Simple Network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\"> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Deep Learning From Scratch</h1>\n",
    "<h2>Simple Network</h2>\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 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": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "watermark  1.8.1\n",
      "seaborn    0.9.0\n",
      "numpy      1.16.2\n",
      "matplotlib 3.1.0\n",
      "pandas     0.24.2\n",
      "Tue Sep 24 2019 2019-09-24T11:47:18-04:00\n",
      "\n",
      "CPython 3.7.3\n",
      "IPython 6.2.1\n",
      "\n",
      "compiler   : Clang 4.0.1 (tags/RELEASE_401/final)\n",
      "system     : Darwin\n",
      "release    : 18.7.0\n",
      "machine    : x86_64\n",
      "processor  : i386\n",
      "CPU cores  : 8\n",
      "interpreter: 64bit\n",
      "Git hash   : 46e8ada9ae78bc5ab280631b85d64d9ea1891da7\n"
     ]
    }
   ],
   "source": [
    "%watermark -i -n -v -m -g -iv"
   ]
  },
  {
   "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):\n",
    "    epsilon = 0.12\n",
    "\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": "markdown",
   "metadata": {},
   "source": [
    "Activation function, just as before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": 13,
   "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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_hot(10, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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",
    "        a2 = np.concatenate(([1], sigmoid(z2)))  # Hidden Layer\n",
    "\n",
    "        z3 = np.dot(Theta2, a2)\n",
    "        a3 = sigmoid(z3)  # Output layer\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": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 3.11220331017834 3.126267085302958 47.339999999999996 44.1\n",
      "20 2.897689418481209 2.932158798491075 59.24 55.1\n",
      "30 2.5855498703231907 2.645522155113906 64.92 59.5\n",
      "40 2.2533597729573493 2.334607785351376 69.74000000000001 65.60000000000001\n",
      "50 1.980935277882805 2.0749078299386237 73.96000000000001 70.3\n",
      "60 1.775095638824831 1.8761989723318997 77.2 73.8\n",
      "70 1.6158343908487522 1.72158838151967 80.02 75.9\n",
      "80 1.4877444503268071 1.5971594802542364 81.88 77.9\n",
      "90 1.3818077961268762 1.494566477395403 83.46000000000001 79.4\n",
      "100 1.2924843615439117 1.4085929642809045 84.58 81.39999999999999\n",
      "110 1.216039033969257 1.3356313150998165 85.56 83.2\n",
      "120 1.1498104764075656 1.2730249724084215 86.6 83.7\n",
      "130 1.0918548005203974 1.2187707371029284 87.28 84.6\n",
      "140 1.0407277418945298 1.1713459959593477 87.8 84.89999999999999\n",
      "150 0.9953337554899521 1.1295852034269276 88.36 85.7\n",
      "160 0.9548200547335193 1.092585402312372 88.66000000000001 86.0\n",
      "170 0.9185040775808653 1.059634655097101 89.05999999999999 86.3\n",
      "180 0.8858251515237292 1.0301596534645094 89.42 86.4\n",
      "190 0.8563128492621025 1.003688802394099 89.66 86.5\n",
      "200 0.8295663684673751 0.9798270315821169 89.94 86.7\n",
      "210 0.8052409116421422 0.9582388999009839 90.2 86.9\n",
      "220 0.7830383410101127 0.938637175377278 90.3 86.8\n",
      "230 0.7627003534432053 0.9207748153606687 90.48 87.2\n",
      "240 0.7440031156520908 0.904438969893497 90.64 87.1\n",
      "250 0.7267527704781455 0.8894461837021377 90.86 87.2\n",
      "260 0.7107815181529323 0.8756383504999251 90.98 87.3\n",
      "270 0.6959441395068122 0.8628791998876779 91.03999999999999 87.5\n",
      "280 0.6821149061342069 0.8510512153370579 91.2 87.5\n",
      "290 0.6691848517619207 0.840052933899176 91.38 87.5\n",
      "300 0.6570593846301076 0.8297965959757558 91.46 87.6\n",
      "310 0.6456562174659659 0.82020611631852 91.64 87.6\n",
      "320 0.6349035870641764 0.8112153457375979 91.72 87.6\n"
     ]
    }
   ],
   "source": [
    "step = 0\n",
    "tol = 1e-3\n",
    "J_old = 1/tol\n",
    "diff = 1\n",
    "\n",
    "acc_train = []\n",
    "acc_test = []\n",
    "J_val = []\n",
    "steps = []\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",
    "    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",
    "    Theta1 -= .5*Theta1_grad\n",
    "    Theta2 -= .5*Theta2_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accuracy during training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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\")\n",
    "plt.gcf().set_size_inches(11, 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "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()\n",
    "plt.gcf().set_size_inches(11, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save the trained model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</div>"
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}