZWvqAeCs7B3sTz0CAMCxNuF3lt3tnalH4Iw4QwkAAECLoAQAAKDl2KCsqrur6nNV9fWq+lpVvX12+Yur6pGq+ubsz9vPflwAwG4GYF2c5Azlz5L8xRjjlUl+N8mfV9Urk7wzyaNjjFckeXT2OQBw9uxmANbCsUE5xrgyxvjy7OMfJXk8yV1J7k3y0OzLHkryxjOaEQA4xG4GYF3c0Gsoq+plSV6V5AtJ7hhjXJld9b0kdyx3NADgOHYzAFM6cVBW1QuTfDLJO8YYPzx83RhjJBkLvu9SVV2uqss/zbOnGhYAeI7dDMDUThSUVXUhVxfWR8cYn5pd/HRV3Tm7/s4kz8z73jHGA2OMi2OMixdyyzJmBoCNZzcDsA5O8i6vleTDSR4fY3zg0FUPJ7l/9vH9ST6z/PEAgOvZzQCsi60TfM2rk/xpkq9W1f7ssncleW+Sf6iqtyT5TpI3n8mEAMD17GYA1sKxQTnG+NckteDq1y13HADgOHYzAOviht7lFQAAAK4RlAAAALSc5DWUwBra3d6ZegQA4JC9g/2pRzhzfv/ges5QAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtW1MPAEfZO9ifeoQzt7u9M/UIAMAhfv+Ak3OGEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABo2Zp6AAAAOAt7B/tTj3Cmdrd3ph4BnKEEAACgR1ACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFq2ph4Abha72ztTjwAAN6W9g/2pRzhTfofgPHOGEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoEZQAAAC0bE09ABxld3tn6hEAgIl1fx/YO9hf6e3BJnKGEgAAgBZBCQAAQMuxQVlVd1fV56rq61X1tap6++zy91TVU1W1P/vnDWc/LgBgNwOwLk7yGsqfJfmLMcaXq+pFSb5UVY/MrvubMcb7zm48AGAOuxmAtXBsUI4xriS5Mvv4R1X1eJK7znowAGA+uxmAdXFDr6GsqpcleVWSL8wueltVfaWqHqyq25c9HABwNLsZgCmdOCir6oVJPpnkHWOMHyb5YJKXJ9nJ1f9K+v4F33epqi5X1eWf5tnTTwwAJLGbAZjeiYKyqi7k6sL66BjjU0kyxnh6jPHzMcYvknwoyT3zvneM8cAY4+IY4+KF3LKsuQFgo9nNAKyDk7zLayX5cJLHxxgfOHT5nYe+7E1JHlv+eADA9exmANbFSd7l9dVJ/jTJV6tqf3bZu5LcV1U7SUaSJ5K89QzmAwD+L7sZgLVwknd5/dckNeeqzy5/HADgOHYzAOviht7lFQAAAK4RlAAAALSc5DWUAABw7uxu70w9Atz0nKEEAACgRVACAADQIigBAABoEZQAAAC0CEoAAABaBCUAAAAtghIAAIAWQQkAAECLoAQAAKBFUAIAANAiKAEAAGgRlAAAALQISgAAAFoEJQAAAC2CEgAAgBZBCQAAQIugBAAAoEVQAgAA0CIoAQAAaBGUAAAAtAhKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABoqTHG6m6s6j+TfGfB1S9J8v2VDXO+ODbzOS6LOTbzOS6LrdOx+dUxxi9NPcSmsJvbHJv5HJfFHJv5HJfF1unYLNzNKw3Ko1TV5THGxannWEeOzXyOy2KOzXyOy2KODfO4Xyzm2MznuCzm2MznuCx2Xo6Np7wCAADQIigBAABoWaegfGDqAdaYYzOf47KYYzOf47KYY8M87heLOTbzOS6LOTbzOS6LnYtjszavoQQAAOB8WaczlAAAAJwjaxGUVfX6qvpGVX2rqt459TzroqqeqKqvVtV+VV2eep4pVdWDVfVMVT126LIXV9UjVfXN2Z+3TznjVBYcm/dU1VOz+85+Vb1hyhmnUFV3V9XnqurrVfW1qnr77PKNvt8ccVw2/j7Dc+zlxezm59jNi9nN89nN85333Tz5U16r6nlJ/iPJHyZ5MskXk9w3xvj6pIOtgap6IsnFMca6/P0zk6mq30vy4yR/P8b4zdllf53kB2OM985+4bl9jPGXU845hQXH5j1JfjzGeN+Us02pqu5McucY48tV9aIkX0ryxiR/lg2+3xxxXN6cDb/PcJW9fDS7+Tl282J283x283znfTevwxnKe5J8a4zx7THGT5J8Ism9E8/EmhljfD7JD667+N4kD80+fihX/4+3cRYcm403xrgyxvjy7OMfJXk8yV3Z8PvNEccFrrGXORG7eTG7eT67eb7zvpvXISjvSvLdQ58/mXN0AM/YSPLPVfWlqro09TBr6I4xxpXZx99LcseUw6yht1XVV2ZPu9mop45cr6peluRVSb4Q95v/cd1xSdxnuMpePprdfDSPsUfzODtjN893HnfzOgQli71mjPHbSf44yZ/Pnj7BHOPqc7e9ZfFzPpjk5Ul2klxJ8v5Jp5lQVb0wySeTvGOM8cPD123y/WbOcXGfgZOxm09okx9jF/A4O2M3z3ded/M6BOVTSe4+9PlLZ5dtvDHGU7M/n0ny6Vx9GhLPeXr2nPNrzz1/ZuJ51sYY4+kxxs/HGL9I8qFs6H2nqi7k6gPzR8cYn5pdvPH3m3nHxX2GQ+zlI9jNx9r4x9hFPM5eZTfPd5538zoE5ReTvKKqfq2qnp/kT5I8PPFMk6uq22Yvyk1V3Zbkj5I8dvR3bZyHk9w/+/j+JJ+ZcJa1cu1BeeZN2cD7TlVVkg8neXyM8YFDV230/WbRcXGf4RB7eQG7+UQ2+jH2KB5n7eZFzvtunvxdXpNk9ha4f5vkeUkeHGP81bQTTa+qfj1X/8tnkmwl+dgmH5eq+niS1yZ5SZKnk7w7yT8m+Yckv5LkO0nePMbYuBfALzg2r83Vp0eMJE8keeuh1yZshKp6TZJ/SfLVJL+YXfyuXH1Nwsbeb444Lvdlw+8zPMdens9u/t/s5sXs5vns5vnO+25ei6AEAADg/FmHp7wCAABwDglKAAAAWgQlAAAALYISAACAFkEJAABAi6AEAACgRVACAADQIigBAABo+f9cO6ktqZ+xRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x1152 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(16,16))\n",
    "ax1.imshow(train_data[0, :784].reshape(28, 28))\n",
    "ax2.imshow(train_data[100, :784].reshape(28, 28))\n",
    "ax3.imshow(test_data[0, :784].reshape(28, 28))\n",
    "ax4.imshow(test_data[100, :784].reshape(28, 28))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I will now modify the minibatch version of the code to return the losses and gradients as well. I will use it later to plot the progress. Moreover, I will allow passing test dataset to obtain real performance of the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    def __init__(self, epochs=100, random_state=None, learning_rate=0.001, batch_size=16):\n",
    "        # use epochs instead of iterations\n",
    "        self.epochs = epochs\n",
    "        self.converged = False\n",
    "        self._rand = np.random.RandomState(random_state)\n",
    "        self._weights = None\n",
    "        self._learning_rate = learning_rate\n",
    "        self._batch_size = batch_size\n",
    "        pass\n",
    "    \n",
    "    def _activation(self, vals):  # activation function\n",
    "        return 1 / (1 + np.exp(-vals))\n",
    "    \n",
    "    def fit(self, X, y, Xtest=None, ytest=None):\n",
    "        # Initialize the weights\n",
    "        self.converged = False\n",
    "        self._weights = self._rand.uniform(-2, 2, X.shape[1])\n",
    "        n_data = len(X)\n",
    "        # store gradients and losses\n",
    "        losses = np.zeros((self.epochs,))\n",
    "        gradients = np.zeros((self.epochs, int(np.ceil(X.shape[0] / self._batch_size))))\n",
    "        accuracies = np.zeros((self.epochs,))\n",
    "        # Learning\n",
    "        for epoch in range(self.epochs):\n",
    "            # shuffle the data\n",
    "            permutation = self._rand.permutation(n_data)\n",
    "            # for each batch\n",
    "            for batch_start in range(0, n_data, self._batch_size):\n",
    "                # get batch\n",
    "                batch_data = X[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                batch_target = y[permutation[batch_start:batch_start+self._batch_size]]\n",
    "                # predict the data\n",
    "                prediction = self.predict(batch_data)\n",
    "                # table of gradient for each weights and gradient in the shape (samples,weights)\n",
    "                gradient = np.reshape(-(batch_target - prediction) * (prediction * (1 - prediction)), newshape=(-1,1)) * batch_data\n",
    "                # sum gradient over the samples\n",
    "                op_gradient = self._learning_rate * np.sum(gradient, axis=0)\n",
    "                # store losses and gradients\n",
    "                losses[epoch] += np.sum((batch_target - prediction) ** 2, axis=0)\n",
    "                gradients[epoch, int(batch_start / self._batch_size)] = op_gradient @ op_gradient\n",
    "                # update the weights\n",
    "                self._weights = self._weights - op_gradient\n",
    "                \n",
    "            # compute accuracy on the test set\n",
    "            if Xtest is not None and ytest is not None:\n",
    "                test_prediction = np.where(self.predict(Xtest) < 0.5, 0, 1) \n",
    "                accuracies[epoch] = np.sum(test_prediction == ytest) / len(ytest)\n",
    "                \n",
    "        return losses / X.shape[0], gradients, accuracies\n",
    "    \n",
    "    def predict(self, X):\n",
    "            return self._activation(X @ self._weights)\n",
    "    \n",
    "    def __call__(self, X):\n",
    "        return self.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before I run the evaluation, I have this small helper class, that I am going to use to measure the execution time of individual configurations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TimeMeasure:\n",
    "    def __init__(self, label = ''):\n",
    "        self._label = label\n",
    "    def __enter__(self):\n",
    "        self._starttime = timeit.default_timer()\n",
    "        return self\n",
    "    def __exit__(self, *args):\n",
    "        end = timeit.default_timer()\n",
    "        print(f\"{self._label}{end - self._starttime:.3f}s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try different configurations and let's see how the gradient and loss will evolve.\n",
    "\n",
    "Note that in the standard approach people are using a test (or validation or development) set to measure the real error - generalization error on unseen data. However, in this case, we are not interested in error but rather in the behavior of the model, so it is fine not to use the test set. I will dive deeper into different datasets later on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stochastic gradient descent: 302.348s\n"
     ]
    }
   ],
   "source": [
    "sgd = Neuron(epochs=400, random_state=47, learning_rate=0.001, batch_size=1)\n",
    "with TimeMeasure('Stochastic gradient descent: '):\n",
    "    sgd_loss, sgd_gradient, sgd_acc = sgd.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minibatch of 4 samples: 82.775s\n"
     ]
    }
   ],
   "source": [
    "mbgd_4 = Neuron(epochs=400, random_state=47, learning_rate=0.001, batch_size=4)\n",
    "with TimeMeasure(\"Minibatch of 4 samples: \"):\n",
    "    mbgd_loss_4, mbgd_gradient_4, mbgd_acc_4 = mbgd_4.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minibatch of 32 samples: 25.670s\n"
     ]
    }
   ],
   "source": [
    "mbgd_32 = Neuron(epochs=400, random_state=53, learning_rate=0.001, batch_size=32)\n",
    "with TimeMeasure(\"Minibatch of 32 samples: \"):\n",
    "    mbgd_loss_32, mbgd_gradient_32, mbgd_acc_32 = mbgd_32.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minibatch of 128 samples: 13.856s\n"
     ]
    }
   ],
   "source": [
    "mbgd_128 = Neuron(epochs=400, random_state=53, learning_rate=0.001, batch_size=128)\n",
    "with TimeMeasure(\"Minibatch of 128 samples: \"):\n",
    "    mbgd_loss_128, mbgd_gradient_128, mbgd_acc_128 = mbgd_128.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Batch gradient descent: 27.345s\n"
     ]
    }
   ],
   "source": [
    "bgd = Neuron(epochs=400, random_state=47, learning_rate=0.001, batch_size=train_data.shape[0])\n",
    "with TimeMeasure('Batch gradient descent: '):\n",
    "    bgd_loss, bgd_gradient, bgd_acc = bgd.fit(train_data, train_target, test_data, test_target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(sgd_loss, label=\"Stochastic\", alpha=0.7)\n",
    "plt.plot(bgd_loss, label=\"Batch\", alpha=0.7)\n",
    "plt.plot(mbgd_loss_4, label=\"Minibatch 4\", alpha=0.7)\n",
    "plt.plot(mbgd_loss_32, label=\"Minibatch 32\", alpha=0.7)\n",
    "plt.plot(mbgd_loss_128, label=\"Minibatch 128\", alpha=0.7)\n",
    "\n",
    "plt.yscale('log')\n",
    "ticks = [0.028, 0.04, 0.056, 0.08, 0.112, 0.16, 0.225, 0.32, 0.45, 0.64]\n",
    "plt.yticks(ticks=ticks, labels=ticks)\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.title(\"Loss evaluation\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(sgd_gradient.sum(axis=1), label=\"Stochastic\", alpha=0.7)\n",
    "plt.plot(bgd_gradient.sum(axis=1), label=\"Batch\", alpha=0.7)\n",
    "plt.plot(mbgd_gradient_4.sum(axis=1), label=\"Minibatch 4\", alpha=0.7)\n",
    "plt.plot(mbgd_gradient_32.sum(axis=1), label=\"Minibatch 32\", alpha=0.7)\n",
    "plt.plot(mbgd_gradient_128.sum(axis=1), label=\"Minibatch 128\", alpha=0.7)\n",
    "\n",
    "plt.yscale('log')\n",
    "plt.ylabel(\"Gradient\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.title(\"Gradient evaluation\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.figure(figsize=(12,8))\n",
    "plt.plot(sgd_acc, label=\"Stochastic\", alpha=0.7)\n",
    "plt.plot(bgd_acc, label=\"Batch\", alpha=0.7)\n",
    "plt.plot(mbgd_acc_4, label=\"Minibatch 4\", alpha=0.7)\n",
    "plt.plot(mbgd_acc_32, label=\"Minibatch 32\", alpha=0.7)\n",
    "plt.plot(mbgd_acc_128, label=\"Minibatch 128\", alpha=0.7)\n",
    "\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.xlabel(\"Epoch\")\n",
    "plt.title(\"Test accuracy\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What may we see in the plots? First of all, the stochastic and minibatch with small batch sizes are almost identical - green and blue lines lays on each other, and it is very hard to distinguish them. Small batches behave identical to stochastic gradient descent - however, the running time is over three times faster.\n",
    "\n",
    "The batch version, when we use only a single update in each epoch, has gradients at the beginning much bigger and decreases under minibatch around 170th epoch - it probably converged to better local optima, as we can see in the loss evaluation loss. This is the main advantage of batch gradient descent - it always decreases the loss. This doesn't mean the algorithm is better (it may overfit). From the \"test accuracy\" plot, all the algorithms reached almost the same value.\n",
    "\n",
    "Minibatch versions with bigger batch sizes have faster training with respect to epochs. We can see that in the first 100 epochs in the loss evaluation and test accuracy plots. The speedup is even in real time, as we can see from running times. The minibatch version runs over ten times faster compared to the stochastic version! That is a huge speed up and it is usually a good tradeoff, as we may train the network much faster. Note that although the minibatch with batch size 32 ran the around same amount of time as the batch version, in reality, the difference would be much bigger. MNIST dataset is not very big and it can fit fully into the memory. For bigger datasets, this doesn't need to be the case.\n",
    "\n",
    "The last thing, that we do not see here is, that the minibatch version with a reasonably big batch size is more stable compare to the stochastic one. Its a bit visible in the test accuracy plot, where the minibatch curve is a little bit smoother. We will see this more significantly later on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is one more thing I want to point out. In the implementation, we sum the gradients of examples. It is this line: `op_gradient = self._learning_rate * np.sum(gradient, axis=0)`. There is a discussion, whether we should sum the gradients or mean them. First of all, it doesn't really matter for the functionality, as with proper learning rate, the resulting value is the same. There are two views - if we use the sum, we may increase the batch size and the neural network will train at the same speed (with respect to epochs). In reality, it would be training a bit faster, as there are fewer iterations in the epoch. However, the batch size needs to fit into the memory and we must be careful about the batch size. If we use too big, the gradient can explode and the result will be the same as if we set the learning rate too big. On the contrary, if we mean gradients over examples, with the bigger batch size the network will train at the same speed, but this time with respect to iterations. As there would be fewer iterations in the epoch, the network would need more epochs to train into the same level, and thus it needs more time. On the other hand, there is no problem with the gradient.\n",
    "\n",
    "Once more, the operation doesn't really matter, as with properly scaled learning rate the resulting gradient values will be same. Both Pytorch and TensorFlow uses sum, so I will stick to it as well."
   ]
  }
 ],
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