03 - Fully Connected Feedforward Networks with TensorFlow.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a href=\"https://colab.research.google.com/github/fmottes/unito-neural-networks/blob/master/03%20-%20Fully%20Connected%20Feedforward%20Networks%20with%20TensorFlow.ipynb\">\n",
    "      <img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\" style=\"width:175px;\"/>\n",
    "    </a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center> **Neural Networks** (MFN0824) </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lectures: _Dr. Matteo Osella_\n",
    "### Notebooks: _Francesco Mottes_\n",
    "<br>\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reference book for the practical part of this course is:\n",
    "- *Hands-on Machine Learning with Scikit-Learn, Keras and Tensorflow - A. Géron*\n",
    "\n",
    "There is also a [github page](https://github.com/ageron/handson-ml2) where you can find some notebooks with the code from the book, a good place to start if you want to look into more advanced topics.\n",
    "\n",
    "**NOTE:** You can easily (and legally) find online a raw and unedited version of the second edition of the book, released by the author before the book was finished. Be advised that, besides not being the revised version, **it is not even the whole book**.\n",
    "\n",
    "If you want to play with a dense feedforward artificial neural network without writing any code and with a nice visualization, you can try out the Tensorflow Playground (link in the section below)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "- Numpy Docs: https://numpy.org/doc/1.18/\n",
    "- Matplotlib Docs: https://matplotlib.org/\n",
    "- Scikit-learn Docs: https://scikit-learn.org/\n",
    "- Keras Docs: https://keras.io/api/\n",
    "- Tensorflow Playground: https://playground.tensorflow.org/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <center> **03 - Fully Connected Feedforward Networks with TensorFlow** </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we will implement a simple dense feedforward ANN using the Keras API, that comes embedded into Tensorflow from version 2.0. We will train the network to recognize hand-written digits found in the famous MNIST dataset. Classification of the less trivial FMNIST dataset will be left as an exercise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First things first, we import the libraries that we will need:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#standard imports\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#import tensorflow and keras\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "\n",
    "\n",
    "#function for fast generation of training and test set from data\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1.0\n",
      "2.2.4-tf\n"
     ]
    }
   ],
   "source": [
    "# check tensorflow and keras versions\n",
    "print(tf.__version__)\n",
    "print(keras.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center> **Loading MNIST** </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some small and simple datasets come with the keras library and can be uploaded into a project almost without any effort. You can find a list of the directly uploadable datasets in the Keras docs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from tensorflow.keras.datasets import mnist\n",
    "\n",
    "#load actual data\n",
    "(X_train, y_train), (X_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The MNIST dataset contains hand-written, single digits in the range 0-9, together with their correct classification. Digits are stored as grayscale images with size 28x28 pixels, represented as Numpy arrays of shape (28,28) and entries in the range 0-255.\n",
    "\n",
    "As for datasets loaded through scikit-learn, also in this case a division into training set and test set is already provided: 60000 images are loaded as training samples and 10000 as test sample. Note that, in order to have a sound machine learning pipeline, we will also need to build ourselves a validation set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAINING SET:\t (60000, 28, 28)\n",
      "TEST SET:\t (10000, 28, 28)\n"
     ]
    }
   ],
   "source": [
    "#check shape of the training set\n",
    "print('TRAINING SET:\\t',X_train.shape)\n",
    "\n",
    "#check shape of the test set\n",
    "print('TEST SET:\\t', X_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#show first image contained in the training data, with its label\n",
    "\n",
    "plt.imshow(X_train[0], cmap='gray')\n",
    "plt.title('NUMBER {}'.format(y_train[0]), fontsize=15)\n",
    "plt.axis('off'); #do not show spines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QWf7/79L3d4Ly+bv2/OAHPwhyJ598souPOOKIILfbbru5uEWLFkEuvlXvt++7774g508pzDKubAIAACAZBpsAAABIhsEmAAAAkmkSczZj48ePd/HcuXODnD/vT5J+/vOfu/jKK68Mch06dHDxFVdcEeTee++9evcTxfXp0ydod+nSxcXxnJa//vWvFelTOfx5mnG/Z82aVenuNBr+3Mf4+3bbbbe5ON4+rhh/KZp4zubq1atdvHz58iD36quvuvjuu+8OcvEWqP6c4Q8//DDILViwwMXxVqlz5swp2ndkR7lbUr799ttBO64PZIO/BaUkLVq0yMVt27YNcv/3f//n4rosl/j++++7eMmSJUFuyy23DNoff/yxix999NGSz5ElXNkEAABAMgw2AQAAkAyDTQAAACTTJOds+mbPnh20jz322KB9+OGHuzhek/OMM85w8Y477hjkevXq1VBdRAHxnDZ/7bOPPvooyD3wwAMV6VMhG2ywgYtHjBhR8HlTpkwJ2sOHD0/VpUbP3yJu3rx5QW6//fYr65jz58938YQJE4Lca6+95uJ//OMfZR0/Nnjw4KDtz/eK5++h8Rg2bJiL67J2brE1OJEd8Xax/lqqjz32WJDz1/yN1/yeOHGii++5554g9+mnn7p43LhxQS6esxnnGyOubAIAACAZBpsAAABIpsnfRo/Fl8fvvfdeF48ePTrI+dvJdevWLcj16NHDxdOmTWu4DqIk/rZ/UuW3E/Vvm0vSxRdf7OKhQ4cGOX+5m+uvvz7IffHFFwl61/RcffXV1e5CWfyl1WJ1WTIH1eUvuyZJBx10UEmv82+jStLrr7/eYH1C5fjbzsZLH5XLH1N07949yMVTM5rClBuubAIAACAZBpsAAABIhsEmAAAAkmnyczb97ekk6Ze//GXQ7tq1q4v9OZoxf7s6SXrmmWcaoHcoVzW2p/TnbcXzMo877jgXx/O0jjnmmLQdQ6Pkb6uLbJs8eXLQ3nTTTQs+1182a9CgQam6hEbOX9ovnqMZb3vJ0kcAAABAEQw2AQAAkEyTuI2+0047Be2zzz7bxUcffXSQ22KLLUo+7tdff+3ieGmduuwagfIYYwq2/R0dJOm8885r8PP/+te/Dtq/+93vXNyqVasgd//997t4wIABDd4XANXTpk2boF3s8/+WW25xMUuboZAnnnii2l2oKK5sAgAAIBkGmwAAAEiGwSYAAACSaTRzNuO5lv369XOxP0dTkjp27FjWOV588cWgfcUVV7i4Gkvt1Lp4+Qe/HdfDH//4RxfffffdQe6TTz5x8T777BPk+vfv7+LOnTsHuW222SZoz58/38XxfBt/nhZQiD/vuFOnTkHOXzIH1TdmzBgXN2tW+nWZ5557LkV30MQcfPDB1e5CRXFlEwAAAMkw2AQAAEAymbqN3q5du6C96667uvimm24KcjvvvHNZ53jhhReC9rXXXuvieOcXljfKrnXWWSdon3XWWS6Od+xZsmSJi3fccceSzxHfDps6daqLL7nkkpKPA3zLnwpSl1uzSM/fIUySevbs6eL4Z8GqVatcfPPNNwe5Dz/8MEHv0NRst9121e5CRfFpBwAAgGQYbAIAACAZBpsAAABIpuJzNjfbbLOgffvtt7s4njNT7pwGf67d9ddfH+TiJWtWrFhR1jmQ3vPPPx+0Z86c6eKuXbsWfF28LFI8F9jnL4s0bty4IJdiC0zgW/vuu2/Qvueee6rTEUiSWrduHbSLbW383nvvuXjIkCHJ+oSma/r06S6O5283xb8X4comAAAAkmGwCQAAgGSS3Eb/6U9/GrSHDh3q4p/85CdBbuutty7rHMuXL3exv3uMJF155ZUuXrZsWVnHR/UtWLAgaB999NEuPuOMM4LcxRdfXNIxR40aFbRvvfVWF7/55pt17SJQJ/4OQgBq1+zZs108d+7cIBdPIdx+++1dvGjRorQdS4QrmwAAAEiGwSYAAACSYbAJAACAZJLM2TzqqKOKtgt59dVXg/Zjjz3m4tWrVwc5f0mjxYsX17WLaIQWLlzo4hEjRgS5uA1kwaRJk4J23759q9QTrM2cOXOCtr+E3gEHHFDp7qCG+H9nIkmjR48O2ldccYWLzznnnCAXj5uyiiubAAAASIbBJgAAAJIx1trCSWMKJ1FR1tpMr5lCrWRHlmuFOsmOLNeJRK1kSZZrpSnUScuWLYP2gw8+GLR79uzp4kceeSTInXzyyS6u9lKPxeqEK5sAAABIhsEmAAAAkmGwCQAAgGSYs9lIZHnOjEStZEmWa4U6yY4s14lErWRJlmulKdZJPIfTX/rozDPPDHK77767i6u9DBJzNgEAAFAVDDYBAACQDLfRG4ks38aQqJUsyXKtUCfZkeU6kaiVLMlyrVAn2cFtdAAAAFQFg00AAAAkw2ATAAAAyRSdswkAAADUB1c2AQAAkAyDTQAAACTDYBMAAADJMNgEAABAMgw2AQAAkEzSwaYxZpoxxhpjukWPv2mMGZSPexhjVq/htcHjxph78se6IHreVsaY1f4uAsaYEfnHvsh/LTTG3G6MaR4d7yvvOd9+9VnDMZYaY97OP1ZwhXxjTG9jzBRjzMfGmM+MMdONMf9Wxreu5tRgrWxtjJlojJmX7+tJZXzbak4N1sm/GWNeMsZ8aoz5PB8fXca3rubUYK3wmVKGWquTqF9n5vt7cYnfrrJV4srmJ5KuK/XNr8Vrkk6LHjtF0htreO40a20La20LSXtL2lfS76Ln/Onb53hfj8XHkNRS0kBJF+T/W8imkm6UtIOktpL+LGmSMeaHJb6/WldLtfKNpMmSTpC0oOR3Bam26uR1SUdJaiOptaTzJd1njNmlxPdX62qpVvhMKV8t1YkkyRjTQdJvJP1vSe+qniox2LxT0jaS+jXAsZ6T9JUxpock5Qvj1Pw5CrLWvifpCUm7lXNSmzNd0ivKFUSh591vrR1vrV1srV1trb1V0opir0GglmplobX2ZmvtDElfl3OuGlZLdfKRtXaezS2IbJQbUDRT7hdarF0t1QqfKeWrmTrx3CXpIkmflnO+uqrEYHOZpEskXWmM2aABjjda0un5uJekzyXNLPaC/Aj+UEnPlnNCY0wzY8zPlCuC1+vwut2VuyIxu5zz1qCarRXUSc3ViTFmsaSVkqZLekG5K1hYu5qrFZSlpurEGHOGpOXW2gfKOVc5KvUHQmMkLZV0XgMca6ykw4wxbSQNVuHfFrobYxYbY5ZIeid//ruj5/TPP8f/ah8fQ7mrk1Py7+PWUjppjPmBpIckXWOtnVvqm0Pt1QrKUlN1Yq1tLamFcrfUH5f0vfljKKimagVlq4k6yb/2YklnlvPGylWRwaa19mvl5hFcmP/m+76S1MwYs070+Hr5XHysTyRNkjREUk9J9xc47dPW2tbW2pbKzWX4H0kzot9a7s0/x/+aHx9D0iaSLpTUQ9JGa3u/xpitJE1V7urD8LU9H9+ptVpBeWqxTqy1K621EyR11/fnhKGAWqwV1F0N1cloSZfnb9tXTMWWPrLWTlLuG3lJlHpHublI20WP7yDp7QKHu0PSMEkTrLWLSzj3UuV+s+ikMuZDWGtXWWtHSlok6dJizzXGdFTuVtcka+3Z+blWqINaqRXUTw3XybqSdqzrOWtZDdcK6qBG6qSXctMFPjbGfCxpf0nDjTHT63rOuqj0OptDlbuk3PbbB/Kj679Lut4Ys4XJ6aLcbwT3FDjONOW+YSVdNTTGbKTcBN1lkt4qt/PKXXo+Kz+3Yk3n2Vm5+Rb/Za0dUo/zoInXSv5cGxpjNlTuQ2y9fHvdepyzFjXpOjHGHGOM+bExZt18fZwu6UDl/pAAddOkayV/Lj5T6q+p18kPJXWW1CX/9aKkmyX9sh7nXKuKDjattS9LGqfc5WLfCZI+UG7i++eS/ku5OQc3FDiOtdY+Za1dWOR0PUx+TSpJ70naU1Lv6DeMgeb761edVaT/05W7alnot4ZhkraWdH50zBOL9BNrUAO1IuXm2KyQ1F65eTorlPugQIlqoE62lPSIpMWS3lduCZV+1toni/QTa1ADtSLxmVJvTb1OrLUL/C/l/vBwibX2wyL9rDfDXV4AAACkwnaVAAAASIbBJgAAAJJhsAkAAIBkGGwCAAAgmaJLIhhj+OuhjLDWmmr3oRhqJTuyXCvUSXZkuU4kaiVLslwr1El2FKsTrmwCAAAgGQabAAAASIbBJgAAAJJhsAkAAIBkGGwCAAAgGQabAAAASIbBJgAAAJJhsAkAAIBkGGwCAAAgGQabAAAASIbBJgAAAJJhsAkAAIBkGGwCAAAgmXWr3QGgkkaNGhW0zz33XBfPnj07yPXp0ydoz5s3L13HAACokKeeesrFxpggd+CBBzb4+biyCQAAgGQYbAIAACAZBpsAAABIpubmbG6yySZBu0WLFi4+7LDDglzbtm1dfMMNNwS5lStXJugdUujYsaOLTzrppCD3zTffuHiXXXYJcjvvvHPQZs5m09apUycXr7feekGuW7duLr7llluCnF9D9TFx4kQXH3/88UFu1apVDXIONLy4Vvbbbz8XX3nllUFu//33r0ifgNh//Md/BG2/TseOHZv8/FzZBAAAQDIMNgEAAJBMk7yN7t82HTZsWJDbd999g/Zuu+1W0jG33HLLoO0vmYNsW7RokYufeeaZIHfEEUdUujuooh/96EcuHjRoUJDr27evi5s1C38P32qrrVwc3za31jZI3/xavO2224Lc+eef7+IlS5Y0yPnQMFq1ahW0p06d6uIPPvggyG2xxRZBO84DDemqq65y8a9+9asg99VXX7nYXwYpFa5sAgAAIBkGmwAAAEiGwSYAAACSabRzNv1lafz5TJJ04oknurh58+ZBLt6W6d1333Xx0qVLg5y/FM6xxx4b5PzlT+bMmVNqt1EFy5YtczHLF9W2kSNHurh3795V7ElxAwYMCNp33XWXi2fMmFHp7qBM8RxN5myikvbZZx8Xx0t0Pfvssy5+8MEHk/eFK5sAAABIhsEmAAAAksn0bXR/SYmrr746yB133HEujncFKmbu3LlB++CDD3ZxfJnZvz2++eabB7m4jexq3bq1izt37lzFnqDannzySRcXu43+0UcfBW3/Nna8LFKxHYT8XTokqXv37iX1E01DPG0LtcvfhUySLrroIhf369cvyH366adlnSM+jr+041tvvRXkhgwZUtY5ysWVTQAAACTDYBMAAADJMNgEAABAMpmes3nUUUe5+LTTTivrGPE8hV69egVtf+mjHXbYoaxzINs22mgjF7dv377k13Xt2jVo+3N4WUKpcbr11ltdPGHChILP87dyk8pfoqZly5ZBe/bs2S72t8CMxX178cUXyzo/qiveynTDDTesUk9QbXfccUfQ3nHHHV286667Bjl/WaK6uPDCC4N2mzZtXHz66acHuZdffrmsc5SLK5sAAABIhsEmAAAAksn0bfS+ffuW9Lx33nknaM+cOdPFw4YNC3L+bfOYv2MQmo7333/fxffcc0+QGzFiRMHXxbnFixe7+KabbmqIrqHCVq9e7eJinwUNxV9aTZI23XTTkl63YMGCoL1y5coG6xOqZ++99w7a//jHP6rUE1Ta8uXLg7Y/xaI+0yu6dOni4g4dOgQ5f1m2ak/h4MomAAAAkmGwCQAAgGQYbAIAACCZTM/Z9P9Uf/DgwUFu8uTJLn7zzTeDXLzVXKnatWtX1uvQeFx22WVBu9icTaAcxx9/vIvj5UaaN29e0jEuueSSBu0T0vHnAUvS559/7mJ/y2VJ2n777SvSJ2SD//Pmxz/+cZB77bXXXFyXZYg23njjoO3/XYq/zJ8Uzgl+6KGHSj5HClzZBAAAQDIMNgEAAJBMpm+j+0vWVOJ257777pv8HMiWZs2++33LXyYCKOTEE08M2r/97W+Dtr8T2XrrrVfycWfNmuXieAcjZJe/JJokTZ8+3cV9+vSpdHdQRT/84Q+Dtj+NJp5ucfbZZ7t40aJFJZ/jhhtuCNr+EpH+mEmS9t9//5KPmxpXNgEAAJAMg00AAAAkw2ATAAAAyWR6zma5zj33XBfHywQUEy9N4HvuueeC9vPPP1/3jiFz/Hma/vZhaJo6duzo4v79+we5nsfeJMAAAAiFSURBVD17lnSMAw44IGjXpW6WLFni4niu5+OPP+7iFStWlHxMANWz2267uXj8+PFBbvPNN3fxjTfeGOSefvrpks8xZMgQFw8aNKjg86644oqSj1lpXNkEAABAMgw2AQAAkEyjuY0er4y/6667uvj3v/99kOvdu3fB4/hL3UjFl7vxlxE4+eSTg9zXX39duLMAMsG/xSVJf/3rX13cvn37SncnWBbnjjvuqPj5UV1t2rSpdhdQhnXX/W6odNJJJwW5u+66y8XFxhfx0orDhw93cbyc0WabbRa0/eWNjDFBbuzYsS6+/fbb1/wGMoArmwAAAEiGwSYAAACSYbAJAACAZDI1ZzPe2m2PPfZw8cMPPxzkttxySxfHy4T4cy3jJYoOOeSQoB3PBfX58zSOPvroIDdq1CgXr1q1quAxAGSHP98pnvtUqrrM+4752xceeuihQW7SpEll9QeNxxFHHFHtLqAMxx9/vItHjx4d5Pylz+LPgjfffNPFe++9d5Dz20ceeWSQ23rrrYO2P96Jt7Y85ZRTivY9K7iyCQAAgGQYbAIAACAZBpsAAABIpupzNtdff30Xx/MpH3nkkYKvu/TSS108ZcqUIDdjxgwXx+tVxc+N1+HztW3b1sUjR44McvPnz3fxhAkTgtzKlSsLHhPZ4s+/W9vcu27durn4pptuStYnNJzZs2cH7R49erg4Xi/viSeecPGXX35Z9jlPPfVUF59zzjllHweN09SpU13sz9FF43HccccF7TFjxrj4q6++CnKLFy928QknnBDkPvvsMxdff/31Qa579+4ujudzxvPJ/Xmh/haYkvTuu++62P98k6S33npLWcGVTQAAACTDYBMAAADJGP/y7PeSxhROlile3ugPf/iDi4cOHVrwdfGyIP3793exfxlbCm9/P/7440Fuzz33DNr+skXXXHNNkPNvscdLE/j+/ve/B+2rr77axf5l9NisWbMK5mLW2vLWaamQFLVSCf62o8X+X4jtvvvuQfvVV19tsD7VV5ZrpbHWSV20atXKxZ988knB5x1++OFBu9JLH2W5TqTGWyvHHHOMi//yl78EuXiZPn/b5Xnz5qXtWD1kuVZS1Ek83a5Dhw4uvvzyy4Ocf4u9GP/fWgq3loy3six2Gz325z//2cUDBgwoqS+pFKsTrmwCAAAgGQabAAAASIbBJgAAAJKpyNJH66yzjosvu+yyIDdkyBAXL1u2LMj99re/dfG4ceOCnD9PM142wF+Wxt/yUpLmzp0btM8880wX+0tWSFLLli1dvN9++wW5E0880cXxFmRPPvmkCvGXKdh2220LPg+Vcdttt7n4jDPOKPl1gwcPDtrnn39+g/UJjdvBBx9c7S6gilavXl0wF8/F22CDDVJ3B2WYOHFi0PaXYfR/htdFvGRRsWUX+/XrF7TjJdx8CxYsKKs/lcaVTQAAACTDYBMAAADJVOQ2un/L0b9tLknLly93cXwbc/LkyS7eZ599gtzJJ5/s4kMPPTTINW/e3MX+0krS95cpKHZJfMmSJS7+7//+7yDnt+NL3vEuAr5f//rXBXOovDlz5lS7C6ineDm1gw46yMXxEibx0jMNwf8skqRRo0Y1+DnQePi3YOPPl5133jlo+9NvzjrrrLQdQ8ka6v9hfxm0vn37Bjl/ml6808+DDz7YIOfPEq5sAgAAIBkGmwAAAEiGwSYAAACSqch2lQsXLnSxv5WkJK1cudLF8fyWjTfe2MU77LBDyecbMWKEi0eOHBnk/O0JG5MsbxcmNd6t5XxvvPFG0N5+++0LPrdZs/D3NL8+4/k3lZblWmmoOjnggANcfNFFFwW5Xr16uTheXqzcZUs222wzF/fu3TvI3XjjjUF7k002KXgcf85ovGRavPRaalmuE6lpfKb853/+Z9CO5/e2a9fOxV9++WVF+lSOLNdKlutk+PDhLo6XfVy0aJGLu3btGuQay3JGMbarBAAAQFUw2AQAAEAyFVn66IMPPnBxfBvd30Ghc+fOBY/x+OOPB+1nnnnGxRMmTAhy77zzjosb621zVN4rr7wStLfbbruCz/3mm29SdwdF+LuEFduJ44ILLgjaS5cuLet8/q35PffcM8gVm4o0bdq0oH3rrbe6uNK3zVF9ca2sWrWqSj1BCh06dAjap512movjf/s77rjDxY31tnldcGUTAAAAyTDYBAAAQDIMNgEAAJBMReZsduvWzcW/+MUvgpw//+mjjz4KcnfffbeLP/vssyDHXBc0NH8OjSQdfvjhVeoJGsqZZ56Z/Bzx59ajjz7q4vPOOy/IZXl5G6Tnb1EoSUceeaSLx48fX+nuoIE9+eSTQdufw3nfffcFud///vcV6VNWcGUTAAAAyTDYBAAAQDIV2UEI9ZflHRykplEr8bIVjz32WNDeZZddXGxM+M/RqVMnF7ODUGENVSddunRx8TnnnBPkBg4cWO/jx/+Gy5cvd/H06dODXDz9Yvbs2fU+fyVkuU6kpvGZ8v777wftTTfdNGjvscceLo530MuSLNdKlurE3zFICncN6tu3b5BritMm2EEIAAAAVcFgEwAAAMkw2AQAAEAyzNlsJLI8Z0aiVrIky7WSok78LW8ladCgQS6+/PLLg5w/Zy7e5tZftmTixIlBzt9yt6nIcp1ITeMzZdy4cUHbn/ctSUcccYSL582bV5E+lSPLtdIU6qSpYM4mAAAAqoLBJgAAAJLhNnojkeXbGBK1kiVZrhXqJDuyXCcStZIlWa4V6iQ7uI0OAACAqmCwCQAAgGQYbAIAACAZBpsAAABIhsEmAAAAkmGwCQAAgGQYbAIAACAZBpsAAABIhsEmAAAAkmGwCQAAgGSKblcJAAAA1AdXNgEAAJAMg00AAAAkw2ATAAAAyTDYBAAAQDIMNgEAAJAMg00AAAAk8/8BLiR+Ks3UUdcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show the first 10 images in the training set\n",
    "\n",
    "fig, axs = plt.subplots(2,5,figsize=(12,4))\n",
    "\n",
    "for i in range(10):\n",
    "    \n",
    "    ax = axs.ravel()[i]\n",
    "    \n",
    "    ax.imshow(X_train[i], cmap='gray')\n",
    "    ax.set_title('NUMBER {}'.format(y_train[i]), fontsize=13)\n",
    "    ax.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the classes in the dataset are not balanced. This is usually something you want to take into account when training a machine learning algorithm, either by balancing classes by eliminating some samples from the most populated ones or by means of more sophisticated techniques. Since this problem is not a real issue for this dataset and is not an argument strictly connected with ANNs we will not address it here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "plt.hlines(6000, -1, 10, linestyles='--')\n",
    "\n",
    "plt.hist(y_train, bins=np.linspace(-.5,9.5,11), rwidth=.8)\n",
    "plt.xticks(range(10));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now need to split the training set into training and validation set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "val_size = .1 #use 6000 samples as validation set\n",
    "\n",
    "#generate training and test set with stratification\n",
    "#this means that we will find the same proportion of classes bot in the validation and in the training set\n",
    "X_train, X_val, y_train, y_val = train_test_split(X_train, y_train, test_size=val_size, stratify=y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally transform the data in a format more suitable for use in training a neural network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rescale pixel values to the range (0,1)\n",
    "X_train = X_train/255\n",
    "X_val = X_val/255\n",
    "X_test = X_test/255"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "#transform integer label into one-hot encodings\n",
    "n_classes=10\n",
    "\n",
    "y_train_cat = keras.utils.to_categorical(y_train, n_classes)\n",
    "y_val_cat = keras.utils.to_categorical(y_val, n_classes)\n",
    "y_test_cat = keras.utils.to_categorical(y_test, n_classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center> **ANNs with the Keras Sequential API** </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keras provides a simple way to build ANNs - as the one shown below - composed only of layers stacked one on top of the other. This is done by passing a list of pre-implemented layer types to the Sequential API. Each layer object manages its own weight matrix, connecting its neurons to their inputs, and its own bias vector, one per neuron."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![A Dense Feed-Forward Artificial Neural Network](img/FF-ANN.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** Unlike most of the python code that we have seen up to now, training a neural network happens in two distinct phases. \n",
    "* The first is a DECLARATIVE one, you have to tell Keras what is the design of your neural network: how many layers do you want? how big each layer will be? which type of activation function do you want? what loss function do you want to minimize? which optimizer do you want to use? what metric you want to keep track of? In this phase no actual training happens quite yet.\n",
    "* The second phase is when you actually train your model. You need to specify some additional parameters like number of epochs, batch size, training and validation data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#a few more imports for readability\n",
    "\n",
    "#import backbone of the model\n",
    "from tensorflow.keras.models import Sequential\n",
    "\n",
    "#import the two types of layes we need\n",
    "from tensorflow.keras.layers import Flatten, Dense"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now create a model with a single hidden layer of 15 neurons, which takes as input the MNIST data and outputs the probability of belonging to one of the 10 classes. There are actually a few different but equivalent ways for creating a Sequential model. Choose the one you like the most!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#very important! do it before you instantiate a brand new model\n",
    "#cleares the backend of all the previous instances of the models \n",
    "#which might interfere with the new instance\n",
    "keras.backend.clear_session()\n",
    "\n",
    "model = Sequential()\n",
    "model.add(Flatten(input_shape=(28,28))) #flattens 2d input image into flat array\n",
    "model.add(Dense(15, activation='tanh')) #15 hidden units with tanh activation\n",
    "model.add(Dense(n_classes, activation='softmax')) #output layer with softmax activations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#alternative way\n",
    "keras.backend.clear_session()\n",
    "\n",
    "model = Sequential([\n",
    "    Flatten(input_shape=(28,28)),\n",
    "    Dense(15, activation='tanh'),\n",
    "    Dense(n_classes, activation='softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a few of parameters that can be chosen for defining a layer, besides activation and number of neurons. An important one is the initialization strategy for the weights. The default is the so-called \"Glorot-uniform\" initialization, but there a few different ones with their pros and cons. A list of initializers with a brief description and references can be found [here](https://keras.io/api/layers/initializers/). Biases are initialized to 0 by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#explicit initialization strategy, equivalent to the preceding cell\n",
    "keras.backend.clear_session()\n",
    "\n",
    "model = Sequential([\n",
    "    Flatten(input_shape=(28,28)),\n",
    "    Dense(15, activation='tanh', kernel_initializer='glorot_uniform', bias_initializer='zeros'),\n",
    "    Dense(n_classes, activation='softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "flatten_1 (Flatten)          (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 15)                11775     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                160       \n",
      "=================================================================\n",
      "Total params: 11,935\n",
      "Trainable params: 11,935\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "#we can now print a summary of the model we created\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the number of parameters shown for the first layer corresponds to 784\\*15=11760 weights + 15 biases, while in the last layer we have 15\\*10+10 parameters.\n",
    "\n",
    "Now we need to specify the optimizer, the loss function and possibly accuracy metrics to keep track of."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(\n",
    "    loss='categorical_crossentropy',\n",
    "    optimizer='sgd',\n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have chosen to minimize the categorical cross-entropy loss with plain (Mini-batch) Stochastic Gradient Descent, and keep track of the accuracy metric (the loss metric is included by default). We can also pass as parameters, instead of strings, functions coming from the Keras internal libraries. Further information can be found in the Keras docs, in the sections [Losses](https://keras.io/api/losses/), [Optimizers](https://keras.io/api/optimizers/) and [Metrics](https://keras.io/api/metrics/). Alternatively, one can also pass custom functions that implement algorithms different from the ones present in keras, as long as their implementation is compatible with the rest of the API (see docs).\n",
    "\n",
    "It is often useful to pass functions, instead of strings. In this case we can also control the parameters of the object that we pass, instead of getting the default parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#compilation equivalent to the one above, only with different learning rate\n",
    "\n",
    "model.compile(\n",
    "    loss='categorical_crossentropy',\n",
    "    optimizer=keras.optimizers.SGD(learning_rate=.02),\n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The network is fully initialized now! We can, for example, look at how the weights are initialized:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(784, 15)\n",
      "(15,)\n",
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "#returns a list with the weight matrices and bias vectors, from the input to the output layer\n",
    "weights = model.get_weights()\n",
    "\n",
    "print(weights[0].shape) #shape of the first weight matrix\n",
    "print(weights[1].shape) #shape of the first bias vector\n",
    "print(weights[1]) #initialized entries of the first bias vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<keras.layers.core.Flatten at 0x7f426c6b4250>,\n",
       " <keras.layers.core.Dense at 0x7f426bae4a90>,\n",
       " <keras.layers.core.Dense at 0x7f426fb08ad0>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.layers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(15, 10)\n",
      "(10,)\n"
     ]
    }
   ],
   "source": [
    "#you can also get the weights of a specific layer\n",
    "\n",
    "output_layer = model.layers[-1]\n",
    "\n",
    "print(output_layer.get_weights()[0].shape) #weights\n",
    "print(output_layer.get_weights()[1].shape) #biases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check the weights distribution in the first layer. From the docs:\n",
    "\n",
    ">(Glorot uniform) ...samples from a uniform distribution within [-limit, limit], where limit = sqrt(6 / (fan_in + fan_out)) (fan_in is the number of input units in the weight tensor and fan_out is the number of output units)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7f41c0139fd0>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#weinght of the first layer\n",
    "w0 = model.layers[1].get_weights()[0]\n",
    "\n",
    "#histogram of the weights\n",
    "plt.hist(w0.flatten());\n",
    "\n",
    "#plot the theoretical boundaries\n",
    "limit = np.sqrt(6/(w0.shape[0]+w0.shape[1]))\n",
    "\n",
    "plt.vlines(limit, 0, 1200, linestyle='--')\n",
    "plt.vlines(-limit, 0, 1200,  linestyle='--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to train the network on the MNIST dataset.\n",
    "\n",
    "Training data are automatically shuffled at the beginning of each epoch, then divided in batches of the requested size. The algorithm then iterates through the batches and updates the weights accordingly, until all the batches are used and the epoch is declared finished."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define some hyperparameters\n",
    "\n",
    "epochs = 30\n",
    "batch_size = 128"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 54000 samples, validate on 6000 samples\n",
      "Epoch 1/30\n",
      "54000/54000 [==============================] - 2s 36us/step - loss: 1.4517 - accuracy: 0.6324 - val_loss: 1.0740 - val_accuracy: 0.7492\n",
      "Epoch 2/30\n",
      "54000/54000 [==============================] - 2s 29us/step - loss: 0.9026 - accuracy: 0.7973 - val_loss: 0.7965 - val_accuracy: 0.8123\n",
      "Epoch 3/30\n",
      "54000/54000 [==============================] - 2s 34us/step - loss: 0.7081 - accuracy: 0.8419 - val_loss: 0.6591 - val_accuracy: 0.8407\n",
      "Epoch 4/30\n",
      "54000/54000 [==============================] - 2s 36us/step - loss: 0.6008 - accuracy: 0.8618 - val_loss: 0.5755 - val_accuracy: 0.8605\n",
      "Epoch 5/30\n",
      "54000/54000 [==============================] - 1s 25us/step - loss: 0.5321 - accuracy: 0.8736 - val_loss: 0.5196 - val_accuracy: 0.8702\n",
      "Epoch 6/30\n",
      "54000/54000 [==============================] - 1s 23us/step - loss: 0.4845 - accuracy: 0.8814 - val_loss: 0.4792 - val_accuracy: 0.8798\n",
      "Epoch 7/30\n",
      "54000/54000 [==============================] - 1s 21us/step - loss: 0.4500 - accuracy: 0.8880 - val_loss: 0.4495 - val_accuracy: 0.8855\n",
      "Epoch 8/30\n",
      "54000/54000 [==============================] - 1s 24us/step - loss: 0.4239 - accuracy: 0.8928 - val_loss: 0.4264 - val_accuracy: 0.8892\n",
      "Epoch 9/30\n",
      "54000/54000 [==============================] - 1s 24us/step - loss: 0.4033 - accuracy: 0.8961 - val_loss: 0.4083 - val_accuracy: 0.8933\n",
      "Epoch 10/30\n",
      "54000/54000 [==============================] - 1s 22us/step - loss: 0.3866 - accuracy: 0.8991 - val_loss: 0.3932 - val_accuracy: 0.8945\n",
      "Epoch 11/30\n",
      "54000/54000 [==============================] - 1s 21us/step - loss: 0.3729 - accuracy: 0.9018 - val_loss: 0.3807 - val_accuracy: 0.8965\n",
      "Epoch 12/30\n",
      "54000/54000 [==============================] - 1s 21us/step - loss: 0.3612 - accuracy: 0.9040 - val_loss: 0.3699 - val_accuracy: 0.8977\n",
      "Epoch 13/30\n",
      "54000/54000 [==============================] - 1s 21us/step - loss: 0.3512 - accuracy: 0.9064 - val_loss: 0.3607 - val_accuracy: 0.8992\n",
      "Epoch 14/30\n",
      "54000/54000 [==============================] - 1s 21us/step - loss: 0.3424 - accuracy: 0.9082 - val_loss: 0.3524 - val_accuracy: 0.9020\n",
      "Epoch 15/30\n",
      "54000/54000 [==============================] - 2s 33us/step - loss: 0.3346 - accuracy: 0.9098 - val_loss: 0.3454 - val_accuracy: 0.9037\n",
      "Epoch 16/30\n",
      "54000/54000 [==============================] - 1s 22us/step - loss: 0.3275 - accuracy: 0.9114 - val_loss: 0.3387 - val_accuracy: 0.9050\n",
      "Epoch 17/30\n",
      "54000/54000 [==============================] - 1s 22us/step - loss: 0.3213 - accuracy: 0.9126 - val_loss: 0.3329 - val_accuracy: 0.9062\n",
      "Epoch 18/30\n",
      "54000/54000 [==============================] - 1s 24us/step - loss: 0.3155 - accuracy: 0.9139 - val_loss: 0.3277 - val_accuracy: 0.9077\n",
      "Epoch 19/30\n",
      "54000/54000 [==============================] - 1s 23us/step - loss: 0.3101 - accuracy: 0.9152 - val_loss: 0.3224 - val_accuracy: 0.9102\n",
      "Epoch 20/30\n",
      "54000/54000 [==============================] - 1s 22us/step - loss: 0.3052 - accuracy: 0.9164 - val_loss: 0.3183 - val_accuracy: 0.9092\n",
      "Epoch 21/30\n",
      "54000/54000 [==============================] - 1s 23us/step - loss: 0.3007 - accuracy: 0.9175 - val_loss: 0.3136 - val_accuracy: 0.9117\n",
      "Epoch 22/30\n",
      "54000/54000 [==============================] - 1s 23us/step - loss: 0.2964 - accuracy: 0.9184 - val_loss: 0.3098 - val_accuracy: 0.9118\n",
      "Epoch 23/30\n",
      "54000/54000 [==============================] - 1s 25us/step - loss: 0.2924 - accuracy: 0.9191 - val_loss: 0.3061 - val_accuracy: 0.9130\n",
      "Epoch 24/30\n",
      "54000/54000 [==============================] - 1s 20us/step - loss: 0.2886 - accuracy: 0.9204 - val_loss: 0.3029 - val_accuracy: 0.9133\n",
      "Epoch 25/30\n",
      "54000/54000 [==============================] - 1s 21us/step - loss: 0.2850 - accuracy: 0.9212 - val_loss: 0.2996 - val_accuracy: 0.9123\n",
      "Epoch 26/30\n",
      "54000/54000 [==============================] - 3s 52us/step - loss: 0.2816 - accuracy: 0.9224 - val_loss: 0.2963 - val_accuracy: 0.9152\n",
      "Epoch 27/30\n",
      "54000/54000 [==============================] - 3s 58us/step - loss: 0.2785 - accuracy: 0.9234 - val_loss: 0.2934 - val_accuracy: 0.9167\n",
      "Epoch 28/30\n",
      "54000/54000 [==============================] - 3s 57us/step - loss: 0.2753 - accuracy: 0.9239 - val_loss: 0.2911 - val_accuracy: 0.9162\n",
      "Epoch 29/30\n",
      "54000/54000 [==============================] - 3s 58us/step - loss: 0.2725 - accuracy: 0.9248 - val_loss: 0.2883 - val_accuracy: 0.9170\n",
      "Epoch 30/30\n",
      "54000/54000 [==============================] - 3s 57us/step - loss: 0.2697 - accuracy: 0.9252 - val_loss: 0.2853 - val_accuracy: 0.9163\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(\n",
    "    X_train,\n",
    "    y_train_cat,\n",
    "    epochs=epochs,\n",
    "    batch_size=batch_size,\n",
    "    validation_data=(X_val,y_val_cat),\n",
    "    verbose=1 #default - show progress bar\n",
    "    shuffle=True #default, RECOMMENDED - shuffles data at the beginning of each epoch\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note:** If you want to re-train the network from scratch after this step, you will have to call the *clear_backend()* function and re-define the whole network. Every model internally stores the state of the training at which it was stopped, if you don't clear it training will be taken up from where it was stopped before."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now evaluate the trained model on the test set and use it to generate predictions for new data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000/10000 [==============================] - 1s 93us/step\n",
      "\n",
      "Test Loss:\t 0.26703420122265814\n",
      "Test Accuracy:\t 0.9248999953269958\n"
     ]
    }
   ],
   "source": [
    "#evaluate model on the test set\n",
    "test_loss, test_acc = model.evaluate(X_test, y_test_cat)\n",
    "\n",
    "print()\n",
    "print('Test Loss:\\t', test_loss)\n",
    "print('Test Accuracy:\\t', test_acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.  , 0.  , 0.  , 0.01, 0.  , 0.  , 0.  , 0.98, 0.  , 0.01],\n",
       "       [0.01, 0.  , 0.88, 0.04, 0.  , 0.01, 0.05, 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.98, 0.01, 0.  , 0.  , 0.  , 0.  , 0.01, 0.  , 0.  ],\n",
       "       [0.99, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],\n",
       "       [0.  , 0.  , 0.  , 0.  , 0.95, 0.  , 0.  , 0.  , 0.  , 0.03]],\n",
       "      dtype=float32)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#generate probability predictions for the first 5 samples in the test set\n",
    "model.predict_proba(X_test[:5]).round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A bunch of logging information about the model and the training is stored in the *history* object. In particular, *history.history* contains the values of the logged accuracy metrics requested at compilation time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]\n"
     ]
    }
   ],
   "source": [
    "print(history.epoch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'batch_size': 128,\n",
       " 'epochs': 30,\n",
       " 'steps': None,\n",
       " 'samples': 54000,\n",
       " 'verbose': 1,\n",
       " 'do_validation': True,\n",
       " 'metrics': ['loss', 'accuracy', 'val_loss', 'val_accuracy']}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "history.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['val_loss', 'val_accuracy', 'loss', 'accuracy'])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#metrics history is saved here\n",
    "history.history.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the data contained in the history dictionary we can construct the **learning curves** associated with the training of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot learning curves\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,6))\n",
    "\n",
    "for metric in history.history:\n",
    "    ax.plot(history.epoch, history.history[metric], label=metric)\n",
    "    \n",
    "ax.grid()    \n",
    "\n",
    "ax.legend(fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how, in this case, both the training and the validation metrics follow the same trend (increasing or decreasing, depending on which metric), which is a sign that no overfitting is occurring. Notice also that the training and validation curves always stay close to each other, which means that our model will likely generalize pretty well to unseen data.\n",
    "\n",
    "**Subtlety:** Note that during the first epochs it seems that the model is performing better on the validation data than on the training data. This is due to the fact that the training metrics are calculated as a mean value over all of the batches in an epoch, while validation metrics are calculated at the end of each epoch. In the first epochs the model learns quickly, thus difference in error between the first and the last batch is higher, and the mean score of the epoch is dragged down by the bad scores of the first batches while the validdation does not suffer from this effect. In order to manually correct for this bias, one can shift the training curves half an epoch to the left as done below: note how now the curves pretty much coincide in the beginning. This effect ususally becomes negligible after a small number of epochs, so this correction can be safely ignored in most cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot learning curves\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,6))\n",
    "\n",
    "for metric in history.history:\n",
    "    if len(metric.split('_')) < 2:\n",
    "        ax.plot(np.array(history.epoch)-.5, history.history[metric], label=metric)\n",
    "    else:\n",
    "        ax.plot(history.epoch, history.history[metric], label=metric)\n",
    "    \n",
    "ax.grid()    \n",
    "\n",
    "ax.legend(fontsize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize the wrong predictions, in order to understand where the model fails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#identify wrong predictions in the training set\n",
    "\n",
    "y_train_pred = model.predict_classes(X_train)\n",
    "\n",
    "idx_wrong = np.where(y_train_pred != y_train)[0] #positions of the wrongly classified data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show the first 10 wrong predictions the training set\n",
    "\n",
    "fig, axs = plt.subplots(2,5,figsize=(12,4))\n",
    "\n",
    "for i in range(10):\n",
    "    \n",
    "    ax = axs.ravel()[i]\n",
    "    \n",
    "    idx = idx_wrong[i]\n",
    "    \n",
    "    ax.imshow(X_train[idx], cmap='gray')\n",
    "    ax.set_title('TRUE: {}, PRED {}'.format(y_train[idx], y_train_pred[idx]), fontsize=13)\n",
    "    ax.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our still makes a few errors after such a short training, but it seems that most of them are somehow *reasonable*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center> **Saving and loading trained models** </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Training a DL model is usually a time and resource consuming activity, so one does not usually want to start all over again every time. Keras provide a very easy way to save and load complete models (and/or their weights). This is also a useful feature if one wants to use big pre-trained models which would be infeasible to train from scratch (like AlexNet, VGG etc.).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "#save trained model in the cache folder\n",
    "model.save('cache/03.SimpleDense.MNIST.h5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Error in loading the saved optimizer state. As a result, your model is starting with a freshly initialized optimizer.\n"
     ]
    }
   ],
   "source": [
    "# load saved model\n",
    "model = keras.models.load_model('cache/03.SimpleDense.MNIST.h5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_1\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "flatten_1 (Flatten)          (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 15)                11775     \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                160       \n",
      "=================================================================\n",
      "Total params: 11,935\n",
      "Trainable params: 11,935\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000/10000 [==============================] - 1s 116us/sample - loss: 0.2670 - accuracy: 0.9249\n",
      "\n",
      "Test Loss:\t 0.26703420122265814\n",
      "Test Accuracy:\t 0.9249\n"
     ]
    }
   ],
   "source": [
    "#evaluate loaded model on the test set\n",
    "test_loss, test_acc = model.evaluate(X_test, y_test_cat)\n",
    "\n",
    "print()\n",
    "print('Test Loss:\\t', test_loss)\n",
    "print('Test Accuracy:\\t', test_acc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center> **Transfer Learning** </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keras allows you to easily load a lot of big and famous models to implement in your pipeline. A list of available models and instructions on how to load them is available [here](https://keras.io/api/applications/) in the keras docs.\n",
    "\n",
    "One of the things that make trained models very useful is the possibility of using them in **transfer learning** strategies. Transfer learning consists of taking a neural network trained on a task different from the one you have at hand, but close enough. For example, you might have a network trained to distingush pictures of cats and dogs, but you want to distingish cats and horses. Its not quite the same task, but you suspect that some of the knowledge that your pre-trained network contains might speed up your learning on the new task. You can take the pre-trained network and, for example, freeze the weights up to the last layer, the re-train only the last layer from scratch using data from the new task. If it works you have saved a lot of training time and got a network fine-tuned for your new task. This is a pretty effective strategy especially when the pre-trained model is so big that it wuold be almost impossible to train from scratch and gives great results in many contexts.\n",
    "\n",
    "Transfer learning will be explained more in detail in the next course lectures. If you want more practical details on how to do this in keras you can look [here](https://keras.io/guides/transfer_learning/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <center> **Exercises** </center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Play with the code \n",
    "\n",
    "As always, the best way to understand is to change things and try to understand what happens. In neural networks there surely is not shortage of things you can change and get very different results: activations, loss function, epochs of training, batch size, optimizer, number of layers, number of neurons per layer, ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### F-MNIST Dataset\n",
    "\n",
    "Another toy dataset which is frequently used is the Fashion-MNIST dataset. It has the advantage of being more difficult to learn for a neural network, while retaining the feature that made MNIST so widespread, like small size, abundance of data both for training and testing and being easy to handle. The ten classes in this case are categories of fashion items and clothes, images are 28x28 b/w as is for MNIST. The dataset is readily available inside keras, follow the steps presented above in order to train a network on this new dataset.\n",
    "\n",
    "**Note:** You will need to apply also here the preprocessing steps!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28)\n",
      "(10000, 28, 28)\n"
     ]
    }
   ],
   "source": [
    "# load FMINST data\n",
    "\n",
    "from tensorflow.keras.datasets import fashion_mnist\n",
    "\n",
    "#load actual data\n",
    "(X_train, y_train), (X_test, y_test) = fashion_mnist.load_data()\n",
    "\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#class names are not provided with the data\n",
    "class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat',\n",
    "               'Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']\n",
    "\n",
    "d_class_name = dict(zip(range(10),class_names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show the first 10 images in the training set\n",
    "\n",
    "fig, axs = plt.subplots(2,5,figsize=(12,4))\n",
    "\n",
    "for i in range(10):\n",
    "    \n",
    "    ax = axs.ravel()[i]\n",
    "    \n",
    "    ax.imshow(X_train[i], cmap='gray')\n",
    "    ax.set_title('{}'.format(d_class_name[y_train[i]]), fontsize=13)\n",
    "    ax.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "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": [
    "plt.hlines(6000, -1, 10, linestyles='--')\n",
    "\n",
    "plt.hist(y_train, bins=np.linspace(-.5,9.5,11), rwidth=.8)\n",
    "plt.xticks(range(10), labels=class_names, rotation=90);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moons Synthethic Dataset\n",
    "\n",
    "Use the code from the previous notebook to generate the moons dataset with scikit-learn, then train a neural network on the data. Since the dataset is 2D you can easily visualize the decision boundary of the trained neural network and make comparisons with the perceptron boundary!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "N = 10000\n",
    "test_size = .1\n",
    "\n",
    "#generate two semi-circles, one for each class, of 2D data\n",
    "#(we don't get to choose the data dimension here, it's always 2D)\n",
    "X_moon, y_moon = make_moons(n_samples=N, noise=.1)\n",
    "\n",
    "#generate training and test set\n",
    "X_moon_train, X_moon_test, y_moon_train, y_moon_test = train_test_split(X_moon, y_moon, test_size=test_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the blob dataset\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "\n",
    "fontsize = 15\n",
    "\n",
    "#plot both classes as above, but all at once\n",
    "for cat in np.unique(y_moon_train): #loop over unique class IDs\n",
    "    \n",
    "    mask = y_moon_train == cat\n",
    "    \n",
    "    ax.plot(X_moon_train[mask][:,0], X_moon_train[mask][:,1], 'o', markersize=1, label='class {}'.format(cat))\n",
    "\n",
    "\n",
    "\n",
    "ax.legend(fontsize=fontsize)\n",
    "\n",
    "ax.set_xlabel('Feature 1', fontsize=fontsize)\n",
    "ax.set_ylabel('Feature 2', fontsize=fontsize)\n",
    "\n",
    "ax.set_title('Moons', fontsize=fontsize);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TRAIN YOUR NEURAL NETWORK HERE\n",
    "\n",
    "model = Sequential()\n",
    "\n",
    "#.......\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#visualize prediction boundary on moons dataset\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "\n",
    "fontsize = 15\n",
    "\n",
    "#----------------------------------------------------------------\n",
    "### VISUALIZE BLOBS TRAINIG DATASET (with correct classification)\n",
    "\n",
    "\n",
    "#plot the points of the first class:\n",
    "mask = y_moon_train == 0\n",
    "\n",
    "ax.plot(X_moon_train[mask][:,0], X_moon_train[mask][:,1], 'o', label='class 0') #plot first feature on x-axis and second feature on y-axis\n",
    "\n",
    "\n",
    "#plot the points of the second class:\n",
    "mask = y_moon_train == 1\n",
    "\n",
    "ax.plot(X_moon_train[mask][:,0], X_moon_train[mask][:,1], 'o', label='class 1') #plot first feature on x-axis and second feature on y-axis\n",
    "\n",
    "#----------------------------------------------------------------\n",
    "### Visualize perceptron's prediction field\n",
    "\n",
    "# generate square mesh of points to evaluate, with \"n_pts_side\" ponits per side\n",
    "n_pts_side = 500\n",
    "pad = .5\n",
    "\n",
    "#extrema change based on generated points\n",
    "xx_min = X_moon[:,0].min()-pad\n",
    "xx_max = X_moon[:,0].max()+pad\n",
    "\n",
    "yy_min = X_moon[:,1].min()-pad\n",
    "yy_max = X_moon[:,1].max()+pad\n",
    "\n",
    "xx = np.linspace(xx_min, xx_max, n_pts_side)  \n",
    "yy = np.linspace(yy_min, yy_max, n_pts_side)\n",
    "\n",
    "\n",
    "# plot decision field\n",
    "xx, yy = np.meshgrid(xx, yy)\n",
    "\n",
    "zz = model.predict_classes(np.vstack([xx.ravel(),yy.ravel()]).T) #generate predictions for each point in field\n",
    "zz = zz.reshape(xx.shape)\n",
    "\n",
    "ax.contourf(xx, yy, zz, levels=2, colors=('deepskyblue','k','orangered'), alpha=.1)\n",
    "\n",
    "#----------------------------------------------------------------\n",
    "\n",
    "ax.set_xlim(xx_min, xx_max)\n",
    "ax.set_ylim(yy_min, yy_max)\n",
    "\n",
    "ax.legend(fontsize=fontsize)\n",
    "\n",
    "ax.set_xlabel('Feature 1', fontsize=fontsize)\n",
    "ax.set_ylabel('Feature 2', fontsize=fontsize)\n",
    "\n",
    "ax.set_title('Blobs', fontsize=fontsize);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}