classification_MNIST.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification on Mnist\n",
    "\n",
    "In this file, we create a neural network with one hidden layer and apply it to the mnist dataset in order to address the classification problem and to compute uncertainty as in "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import keras\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation, Dropout\n",
    "from keras.datasets import mnist\n",
    "from keras.optimizers import RMSprop\n",
    "from keras import regularizers\n",
    "\n",
    "# useful functions for classification task\n",
    "from utils_classifNN import *\n",
    "from utils_visu_classif import *\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.cm as cm\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import gridspec\n",
    "import imutils\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28) (60000,) (10000, 28, 28)\n",
      "60000 train samples\n",
      "10000 test samples\n"
     ]
    }
   ],
   "source": [
    "# loading mnist and split between train and test sets\n",
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n",
    "print(x_train.shape, y_train.shape, x_test.shape)\n",
    "x_train = x_train.reshape(60000, 784)\n",
    "x_test = x_test.reshape(10000, 784)\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print(x_train.shape[0], 'train samples')\n",
    "print(x_test.shape[0], 'test samples')\n",
    "\n",
    "\n",
    "# network parameters\n",
    "batch_size = 128\n",
    "num_classes = 10\n",
    "epochs = 20\n",
    "\n",
    "# dimensions for the NN:\n",
    "# input dimension\n",
    "Q = x_train.shape[1]\n",
    "# hidden layer dimension\n",
    "K = 100\n",
    "# output dimension : classification\n",
    "D = num_classes\n",
    "\n",
    "# dropout rate\n",
    "DROP_OUT = 0.5\n",
    "N = x_train.shape[0]\n",
    "# l2 regularization\n",
    "#prior length scale\n",
    "l = 1e-2\n",
    "# precision parameter, un peu au pif pour l'instant\n",
    "tau = 1e-1\n",
    "\n",
    "lambd = DROP_OUT*l**2/(2*N)\n",
    "\n",
    "# convert class vectors to binary class matrices\n",
    "y_train = keras.utils.to_categorical(y_train, num_classes)\n",
    "y_test = keras.utils.to_categorical(y_test, num_classes)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create a sequential model with Keras "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(K, input_shape = (Q, ), activation = 'relu', use_bias= True, kernel_regularizer = regularizers.l2(lambd),\n",
    "               bias_regularizer = regularizers.l2(lambd)))\n",
    "model.add(Dropout(DROP_OUT))\n",
    "# softmax layer\n",
    "model.add(Dense(num_classes, use_bias = False, activation = None, kernel_regularizer = regularizers.l2(lambd)))\n",
    "model.add(Dropout(DROP_OUT))\n",
    "model.add(Activation('softmax'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 100)               78500     \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 100)               0         \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                1000      \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 10)                0         \n",
      "_________________________________________________________________\n",
      "activation_1 (Activation)    (None, 10)                0         \n",
      "=================================================================\n",
      "Total params: 79,500\n",
      "Trainable params: 79,500\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()\n",
    "model.compile(loss='categorical_crossentropy',\n",
    "              optimizer=RMSprop(),\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training the network\n",
    "history = model.fit(x_train, y_train,\n",
    "                    batch_size=batch_size,\n",
    "                    epochs=epochs,\n",
    "                    verbose=0,\n",
    "                    validation_data=(x_test, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test loss: 0.127521866213\n",
      "Test accuracy: 0.969\n"
     ]
    }
   ],
   "source": [
    "# Evaluation of the network\n",
    "score = model.evaluate(x_test, y_test, verbose = 0)\n",
    "print('Test loss:', score[0])\n",
    "print('Test accuracy:', score[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Obtaining model uncertainty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vizualise data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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Agpo8ebKJ8/LyTDxp0iQTT58+3cTl5eXN2rKyskx83XXXmfjNN9+UJNXU1IRvwMeAGSEA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\n5plnSpKKi4tNG6U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BABDEvn37NGPGDElSfX29rrjiCp1zzjntes6vNyEtkpgRam8kQgCA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\nsP4fsfincy49UxkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6c458e3d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# change that parameter to see more classes on the plot\n",
    "nb_show = 10\n",
    "# index for the image sample\n",
    "ix = 9\n",
    "x_ex = x_test[ix]\n",
    "#plot_pred_img(x_ex, model, nb_class=10)\n",
    "#plt.show()\n",
    "plot_rotated(x_ex, model , nb_class=10, nb_show= nb_show)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot one example with its classification values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Network prediction: [[  9.35221038e-08   1.39389382e-13   3.27661184e-07   7.79308884e-09\n",
      "    1.08243548e-05   7.15423465e-01   2.84561843e-01   1.97325503e-10\n",
      "    1.42953581e-07   3.30846569e-06]]\n",
      "Networ label: 5\n",
      "dropout prediction: [ 0.02381992  0.00348489  0.0326532   0.01218294  0.08411301  0.48557647\n",
      "  0.28051745  0.00879498  0.02148962  0.04736752]\n",
      "dropout label: 5\n",
      "real label: 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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CxPsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6c38474390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6c38443c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# change the drop_out rate to be more or less close to the classic network prediction\n",
    "DROP_OUT = 0.5\n",
    "\n",
    "ix = 8\n",
    "x_ex = x_test[ix]\n",
    "print(\"Network prediction: \" + str(model.predict(x_ex.reshape((1, -1)))))\n",
    "print(\"Networ label: \"+ str(np.argmax(model.predict(x_ex.reshape((1, -1))))))\n",
    "\n",
    "print(\"dropout prediction: \"+ str(dropout_pred(x_ex, model, nb_cl=10, drop_out=DROP_OUT)))\n",
    "print(\"dropout label: \"+ str(dropout_pred(x_ex, model, nb_cl=10, label=True, drop_out = DROP_OUT)))\n",
    "\n",
    "print(\"real label: \" + str(np.argmax(y_test[ix])))\n",
    "\n",
    "x_pl = x_ex.reshape((28,28))\n",
    "plt.imshow(x_pl, cmap = \"gray\")\n",
    "plt.show()\n",
    "\n",
    "classes = np.argsort(model.predict(x_ex.reshape(1,-1))[0])[-3:]\n",
    "S_in, S_out = softmax_in_out(x_ex, model, nb_cl=10, drop_out= DROP_OUT)\n",
    "plot_pred(S_out, classes, legend=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}