5. Simple Network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/DeepLearning/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\"> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> \n",
    "        <h1>Deep Learning From Scratch</h1>\n",
    "        <h1>Simple Network</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "        @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.10.9\n",
      "IPython version      : 8.10.0\n",
      "\n",
      "Compiler    : Clang 14.0.6 \n",
      "OS          : Darwin\n",
      "Release     : 22.5.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 0a19814306bc315e122d1b21878507f2b920977d\n",
      "\n",
      "numpy     : 1.23.5\n",
      "pandas    : 1.5.3\n",
      "seaborn   : 0.12.2\n",
      "watermark : 2.4.2\n",
      "matplotlib: 3.7.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -i -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('d4sci.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = np.load('input/X_train.npy')\n",
    "X_test = np.load('input/X_test.npy')\n",
    "y_train = np.load('input/y_train.npy')\n",
    "y_test = np.load('input/y_test.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_layer_size = X_train.shape[1]\n",
    "\n",
    "X_train /= 255.\n",
    "X_test /= 255."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 784)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 784)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize weights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define the initializatino function as we'll have to call it more than once"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_weights(L_in, L_out, epsilon = 0.12):\n",
    "    return 2*np.random.rand(L_out, L_in+1)*epsilon - epsilon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the layer sizes we'll be using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "hidden_layer_size = 50\n",
    "num_labels = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Theta1 = init_weights(input_layer_size, hidden_layer_size)\n",
    "Theta2 = init_weights(hidden_layer_size, num_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One-hot encoding to define the labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_hot(K, pos):\n",
    "    y0 = np.zeros(K)\n",
    "    y0[pos] = 1\n",
    "\n",
    "    return y0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 4, ..., 2, 1, 2], dtype=uint8)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 1., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_hot(10, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Activation function, just as before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1./(1+np.exp(-z))\n",
    "\n",
    "def sigmoidGradient(z):\n",
    "    h = sigmoid(z)\n",
    "    return h*(1-h)\n",
    "\n",
    "def accuracy(y_, y):\n",
    "    return np.mean((y_ == y.flatten()))*100."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward Propagation and Prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Same functions defined above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward(Theta, X, active):\n",
    "    N = X.shape[0]\n",
    "\n",
    "    # Add the bias column\n",
    "    X_ = np.concatenate((np.ones((N, 1)), X), 1)\n",
    "\n",
    "    # Multiply by the weights\n",
    "    z = np.dot(X_, Theta.T)\n",
    "\n",
    "    # Apply the activation function\n",
    "    a = active(z)\n",
    "\n",
    "    return a\n",
    "\n",
    "def predict(Theta1, Theta2, X):\n",
    "    h1 = forward(Theta1, X, sigmoid)\n",
    "    h2 = forward(Theta2, h1, sigmoid)\n",
    "\n",
    "    return np.argmax(h2, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Back propagation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def backprop(Theta1, Theta2, X, y):\n",
    "    N = X.shape[0]\n",
    "    K = Theta2.shape[0]\n",
    "\n",
    "    J = 0\n",
    "\n",
    "    Delta2 = np.zeros(Theta2.shape)\n",
    "    Delta1 = np.zeros(Theta1.shape)\n",
    "\n",
    "    for i in range(N):\n",
    "        # Forward propagation, saving intermediate results\n",
    "        a1 = np.concatenate(([1], X[i]))  # Input layer\n",
    "\n",
    "        z2 = np.dot(Theta1, a1)\n",
    "        h2 = sigmoid(z2)\n",
    "        \n",
    "        a2 = np.concatenate(([1], h2))  # Hidden Layer\n",
    "\n",
    "        z3 = np.dot(Theta2, a2)\n",
    "        h3 = sigmoid(z3)  # Output layer\n",
    "        a3 = h3\n",
    "        \n",
    "        y0 = one_hot(K, y[i])\n",
    "\n",
    "        # Cross entropy\n",
    "        J -= np.dot(y0.T, np.log(a3))+np.dot((1-y0).T, np.log(1-a3))\n",
    "\n",
    "        # Calculate the weight deltas\n",
    "        delta_3 = a3-y0\n",
    "        delta_2 = np.dot(Theta2.T, delta_3)[1:]*sigmoidGradient(z2)\n",
    "\n",
    "        Delta2 += np.outer(delta_3, a2)\n",
    "        Delta1 += np.outer(delta_2, a1)\n",
    "\n",
    "    J /= N\n",
    "\n",
    "    Theta1_grad = Delta1/N\n",
    "    Theta2_grad = Delta2/N\n",
    "\n",
    "    return [J, Theta1_grad, Theta2_grad]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training procedure\n",
    "The basic idea is the same as for the linear and logistic regression cases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 3.126973464005142 3.1212550919991746 45.14 40.2\n",
      "20 2.912538013459252 2.9144588294863856 55.300000000000004 50.2\n",
      "30 2.606854955607943 2.6266286601462223 60.84 56.49999999999999\n",
      "40 2.289653494466329 2.3346332936760543 66.88 63.4\n",
      "50 2.0282706206854217 2.0945473506862164 71.78 68.4\n",
      "60 1.8257460008426916 1.9066773822813394 75.94 72.39999999999999\n",
      "70 1.6650824322596873 1.7562127275910207 79.06 74.6\n",
      "80 1.5334559670959202 1.632323279714511 81.12 77.2\n",
      "90 1.4233143984985122 1.5285820077070396 82.82000000000001 78.60000000000001\n",
      "100 1.3298583127429586 1.4407653650775898 83.86 80.2\n",
      "110 1.2496332349632688 1.3656988925523097 84.74000000000001 81.69999999999999\n",
      "120 1.1800151721285725 1.3008839478610168 85.92 83.1\n",
      "130 1.1190134452198397 1.244378696834078 86.6 83.7\n",
      "140 1.065135313409679 1.1947068374330456 87.36 84.1\n",
      "150 1.017258854737831 1.1507544382960664 88.1 84.7\n",
      "160 0.9745220403995383 1.1116698506714893 88.6 85.2\n",
      "170 0.9362380788882525 1.0767817315027572 89.08 85.8\n",
      "180 0.9018379992570357 1.0455403420851754 89.34 86.3\n",
      "190 0.8708354545470871 1.0174800837511757 89.58 86.7\n",
      "200 0.8428068569794698 0.9921978657802228 89.78 86.7\n",
      "210 0.8173806014581924 0.9693413992785702 89.98 86.8\n",
      "220 0.7942308378939447 0.9486026667918066 90.22 86.7\n",
      "230 0.7730730540647616 0.9297135194165044 90.48 86.8\n",
      "240 0.7536601339964725 0.9124418497953808 90.74 87.0\n",
      "250 0.7357784327021087 0.8965877799762352 90.92 87.1\n",
      "260 0.7192438429444303 0.8819798120508562 91.08000000000001 87.3\n",
      "270 0.7038979813952805 0.8684710737942395 91.2 87.1\n",
      "280 0.6896046297509147 0.855935807521375 91.28 87.2\n",
      "290 0.67624652167437 0.8442662032005469 91.44 87.2\n",
      "300 0.6637225152752217 0.8333696209439447 91.7 87.2\n",
      "310 0.6519451510787102 0.8231662044002992 91.84 87.4\n",
      "320 0.6408385703962248 0.8135868592763636 91.84 87.5\n",
      "330 0.6303367562310983 0.8045715574571912 91.96 87.7\n",
      "335 0.6252943283877603 0.8045715574571912 91.96 87.7\n",
      "DONE\n"
     ]
    }
   ],
   "source": [
    "step = 0\n",
    "tol = 1e-3 # Minimum different in error between two consecutive steps\n",
    "J_old = 1/tol\n",
    "diff = 1\n",
    "\n",
    "acc_train = []\n",
    "acc_test = []\n",
    "J_val = []\n",
    "steps = []\n",
    "alpha = 0.5\n",
    "\n",
    "while diff > tol:\n",
    "    J_train, Theta1_grad, Theta2_grad = backprop(Theta1, Theta2, X_train, y_train)\n",
    "\n",
    "    diff = abs(J_old-J_train)\n",
    "    J_old = J_train\n",
    "    J_val.append(J_train)\n",
    "    \n",
    "    step += 1\n",
    "\n",
    "    Theta1 -= alpha*Theta1_grad\n",
    "    Theta2 -= alpha*Theta2_grad\n",
    "\n",
    "    \n",
    "    if step % 10 == 0:\n",
    "        pred_train = predict(Theta1, Theta2, X_train)\n",
    "        pred_test = predict(Theta1, Theta2, X_test)\n",
    "\n",
    "        J_test, T1_grad, T2_grad = backprop(Theta1, Theta2, X_test, y_test)\n",
    "        \n",
    "        acc_train.append(accuracy(pred_train, y_train))\n",
    "        acc_test.append(accuracy(pred_test, y_test))\n",
    "        steps.append(step)\n",
    "        \n",
    "        print(step, J_train, J_test, acc_train[-1], acc_test[-1])\n",
    "\n",
    "    \n",
    "print(step, J_train, J_test, acc_train[-1], acc_test[-1])\n",
    "print('DONE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accuracy during training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cost function')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(1, len(J_val)+1), J_val)\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"Cost function\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fa2a022d720>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(steps, acc_train, label='Training dataset')\n",
    "plt.plot(steps, acc_test, label='Testing dataset')\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"Accuracy (%)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save the trained model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('Theta1_short.npy', Theta1)\n",
    "np.save('Theta2_short.npy', Theta2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "     <img src=\"https://raw.githubusercontent.com/DataForScience/DeepLearning/master/data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
   ]
  }
 ],
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   "display_name": "Python 3 (ipykernel)",
   "language": "python",
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    "name": "ipython",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
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  "toc": {
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  "varInspector": {
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   "kernels_config": {
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     "delete_cmd_postfix": ") ",
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   "types_to_exclude": [
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