Hwk2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implémentation du réseau de neurones et expérimentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=np.VisibleDeprecationWarning)\n",
    "warnings.filterwarnings(\"ignore\", category=RuntimeWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 0. Implémentation de fonctions utiles\n",
    "Calcul numériquement stable du softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax_vector(x):\n",
    "    '''\n",
    "    x:  is a data vector.\n",
    "    returns: the result of the softmax function applied to the data vector.\n",
    "    '''\n",
    "    max_comp = np.amax(x)\n",
    "    normalized  = x - max_comp\n",
    "    \n",
    "    exponential = np.exp(normalized)\n",
    "    \n",
    "    return exponential/np.sum(exponential)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def softmax(X):\n",
    "    '''\n",
    "    X: matrix that holds the data, every row is a data vector.\n",
    "    returns: matrix where every row is the result of the softmax function applied to the corresponding data vector.\n",
    "    '''\n",
    "    \n",
    "    max_comp = np.amax(X, axis=1)\n",
    "    normalized  = X - max_comp.reshape(X.shape[0], 1)\n",
    "    \n",
    "    exponential = np.exp(normalized)\n",
    "    \n",
    "    return exponential/np.sum(exponential, axis=1).reshape(X.shape[0], 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fonction utilitaire pour calculer relu($x$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def relu(x):\n",
    "    return np.maximum(x, np.zeros(x.shape))\n",
    "\n",
    "def onehot(m, y):\n",
    "    return np.eye(m)[y]\n",
    "\n",
    "def onehot_matrix(m, targets):\n",
    "    \"\"\"\n",
    "    Returns: onehot matrix where every column is a onehot vector of the coressponding target\n",
    "    \"\"\"\n",
    "    eye = np.eye(m)\n",
    "    onehot_matrix = np.zeros((m,len(targets)))\n",
    "    \n",
    "    for i, y in enumerate(targets):\n",
    "        onehot_matrix[:,i] = eye[y]\n",
    "        \n",
    "    return onehot_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Calcul du gradient sur un exemple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implementation de fprop et bprop pour calculer le gradient sur un exemple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class NeuralNet_basic:\n",
    "    \n",
    "    def __init__(self, n_input, n_hidden, n_out):\n",
    "        \n",
    "        self.n_in = n_input\n",
    "        self.n_h = n_hidden\n",
    "        self.n_o = n_out\n",
    "        \n",
    "        low_bound = -1 / np.sqrt([self.n_in, self.n_h])\n",
    "        up_bound = 1 / np.sqrt([self.n_in, self.n_h])\n",
    "        \n",
    "        # Initialize the parameters\n",
    "        self.W1 = np.random.uniform(low_bound[0], up_bound[0], size=(self.n_h, self.n_in))  # d_h x d\n",
    "        self.W2 = np.random.uniform(low_bound[1], up_bound[1], size=(self.n_o, self.n_h))  # m x d_h\n",
    "        self.b1 = np.zeros(self.n_h)  # dimension d_h\n",
    "        self.b2 = np.zeros(self.n_o) # dimension m\n",
    "    \n",
    "    def fprop(self, x):\n",
    "        '''Computes activations for every layer'''\n",
    "        self.ha = self.W1.dot(x) + self.b1\n",
    "        self.hs = relu(self.ha)\n",
    "        self.oa = self.W2.dot(self.hs) + self.b2\n",
    "        self.os = softmax_vector(self.oa)\n",
    "            \n",
    "    def bprop(self, x, y):\n",
    "        '''Computes the gradients, must be executed after fprop'''\n",
    "                      \n",
    "        grad_oa = self.os - onehot(self.n_o, y)\n",
    "        grad_b2 = grad_oa\n",
    "        grad_W2 = np.outer(grad_oa, self.hs)\n",
    "        grad_hs = self.W2.T.dot(grad_oa)\n",
    "        grad_ha = grad_hs * (self.ha > 0)\n",
    "        grad_W1 = np.outer(grad_ha, x)\n",
    "        grad_b1 = grad_ha\n",
    "        \n",
    "        return grad_W1, grad_W2, grad_b1, grad_b2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Vérification du gradient par différences finies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va maintenant vérifier que le gradient calculé est juste. Pour cela on va calculer une approximation du gradient en utilisant la méthode de la différence finie.\n",
    "\n",
    "Pour chaque composante de w1, on va:\n",
    " 1. calculer la valeur de la fonction objectif $L$\n",
    " 2. ajouter une petite valeur $\\epsilon$ à la composante\n",
    " 3. recalculer la valeur de la fonction objectif $L'$\n",
    " 4. remettre à l'ancienne valeur la composante (c'est à dire soustraire $\\epsilon$)\n",
    "\n",
    "Le gradient par différences finies sera dans ce cas donné par:\n",
    "$\\Big( \\frac{\\partial L}{\\partial W_{1}} \\Big)_{ij} = \\frac{1}{\\epsilon} (L' - L)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def compute_loss(x, y, W1, W2, b1, b2):\n",
    "    ha = W1.dot(x) + b1\n",
    "    hs = relu(ha)\n",
    "    oa = W2.dot(hs) + b2\n",
    "    os = softmax_vector(oa)\n",
    "    \n",
    "    return -np.log(os[y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fonction pour calculer le gradient par differences finies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def finite_diff(x, y, neural_net, eps=1e-5):\n",
    "    \n",
    "    # params\n",
    "    W1 = neural_net.W1\n",
    "    W2 = neural_net.W2\n",
    "    b1 = neural_net.b1\n",
    "    b2 = neural_net.b2\n",
    "    \n",
    "    # gradients\n",
    "    grad_w1_diff = np.zeros(W1.shape)\n",
    "    grad_w2_diff = np.zeros(W2.shape)\n",
    "    grad_b1_diff = np.zeros(b1.shape)\n",
    "    grad_b2_diff = np.zeros(b2.shape)\n",
    "    \n",
    "    neural_net.fprop(x)\n",
    "    loss = compute_loss(x, y, W1, W2, b1, b2)\n",
    "    \n",
    "    for i in range(W1.shape[0]):\n",
    "        for j in range(W1.shape[1]):\n",
    "            W1[i,j] = W1[i,j] + eps\n",
    "            loss_prime = compute_loss(x, y, W1, W2, b1, b2)\n",
    "            grad_w1_diff[i, j] = (loss_prime - loss) / epsilon\n",
    "            W1[i,j] = W1[i,j] - eps\n",
    "    for i in range(W2.shape[0]):\n",
    "        for j in range(W2.shape[1]):\n",
    "            W2[i,j] = W2[i,j] + eps\n",
    "            loss_prime = compute_loss(x, y, W1, W2, b1, b2)\n",
    "            grad_w2_diff[i, j] = (loss_prime - loss) / epsilon\n",
    "            W2[i,j] = W2[i,j] - eps\n",
    "    for i in range(b1.shape[0]):\n",
    "            b1[i] = b1[i] + eps\n",
    "            loss_prime = compute_loss(x, y, W1, W2, b1, b2)\n",
    "            grad_b1_diff[i] = (loss_prime - loss) / epsilon\n",
    "            b1[i] = b1[i] - eps\n",
    "    for i in range(b1.shape[0]):\n",
    "            b2[i] = b2[i] + eps\n",
    "            loss_prime = compute_loss(x, y, W1, W2, b1, b2)\n",
    "            grad_b2_diff[i] = (loss_prime - loss) / epsilon\n",
    "            b2[i] = b2[i] - eps\n",
    "            \n",
    "    return grad_w1_diff, grad_w2_diff, grad_b1_diff, grad_b2_diff\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Affichage de vérification du gradient par différence finie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.loadtxt(open('2moons.txt','r'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Différence entre les deux gradients pour W1, W2, b1, b2:\n",
      "[[ 1.00000019  0.99999906]\n",
      " [        nan         nan]]\n",
      "[[ 1.00000091         nan]\n",
      " [ 0.99999909         nan]]\n",
      "[ 1.00000052         nan]\n",
      "[ 1.00000259  0.99999741]\n"
     ]
    }
   ],
   "source": [
    "nn = NeuralNet_basic(2, 2, 2)\n",
    "x = data[0,:-1]\n",
    "y = data[0,-1]\n",
    "epsilon = 1e-5\n",
    "\n",
    "# gradients par différence finie\n",
    "grad_w1_diff, grad_w2_diff, grad_b1_diff, grad_b2_diff = finite_diff(x, y, nn, epsilon)\n",
    "\n",
    "# gradients par implémentation dans classe neural_net\n",
    "grad_W1, grad_W2, grad_b1, grad_b2 = nn.bprop(x,y)\n",
    "\n",
    "# affichage de la différence\n",
    "print('Différence entre les deux gradients pour W1, W2, b1, b2:')\n",
    "print(grad_W1 / grad_w1_diff)\n",
    "print(grad_W2 / grad_w2_diff)\n",
    "print(grad_b1 / grad_b1_diff)\n",
    "print(grad_b2 / grad_b2_diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque q'effectivement les ratio sont entre 0.99 et 1.01. Les NaN apparaissent lorsque les deux paramètres (ceux calculé avec la différence finie et le gradient) sont égales à zéro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient de W1 par difference finie:\n",
      "[[-0.03556993  0.17480137]\n",
      " [ 0.          0.        ]]\n",
      "Gradient de W1:\n",
      "[[-0.03556994  0.17480121]\n",
      " [ 0.         -0.        ]]\n",
      "Gradient de W2 par difference finie:\n",
      "[[-0.16879107  0.        ]\n",
      " [ 0.16879138  0.        ]]\n",
      "Gradient de W2:\n",
      "[[-0.16879122 -0.        ]\n",
      " [ 0.16879122  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Gradient de W1 par difference finie:\")\n",
    "print(grad_w1_diff)\n",
    "print(\"Gradient de W1:\")\n",
    "print(grad_W1)\n",
    "\n",
    "print(\"Gradient de W2 par difference finie:\")\n",
    "print(grad_w2_diff)\n",
    "print(\"Gradient de W2:\")\n",
    "print(grad_W2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Ajout de hyperparamètre de taille de lot K\n",
    "La fonction bprop est modifiée pour calculer le gradient sur un batch d'exemple. La fonction train est également ajoutée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class NeuralNet_loop:\n",
    "    \n",
    "    def __init__(self, n_input, n_hidden, n_out, lambdas, K = 1):\n",
    "        \n",
    "        self.n_in = n_input\n",
    "        self.n_h = n_hidden\n",
    "        self.n_o = n_out\n",
    "        self.K = K\n",
    "        self.lambdas = lambdas\n",
    "        \n",
    "        low_bound = -1 / np.sqrt([self.n_in, self.n_h])\n",
    "        up_bound = 1 / np.sqrt([self.n_in, self.n_h])\n",
    "        \n",
    "        np.random.seed(123)\n",
    "        \n",
    "        # Initialize the parameters\n",
    "        self.W1 = np.random.uniform(low_bound[0], up_bound[0], size=(self.n_h, self.n_in))  # d_h x d\n",
    "        self.W2 = np.random.uniform(low_bound[1], up_bound[1], size=(self.n_o, self.n_h))  # m x d_h\n",
    "        self.b1 = np.zeros(self.n_h)  # dimension d_h\n",
    "        self.b2 = np.zeros(self.n_o) # dimension m\n",
    "    \n",
    "    def fprop(self, x):\n",
    "        '''Computes activations for every layer'''\n",
    "        ha = self.W1.dot(x) + self.b1\n",
    "        hs = relu(ha)\n",
    "        oa = self.W2.dot(hs) + self.b2\n",
    "        os = softmax_vector(oa)\n",
    "        return ha, hs, oa, os\n",
    "            \n",
    "    def bprop(self, X, Y):\n",
    "        '''Computes the gradients over all examples in (X,Y) with loop'''\n",
    "        grad_W1_mean = np.zeros((self.n_h, self.n_in))\n",
    "        grad_W2_mean = np.zeros((self.n_o, self.n_h))\n",
    "        grad_b1_mean = np.zeros(self.n_h)\n",
    "        grad_b2_mean = np.zeros(self.n_o)\n",
    "        \n",
    "        n = X.shape[0]\n",
    "        loss = 0.\n",
    "        \n",
    "        for i in range(n):\n",
    "            \n",
    "            ha, hs, oa, os = self.fprop(X[i,:])\n",
    "            loss += -np.log(os[Y[i]])\n",
    "            \n",
    "            grad_oa = os - onehot(self.n_o, Y[i])\n",
    "            grad_b2 = grad_oa\n",
    "            grad_W2 = np.outer(grad_oa, hs)\n",
    "            grad_hs = self.W2.T.dot(grad_oa)\n",
    "            grad_ha = grad_hs * (ha > 0)\n",
    "            grad_W1 = np.outer(grad_ha, X[i,:])\n",
    "            grad_b1 = grad_ha\n",
    "            \n",
    "            grad_W1_mean = grad_W1_mean + grad_W1 / n\n",
    "            grad_W2_mean = grad_W2_mean + grad_W2 / n\n",
    "            grad_b1_mean = grad_b1_mean + grad_b1 / n\n",
    "            grad_b2_mean = grad_b2_mean + grad_b2 / n\n",
    "        \n",
    "        return grad_W1_mean, grad_W2_mean, grad_b1_mean, grad_b2_mean, loss \n",
    "    \n",
    "    def compute_loss(self, x, y):\n",
    "        _, _, _, os = self.fprop(x)\n",
    "        return -np.log(self.os[y])\n",
    "    \n",
    "    def train(self, train_data, max_iter, eta=0.05):\n",
    "        \n",
    "        n_batches = int(np.ceil(train_data.shape[0]/self.K)) # number of batches\n",
    "        \n",
    "        # Initialize batch start and end indices\n",
    "        \n",
    "        for i in range(max_iter):\n",
    "            loss = 0.\n",
    "            for j in range(0,train_data.shape[0],self.K):\n",
    "                batch = train_data[j:j+self.K]\n",
    "                \n",
    "                grad_W1_mean, grad_W2_mean, grad_b1_mean, grad_b2_mean, bloss = self.bprop(batch[:,:-1], batch[:,-1]) \n",
    "                loss += bloss\n",
    "                \n",
    "                n = len(batch)\n",
    "                \n",
    "                #regularization\n",
    "                penality_grad_W1 = self.lambdas[0][0] * np.sign(self.W1) + 2 * self.lambdas[0][1] * self.W1\n",
    "                penality_grad_W2 = self.lambdas[1][0] * np.sign(self.W2) + 2 * self.lambdas[1][1] * self.W2\n",
    "                \n",
    "                self.W1 = self.W1 - eta * (grad_W1_mean + penality_grad_W1)\n",
    "                self.W2 = self.W2 - eta * (grad_W2_mean + penality_grad_W2)\n",
    "                self.b1 = self.b1 - eta * grad_b1_mean\n",
    "                self.b2 = self.b2 - eta * grad_b2_mean\n",
    "                \n",
    "            #if i%100 == 0:\n",
    "                #print('The loss after epoque ', i, ' is ', loss / train_data.shape[0])\n",
    "                    \n",
    "    def compute_predictions(self, test_data):\n",
    "\n",
    "        pred = np.empty((test_data.shape[0],self.n_o))\n",
    "\n",
    "        for i in range(test_data.shape[0]):\n",
    "            _, _, _, os = self.fprop(test_data[i,:])\n",
    "            pred[i,:] = os\n",
    "\n",
    "        return pred\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Vérification du gradient par différence finie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Affichage de vérification du gradient pour un lot de 10 exemples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Différence entre les deux gradients pour W1, W2, b1, b2:\n",
      "[[ 1.00000483  1.00000193]\n",
      " [ 0.9999974   1.00000191]]\n",
      "[[ 1.00000193  0.99999863]\n",
      " [ 0.99999807  1.00000138]]\n",
      "[ 0.99999848  1.00000208]\n",
      "[ 0.9999829  1.0000171]\n"
     ]
    }
   ],
   "source": [
    "lambdas = np.array([[0, 0],\n",
    "       [0, 0]])\n",
    "nn = NeuralNet_loop(2, 2, 2, lambdas)\n",
    "X = data[0:10,:-1]\n",
    "Y = data[0:10,-1]\n",
    "\n",
    "# params\n",
    "W1 = nn.W1\n",
    "W2 = nn.W2\n",
    "b1 = nn.b1\n",
    "b2 = nn.b2\n",
    "\n",
    "# gradients par différence finie\n",
    "grad_w1_diff = np.zeros(W1.shape)\n",
    "grad_w2_diff = np.zeros(W2.shape)\n",
    "grad_b1_diff = np.zeros(b1.shape)\n",
    "grad_b2_diff = np.zeros(b2.shape)\n",
    "\n",
    "for i in range(X.shape[0]):\n",
    "    grad_w1, grad_w2, grad_b1, grad_b2 = finite_diff(X[i,:], Y[i], nn, epsilon)\n",
    "    grad_w1_diff += grad_w1 / X.shape[0]\n",
    "    grad_w2_diff += grad_w2 / X.shape[0]\n",
    "    grad_b1_diff += grad_b1 / X.shape[0]\n",
    "    grad_b2_diff += grad_b2 / X.shape[0]\n",
    "    \n",
    "# gradients par implémentation dans classe neural_net    \n",
    "grad_W1, grad_W2, grad_b1, grad_b2, _ = nn.bprop(X,Y)\n",
    "\n",
    "# affichage de la différence\n",
    "print('Différence entre les deux gradients pour W1, W2, b1, b2:')\n",
    "\n",
    "print(grad_W1 / grad_w1_diff)\n",
    "print(grad_W2 / grad_w2_diff)\n",
    "print(grad_b1 / grad_b1_diff)\n",
    "print(grad_b2 / grad_b2_diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque que les ration sont effectivement entre 0.99 et 1.01."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Entraînement sur 2 moons et visualisation des régions de décision"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fonction de calcul du taux d'erreur de classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Cette fonction renvoie le taux d'erreur étant donné un classifieur et un ensemble de données\n",
    "def taux_erreur(classifieur, data):\n",
    "    x = data[:, :-1]\n",
    "    y = data[:, -1]\n",
    "    data_prob = classifieur.compute_predictions(x)\n",
    "    data_classe_pred = np.argmax(data_prob, axis=1)\n",
    "    \n",
    "    return 100. * np.mean(data_classe_pred != y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fonction d'affichage des régions de décision "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# fonction plot\n",
    "import pylab\n",
    "def gridplot(classifieur,train,test,n_points=50):\n",
    "\n",
    "    train_test = np.vstack((train,test))\n",
    "    (min_x1,max_x1) = (min(train_test[:,0]),max(train_test[:,0]))\n",
    "    (min_x2,max_x2) = (min(train_test[:,1]),max(train_test[:,1]))\n",
    "\n",
    "    xgrid = np.linspace(min_x1,max_x1,num=n_points)\n",
    "    ygrid = np.linspace(min_x2,max_x2,num=n_points)\n",
    "\n",
    "\t# calcule le produit cartesien entre deux listes\n",
    "    # et met les resultats dans un array\n",
    "    thegrid = np.array(combine(xgrid,ygrid))\n",
    "\n",
    "    les_comptes = classifieur.compute_predictions(thegrid)\n",
    "    classesPred = np.argmax(les_comptes,axis=1)+1\n",
    "\n",
    "    # La grille\n",
    "    pylab.pcolormesh(xgrid, ygrid, classesPred.reshape((n_points, n_points)).T, alpha=.3)\n",
    "\t# Les points d'entrainment\n",
    "    pylab.scatter(train[:,0], train[:,1], c = train[:,-1], marker = 'v', s=50)\n",
    "    # Les points de test\n",
    "    pylab.scatter(test[:,0], test[:,1], c = test[:,-1], marker = 's', s=50)\n",
    "\n",
    "    ## Un petit hack, parce que la fonctionalite manque a pylab...\n",
    "    h1, = pylab.plot([min_x1], [min_x2], marker='o', c = 'w',ms=5) \n",
    "    h2, = pylab.plot([min_x1], [min_x2], marker='v', c = 'w',ms=5) \n",
    "    h3, = pylab.plot([min_x1], [min_x2], marker='s', c = 'w',ms=5) \n",
    "    handles = [h1,h2,h3]\n",
    "    ## fin du hack\n",
    "\n",
    "    labels = ['grille','train','test']\n",
    "    pylab.legend(handles,labels)\n",
    "\n",
    "    pylab.axis('equal')\n",
    "    pylab.show()\n",
    "    \n",
    "## http://code.activestate.com/recipes/302478/\n",
    "def combine(*seqin):\n",
    "    '''returns a list of all combinations of argument sequences.\n",
    "for example: combine((1,2),(3,4)) returns\n",
    "[[1, 3], [1, 4], [2, 3], [2, 4]]'''\n",
    "    def rloop(seqin,listout,comb):\n",
    "        '''recursive looping function'''\n",
    "        if seqin:                       # any more sequences to process?\n",
    "            for item in seqin[0]:\n",
    "                newcomb=comb+[item]     # add next item to current comb\n",
    "                # call rloop w/ rem seqs, newcomb\n",
    "                rloop(seqin[1:],listout,newcomb)\n",
    "        else:                           # processing last sequence\n",
    "            listout.append(comb)        # comb finished, add to list\n",
    "    listout=[]                      # listout initialization\n",
    "    rloop(seqin,listout,[])         # start recursive process\n",
    "    return listout\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entraînement sur les données 2 moons: définition d'ensembles de train et validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(732, 3)\n",
      "(368, 3)\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "ntrain = 2* (data.shape[0] // 3)\n",
    "\n",
    "inds = [i for i in range(data.shape[0])]\n",
    "np.random.seed(123)\n",
    "np.random.shuffle(inds)\n",
    "\n",
    "test_inds = inds[:ntrain]\n",
    "validation_inds = inds[ntrain:]\n",
    "\n",
    "#On définit l'ensemble d'entraînement et l'ensemble de validation\n",
    "train_data = data[test_inds,]\n",
    "validation_data = data[validation_inds,]\n",
    "print(train_data.shape)\n",
    "print(validation_data.shape)\n",
    "\n",
    "#définition de la fonction frange\n",
    "def frange(start, stop, step):\n",
    "    i = start\n",
    "    while i < stop:\n",
    "        yield i\n",
    "        i += step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On teste ici différentes combinaisons d'hyperparamètres contrôlant la capacité: nombres de neurones dans couche cachées (10, 20, 100 ou 200), valeurs des lambdas (0.1, 0.001, 0.00001, 0), et nombre d'époques (50, 100, 400, 1000). Nous affichons le taux d'erreur de classification pour chaque combinaison. Pour tester ces combinaisons, on fixe le learning rate à 0.05 et la taille des lots à 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-e76b9b7906ee>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mepoque\u001b[0m \u001b[0;32min\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m400\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1000\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m         \u001b[0mnn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNeuralNet_loop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlambdas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m         \u001b[0mnn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_data\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepoque\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.05\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     16\u001b[0m         \u001b[0merreurs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtaux_erreur\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalidation_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m         \u001b[0mj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mj\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mtrain\u001b[0;34m(self, train_data, max_iter, eta)\u001b[0m\n\u001b[1;32m     73\u001b[0m                 \u001b[0mbatch\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     74\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 75\u001b[0;31m                 \u001b[0mgrad_W1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_W2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     76\u001b[0m                 \u001b[0mloss\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mbloss\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     77\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mbprop\u001b[0;34m(self, X, Y)\u001b[0m\n\u001b[1;32m     40\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m             \u001b[0mha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mos\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     43\u001b[0m             \u001b[0mloss\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mos\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mY\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mfprop\u001b[0;34m(self, x)\u001b[0m\n\u001b[1;32m     25\u001b[0m         \u001b[0mhs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrelu\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m         \u001b[0moa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mW2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mb2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 27\u001b[0;31m         \u001b[0mos\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msoftmax_vector\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moa\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     28\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mha\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     29\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-2-79f2a6396d06>\u001b[0m in \u001b[0;36msoftmax_vector\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0mexponential\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnormalized\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mexponential\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexponential\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/home/danglewaggle/.pyenv/versions/3.5.2/lib/python3.5/site-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36msum\u001b[0;34m(a, axis, dtype, out, keepdims)\u001b[0m\n\u001b[1;32m   1846\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1847\u001b[0m         return _methods._sum(a, axis=axis, dtype=dtype,\n\u001b[0;32m-> 1848\u001b[0;31m                             out=out, **kwargs)\n\u001b[0m\u001b[1;32m   1849\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1850\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/danglewaggle/.pyenv/versions/3.5.2/lib/python3.5/site-packages/numpy/core/_methods.py\u001b[0m in \u001b[0;36m_sum\u001b[0;34m(a, axis, dtype, out, keepdims)\u001b[0m\n\u001b[1;32m     30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     31\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mumr_sum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     33\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_prod\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeepdims\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "#Optimisation des paramètres de capacité: nbre couches cachées et lambdas\n",
    "#lambdas = np.array([[0.1, 0.1],\n",
    "#       [0.1, 0.1]])\n",
    "#lambdas = np.array([[0.001, 0.001],\n",
    "#       [0.001, 0.001]])\n",
    "lambdas = np.array([[0.00001, 0.00001],\n",
    "       [0.00001, 0.00001]])\n",
    "\n",
    "erreurs = np.zeros([4,4])\n",
    "i = 0\n",
    "for C in [10, 20, 100, 200]:\n",
    "    j = 0\n",
    "    for epoque in [50, 100, 400, 1000]:\n",
    "        nn = NeuralNet_loop(2,C,2,lambdas, 100)   \n",
    "        nn.train(train_data,epoque,0.05)  \n",
    "        erreurs[i,j] = taux_erreur(nn, validation_data)\n",
    "        j = j + 1\n",
    "    i = i + 1\n",
    "print(erreurs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque que les lambdas doivent prendre des valeurs très petites pour que l'aprentissage fonctionne: à partir de 0.1 les lambdas sont déjà trop élevés et les $W_{ij}$ appris ont des valeurs trop petites. On obtient un taux d'erreur mauvais de 51.63%. Si on baisse la valeur des lambdas à 0.001 on peut obtenir des taux d'erreur jusqu'à 1.35%, et les meilleurs résultats sont obtenus en baissant lambda à 0.00001 ou à 0. Le meilleur taux d'erreur obtenu dans ces deux cas là est 0.81%\n",
    "\n",
    "On remarque qu'on peut obtenir des bon résultats, que ce soit avec 10, 20, 100 ou 200 neurones cachés. En revanche, plus le nombre de neurones dans la couche cachée est élevé, plus il faudra diminuer le nombre d'époques pour éviter l'overfitting.\n",
    "Avec 100 ou 200 neurones, le taux d'erreur est le meilleur après 400 itérations (0.81%), ensuite il remonte à 1.08%.\n",
    "\n",
    "Finalement, on constate que 50 ou 100 époques n'est pas suffisant pour diminuer le taux d'erreur (qui varie entre 9% et 20% selon le nombre de neurones dans la couche cachées). Nous avons besoin d'au moins 400 époques.\n",
    "\n",
    "Dans ce qui suit, on fixe le nombre de neurones dans la couche cachée à 20, on fixe lambda à 0.00001, et on optimise les paramètres d'optimisation. Nous testons différentes valeurs de learning rate, de taille de lot, et nous réoptimisons le nombre d'époques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-17-aff8ff84c944>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     11\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0meta\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mfrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.01\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.02\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m         \u001b[0mnn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNeuralNet_loop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlambdas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 13\u001b[0;31m         \u001b[0mnn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_data\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mepoque\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     14\u001b[0m         \u001b[0merreurs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtaux_erreur\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalidation_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     15\u001b[0m         \u001b[0mj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mj\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mtrain\u001b[0;34m(self, train_data, max_iter, eta)\u001b[0m\n\u001b[1;32m     73\u001b[0m                 \u001b[0mbatch\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     74\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 75\u001b[0;31m                 \u001b[0mgrad_W1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_W2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     76\u001b[0m                 \u001b[0mloss\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mbloss\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     77\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mbprop\u001b[0;34m(self, X, Y)\u001b[0m\n\u001b[1;32m     51\u001b[0m             \u001b[0mgrad_b1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad_ha\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 53\u001b[0;31m             \u001b[0mgrad_W1_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad_W1_mean\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mgrad_W1\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     54\u001b[0m             \u001b[0mgrad_W2_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad_W2_mean\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mgrad_W2\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     55\u001b[0m             \u001b[0mgrad_b1_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad_b1_mean\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mgrad_b1\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "#Optimisation des paramètres d'optimisation: eta et K\n",
    "lambdas = np.array([[0.00001, 0.00001],\n",
    "       [0.00001, 0.00001]])\n",
    "\n",
    "epoque = 400\n",
    "#epoque = 1000\n",
    "erreurs = np.zeros([3,5])\n",
    "i = 0\n",
    "for K in [20, 100, 200]:\n",
    "    j = 0\n",
    "    for eta in frange(0.01,0.1,0.02):\n",
    "        nn = NeuralNet_loop(2,20,2,lambdas, K)   \n",
    "        nn.train(train_data,epoque,eta)  \n",
    "        erreurs[i,j] = taux_erreur(nn, validation_data)\n",
    "        j = j + 1\n",
    "    i = i + 1\n",
    "print(erreurs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En entraînant le modèle pendant 1000 époques, on constate que pour des mini-batches de taille 20, l'erreur descend même avec des valeurs de learning rates faibles, mais elle ne descend pas plus que 1.08%. En augmentant la taille de batch à 100 ou 200, on peut obtenir des taux d'erreurs à 0.81%, et dans ce cas l'algorithme est plus sensible au learning rate $\\eta$.\n",
    "\n",
    "Lorsque la taille de lot est 100, le meilleur taux d'erreur de 0.81% est obtenu avec $\\eta$ entre 0.03 et 0.05. Lorsque la taille de lot est 200, le meilleur taux d'erreur est obtenu avec $\\eta$ = 0.05. En revanche, pour des valeurs de $\\eta$ plus faibles, le taux d'erreur remonte sensiblement. Si on prend beaucoup d'exemples par batch, il est donc crucial de ne pas choisir un learning rate trop faible, et similairement, si le batch contient peu d'exemples, le learning rate ne doit pas être trop élevé.\n",
    "\n",
    "On observe aussi en diminuant le nombre d'époques, il faut augmenter un peu le learning rate pour garder un bon taux d'erreur. Par exemple, avec 400 époques, on obtient 0.81% avec $\\eta$ = 0.07."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous affichons les régions de décisions pour plusieurs combinaisons d'hyperparamètres afin d'illustrer leur effet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bonne combinaison d hyperparamètres\n",
      "hyperparamètres: 20 neurones cachés, lambdas à 0.00001, taille de lot 100, learning rate 0.05, 1000 époques\n",
      "le taux d erreur est : 0.815217391304 %\n",
      "les régions de décisions sont:\n"
     ]
    },
    {
     "data": {
      "image/png": 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3lyEIoaKRiRD87mCtKYNzbXkC4nSCHsF6AJHY5phpfj0Q/whmIY7M2ccDqEqr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\npEm3sX37n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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff87119e390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valeur de lambdas trop élevée\n",
      "hyperparamètres: 20 neurones cachés, lambdas à 0.1, taille de lot 100, learning rate 0.05, 1000 époques\n",
      "le taux d erreur est : 51.6304347826 %\n",
      "les régions de décisions sont:\n"
     ]
    },
    {
     "data": {
      "image/png": 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S2x5FURgY+wjfffcqbQFHu3ovIrR3X0WhWFWpBdxrunYOobErqsqZU0c5c+oo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\nBn+llFIqwfw/z9QvFCA7IOYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff86f0e3080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Taille de lot trop élevée pour learning rate trop faible\n",
      "hyperparamètres: 20 neurones cachés, lambdas à 0.00001, taille de lot 200, learning rate 0.01, 1000 époques\n",
      "le taux d erreur est : 3.53260869565 %\n",
      "les régions de décisions sont:\n"
     ]
    },
    {
     "data": {
      "image/png": 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V+IMH6T99OipCE/Ahlj9k7VwXwDogaiFiet1drA29ZmT1GucmOsuVuYii5gqp7pdIqo40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\nDVlZPZk2b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8mSJbEugghCPpv4Jp9P/JLPJn7F22cT1eCvlHpLKfWVUuqUUuqAUmqRUioz\nms+0K94+COEhn018k88nfslnE7/i7bOJdst/OTAd6ANMBXoCr0b5mUIIIYQIoUU0b661/pPX4V6l\n1KPAG0opp9a6JprPFkIIIURgTTbmr5RqC8wG1kjgF0IIIWInqi1/AHdr/3YgBfgImBTi9FYAW7Zs\niXaxKCsro6ioKOrPEeGTzya+yecTv+SziV9N8dl4xc5W9Z2rtNZh3Vwp9TvgvhCnaKCf1nq7+/y2\nQFugG/BroFxrHbACoJSaBbwUVoGEEEII4W221vqfoU6IJPi3A9rVc9qXWuvqANd2BvYCI7TWnwS5\n92XAbuB0WAUTQgghElsroDvwvta6NNSJYQf/hlBKdcUE9lytdUGTPVgIIYQQtaIW/JVSw4DhwGrg\nGNALeBjoAGRrraui8mAhhBBChBTNbP9TmLn9/wW2An8FPsO0+iXwCyGEEDHSpN3+QgghhIi9hF3b\nXwghhEhUEvyFEEKIBCPB300pdY5S6jOllEspNTDW5RGglOqmlPqbUupLpdRJpdQOpdSDSqmWsS5b\nIlJK3aaU2uXeqOtjd1KviDGl1C+UUuuUUuVKqUNKqTeUUn1iXS5Rl/uzcimlnoh1WST4ezwG7MMs\nUiTiQ19AATcD/YG7gFuAR2JZqESklLoOeByzUNcg4HPgfaVU+5gWTACMBv4M5ADjgZZAnlIqOaal\nEj7cleWbMf93Yk4S/gCl1BXAH4FpQAlwkdZ6Y2xLJQJRSt0N3KK17hXrsiQSpdTHwCda65+5jxVm\nwa6ntNaPxbRwwoe7QnYYGKO1Xh3r8ghQSqUBhcCtwAPABq31/FiWKeFb/kqp84C/AHMw0xNFfMsA\njsa6EInEPcwyBPjQek2bVsN/gRGxKpcIKgPTgyn/T+LHM8A7WuvlsS6IJeob+zQD/wAWaq03KKW6\nxbowIjilVC/MJlExrTEnoPaAEzjk9/oh4IKmL44Ixt0jswBYrbUuiXV5BCilZgAXAUNjXRZvZ2XL\nXyn1O3dSRbCvGqVUH6XU/wDpwO+tS2NY7IRh9/Pxu6Yz8C7wstb6udiUXPhRSI5MvFmIyY+ZEeuC\nCFBKdcFUxubE2+J2Z+WYv83Nh3YBr1B3i2EnUA28pLW+IQrFS3jhbg6llMoC8oG18pk0PXe3/0lg\nmtb6ba/XnwfO1VpPiVXZhIdS6mngKmC01npPrMsjQCl1NfAvoAZP49KJqTTXAEk6RkH4rAz+drlr\nZa29XsoC3sck/q3TWh+IScFELXeLfzmwHpgbq/8oiS5Iwt8eTMLfH2JaOGEF/quBsVrrL2NdHmEo\npVIx29l7ex7YAjyqtd7S5IVyS+gxf631Pu9jpVQFpnb2pQT+2FNKZQIrMDtB3gt0NDEHtNb+488i\nup4AXlBKFQLrMNMuUzC/yEQMKaUWAjOByUCFO4kZoExrLVujx5DWugIzg6yWO86UxjLwQ4IH/yCk\nZRk/JgA93F973a9Z48zOWBUqEWmtX3FPIXsYOA+zSddlWutvYlsygVn7QmMqyt5uABY1eWlEfeIi\nxiR0t78QQgiRiM7KbH8hhBBCBCfBXwghhEgwEvyFEEKIBCPBXwghhEgwEvyFEEKIBCPBXwghhEgw\nEvyFEEKIBCPBXwghhEgwEvyFEEKIBCPBXwghhEgwEvyFEEKIBPP/NWVj9wgBonwAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff86f067e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de neurones dans couche cachées trop élevé amenant à léger sur-apprentissage\n",
      "hyperparamètres: 100 neurones cachés, lambdas à 0.00001, taille de lot 100, learning rate 0.05, 1000 époques\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-18-61bd8d4653cd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     34\u001b[0m        [0.0001, 0.0001]])\n\u001b[1;32m     35\u001b[0m \u001b[0mnn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNeuralNet_loop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlambdas\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 36\u001b[0;31m \u001b[0mnn\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain_data\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.05\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     37\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'le taux d erreur est :'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtaux_erreur\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalidation_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m'%'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'les régions de décisions sont:'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mtrain\u001b[0;34m(self, train_data, max_iter, eta)\u001b[0m\n\u001b[1;32m     73\u001b[0m                 \u001b[0mbatch\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     74\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 75\u001b[0;31m                 \u001b[0mgrad_W1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_W2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbloss\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     76\u001b[0m                 \u001b[0mloss\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mbloss\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     77\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-11-a5db753c189d>\u001b[0m in \u001b[0;36mbprop\u001b[0;34m(self, X, Y)\u001b[0m\n\u001b[1;32m     45\u001b[0m             \u001b[0mgrad_oa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mos\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0monehot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_o\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     46\u001b[0m             \u001b[0mgrad_b2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad_oa\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 47\u001b[0;31m             \u001b[0mgrad_W2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mouter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrad_oa\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     48\u001b[0m             \u001b[0mgrad_hs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mW2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrad_oa\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     49\u001b[0m             \u001b[0mgrad_ha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad_hs\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mha\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/danglewaggle/.pyenv/versions/3.5.2/lib/python3.5/site-packages/numpy/core/numeric.py\u001b[0m in \u001b[0;36mouter\u001b[0;34m(a, b, out)\u001b[0m\n\u001b[1;32m   1091\u001b[0m     \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1092\u001b[0m     \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0masarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1093\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mmultiply\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mravel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnewaxis\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mravel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnewaxis\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1094\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1095\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "print('Bonne combinaison d hyperparamètres')\n",
    "print('hyperparamètres: 20 neurones cachés, lambdas à 0.00001, taille de lot 100, learning rate 0.05, 1000 époques')\n",
    "lambdas = np.array([[0.0001, 0.0001],\n",
    "       [0.0001, 0.0001]])\n",
    "nn = NeuralNet_loop(2,20,2,lambdas, 100)   \n",
    "nn.train(train_data,1000,0.05) \n",
    "print('le taux d erreur est :', taux_erreur(nn, validation_data),'%')\n",
    "print('les régions de décisions sont:')\n",
    "gridplot(nn, train_data, validation_data, 50)\n",
    "\n",
    "print('Valeur de lambdas trop élevée')\n",
    "print('hyperparamètres: 20 neurones cachés, lambdas à 0.1, taille de lot 100, learning rate 0.05, 1000 époques')\n",
    "lambdas = np.array([[0.1, 0.1],\n",
    "       [0.1, 0.1]])\n",
    "nn = NeuralNet_loop(2,20,2,lambdas, 100)   \n",
    "nn.train(train_data,1000,0.05) \n",
    "print('le taux d erreur est :', taux_erreur(nn, validation_data),'%')\n",
    "print('les régions de décisions sont:')\n",
    "gridplot(nn, train_data, validation_data, 50)\n",
    "\n",
    "print('Taille de lot trop élevée pour learning rate trop faible')\n",
    "print('hyperparamètres: 20 neurones cachés, lambdas à 0.00001, taille de lot 200, learning rate 0.01, 1000 époques')\n",
    "lambdas = np.array([[0.0001, 0.0001],\n",
    "       [0.0001, 0.0001]])\n",
    "nn = NeuralNet_loop(2,20,2,lambdas, 100)   \n",
    "nn.train(train_data,1000,0.01) \n",
    "print('le taux d erreur est :', taux_erreur(nn, validation_data),'%')\n",
    "print('les régions de décisions sont:')\n",
    "gridplot(nn, train_data, validation_data, 50)\n",
    "\n",
    "print('Nombre de neurones dans couche cachées trop élevé amenant à léger sur-apprentissage')\n",
    "print('hyperparamètres: 100 neurones cachés, lambdas à 0.00001, taille de lot 100, learning rate 0.05, 1000 époques')\n",
    "lambdas = np.array([[0.0001, 0.0001],\n",
    "       [0.0001, 0.0001]])\n",
    "nn = NeuralNet_loop(2,100,2,lambdas, 100)   \n",
    "nn.train(train_data,1000,0.05) \n",
    "print('le taux d erreur est :', taux_erreur(nn, validation_data),'%')\n",
    "print('les régions de décisions sont:')\n",
    "gridplot(nn, train_data, validation_data, 50)\n",
    "\n",
    "print('Nombre d époques trop faible, arrêt trop prématuré de l apprentissage')\n",
    "print('hyperparamètres: 100 neurones cachés, lambdas à 0.00001, taille de lot 100, learning rate 0.05, 50 époques')\n",
    "lambdas = np.array([[0.0001, 0.0001],\n",
    "       [0.0001, 0.0001]])\n",
    "nn = NeuralNet_loop(2,100,2,lambdas, 100)   \n",
    "nn.train(train_data,50,0.05) \n",
    "print('le taux d erreur est :', taux_erreur(nn, validation_data),'%')\n",
    "print('les régions de décisions sont:')\n",
    "gridplot(nn, train_data, validation_data, 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Implémentation du calcul de gradient avec expressions matricielles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ici, on va représenter nos données par une matrice $\\mathbf{X}$ de dimension $n \\times d$  où chaque ligne de la matrice est un exemple $\\mathbf{x}^{(i)}$. On définit une matrice $\\mathbf{B}^{(1)}$ où chaque colonne est une copie du vecteur $\\mathbf{b}^{(1)}$. On applique donc l'équation suivante pour calculer $\\mathbf{h}^{a}$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\mathbf{W}^{(1)} \\in \\mathbb{R}^{d_h \\times d}, \\;\\; \\mathbf{X} \\in \\mathbb{R}^{n \\times d} \\;$ et $\\;\\mathbf{B}^{(1)} \\in \\mathbb{R}^{d_h \\times n}$\n",
    "\n",
    "$$\\mathbf{h}^{a} = \\mathbf{W}^{(1)}\\mathbf{X}^{\\top} + \\mathbf{B}^{(1)} \\in \\mathbb{R}^{d_h \\times n}$$\n",
    "\n",
    "Remarquez qu'avec numpy nous n'avons pas besoin de recopier le vecteur $\\mathbf{b}^{(1)}$ n fois. Nous pouvons simplement faire la somme de chaque colonnes de $\\mathbf{X}$ avec le vecteur colonne $\\mathbf{b}^{(1)}$:\n",
    "\n",
    "```self.W1.dot(X.T) + self.b1.reshape(self.n_h, 1)```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alors $\\mathbf{h}^{a}$ sera une matrice de dimension $d_h \\times n$ où chaque colonne $j$ est le vecteur de preactivation des neuronnes de la couche cachée pour le $j^{ieme}$ exemple. Ensuite, pour le calcul, $\\mathbf{h}^s$ on applique la fonction relu$(\\mathbf{h}^{a})$ qui retourne une matrice  de dimension $d_h \\times n$ où la colonne $j$ est le vecteur de sortie des neuronnes de la couche cachée qui correspond au $j^{ieme}$ exemple d'entraînement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Pour le calcule de $\\mathbf{o}^a$, on applique le même principe:\n",
    "\n",
    "$\\mathbf{W}^{(2)} \\in \\mathbb{R}^{m \\times d_h}, \\;\\; \\mathbf{h}^{s} \\in \\mathbb{R}^{d_h \\times n} \\;$ et $\\;\\mathbf{B}^{(2)} \\in \\mathbb{R}^{m \\times n}$\n",
    "\n",
    "$$\\mathbf{o}^{a} = \\mathbf{W}^{(2)}\\mathbf{h}^{s} + \\mathbf{B}^{(2)} \\in \\mathbb{R}^{m \\times n}$$\n",
    "et,\n",
    "$$\\mathbf{o}^{s} = \\text{softmax}(\\mathbf{o}^{a}) \\in \\mathbb{R}^{m \\times n}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "où la colonne $j$ de $\\mathbf{o}^a$ est le vecteur de preactivation de la couche cachee pour le $j^{ieme}$ exemple de notre ensemble d'entraînement. Pour la matrice $\\mathbf{o}^{s}$, chaque colonne correspond au vecteur de sortie pour chaque exemple."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour le calcul des gradient, on a:\n",
    "$$\\mathbf{Y} \\in \\mathbb{R}^{n}$$ est un vecteur où chaque composante est la classes de l'exemple d'entraînement coresspondant. On redéfinit la fonction onehot pour l'appliquer sur le vecteur $\\mathbf{Y}$. Cette nouvelle fonction va retourner une matrice ou chaque colonne est le vecteur onehot qui correspond chaque composante.\n",
    "\n",
    "$$\\nabla_{\\mathbf{o}^a} = \\mathbf{o}^s - \\text{onehot}(\\mathbf{Y}) \\in \\mathbb{R}^{m \\times n}$$\n",
    "\n",
    "\n",
    "$$\\nabla_{\\mathbf{B}^{(2)}} = \\nabla_{\\mathbf{o}^a} \\in \\mathbb{R}^{m \\times n}$$\n",
    "\n",
    "\n",
    "$$\\sum_{\\mathbf{W}^{(2)}} = \\nabla_{\\mathbf{W}^{(2)}} = \\mathbf{W}^{(2)^{\\top}} \\nabla_{\\mathbf{o}^a} \\in \\mathbb{R}^{m \\times n}$$\n",
    "\n",
    "Correspond a la sommes des gradients par rapport a $\\mathbf{W}^{(2)}$ sur tout l'ensemble d'entraînement\n",
    "\n",
    "\n",
    "$$\\sum_{\\mathbf{W}^{(1)}} = \\nabla_{\\mathbf{W}^{(1)}} = \\mathbf{h}^{a} \\mathbf{X} \\in \\mathbb{R}^{d_h \\times n}$$\n",
    "\n",
    "\n",
    "$$\\nabla_{\\mathbf{B}^{(1)}} = \\nabla_{\\mathbf{h}^a} \\in \\mathbb{R}^{d_h \\times n}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class NeuralNetVectorized:\n",
    "    \n",
    "    def __init__(self, n_input, n_hidden, n_out, lambdas, K=1):\n",
    "        \n",
    "        self.n_in = n_input\n",
    "        self.n_h = n_hidden\n",
    "        self.n_o = n_out\n",
    "        self.lambdas = lambdas\n",
    "        self.K = K\n",
    "        \n",
    "        low_bound = -1 / np.sqrt([self.n_in, self.n_h])\n",
    "        up_bound = 1 / np.sqrt([self.n_in, self.n_h])\n",
    "        \n",
    "        # Initialize the parameters\n",
    "        np.random.seed(123)\n",
    "        self.W1 = np.random.uniform(low_bound[0], up_bound[0], size=(self.n_h, self.n_in))  # d_h x d\n",
    "        self.W2 = np.random.uniform(low_bound[1], up_bound[1], size=(self.n_o, self.n_h))  # m x d_h\n",
    "        self.b1 = np.zeros(self.n_h)  # dimension d_h\n",
    "        self.b2 = np.zeros(self.n_o) # dimension m\n",
    "    \n",
    "    def fprop(self, X):\n",
    "        '''\n",
    "        Computes activations for every layer\n",
    "        X: input data set\n",
    "        '''\n",
    "        self.ha = self.W1.dot(X.T) + self.b1.reshape(self.n_h, 1)\n",
    "        self.hs = relu(self.ha)\n",
    "        self.oa = self.W2.dot(self.hs) + self.b2.reshape(self.n_o, 1)\n",
    "        self.os = np.transpose(softmax(self.oa.T))\n",
    "            \n",
    "    def bprop(self, X, Y):\n",
    "        '''\n",
    "        Computes the gradients, must be executed after fprop\n",
    "        X: Input data set\n",
    "        Y: targets\n",
    "        '''\n",
    "        n = X.shape[0]\n",
    "                      \n",
    "        grad_oa = self.os - onehot_matrix(self.n_o, Y)\n",
    "        grad_b2 = np.sum(grad_oa, axis =1) # sum of b2 vectors on all training examples (m x 1)\n",
    "        grad_W2 = np.dot(grad_oa, self.hs.T) # sum of gradients grad_W2 for each example\n",
    "        grad_hs = self.W2.T.dot(grad_oa) # d_h x n\n",
    "        grad_ha = grad_hs * (self.ha > 0) # d_h x n\n",
    "        grad_W1 = np.dot(grad_ha, X) # sum of gradients grad_W1 for each example\n",
    "        grad_b1 = np.sum(grad_ha, axis =1) # sum of b1 vectors on all training examples (d_h x 1)\n",
    "        \n",
    "        return grad_W1 / n, grad_W2 / n, grad_b1 / n, grad_b2 / n #returns average of the gradient\n",
    "    \n",
    "    def compute_loss(self, Y):\n",
    "        loss = 0\n",
    "        for i in range(Y.shape[0]):\n",
    "            loss = loss -np.log(self.os[Y[i],i])\n",
    "        return loss\n",
    "    \n",
    "    def train(self, train_data, max_iter, eta=0.05):\n",
    "        \n",
    "        n_batches = int(np.ceil(train_data.shape[0]/self.K)) # number of batches\n",
    "        \n",
    "        for i in range(max_iter):\n",
    "            for j in range(0,train_data.shape[0],self.K):\n",
    "                batch = train_data[j:j+self.K]\n",
    "                \n",
    "                self.fprop(batch[:,:-1])\n",
    "                grad_W1_mean, grad_W2_mean, grad_b1_mean, grad_b2_mean = self.bprop(batch[:,:-1], batch[:,-1]) \n",
    "                \n",
    "                n = len(batch)\n",
    "                \n",
    "                #regularization\n",
    "                penality_grad_W1 = self.lambdas[0][0] * np.sign(self.W1) + 2 * self.lambdas[0][1] * self.W1\n",
    "                penality_grad_W2 = self.lambdas[1][0] * np.sign(self.W2) + 2 * self.lambdas[1][1] * self.W2\n",
    "                \n",
    "                self.W1 = self.W1 - eta * (grad_W1_mean + penality_grad_W1)\n",
    "                self.W2 = self.W2 - eta * (grad_W2_mean + penality_grad_W2)\n",
    "                self.b1 = self.b1 - eta * grad_b1_mean\n",
    "                self.b2 = self.b2 - eta * grad_b2_mean\n",
    "                    \n",
    "    def compute_predictions(self, test_data):\n",
    "        self.fprop(test_data)\n",
    "        pred = self.os\n",
    "\n",
    "        return pred\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 7. Comparaison du gradient des deux implémentations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Différence entre les deux gradients pour W1, W2, b1, b2 lorsque la taille du lot est  1\n",
      "[[ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[[ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[ 1.  1.]\n",
      "[ 1.  1.]\n",
      "Différence entre les deux gradients pour W1, W2, b1, b2 lorsque la taille du lot est  10\n",
      "[[ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[[ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[ 1.  1.]\n",
      "[ 1.  1.]\n"
     ]
    }
   ],
   "source": [
    "#initialize a neural network of each implementation, with K=1 and K=10\n",
    "for K in range(1,11,9):\n",
    "    lambdas = np.array([[0, 0],\n",
    "           [0, 0]])\n",
    "    nn_loop = NeuralNet_loop(2,2,2,lambdas, K)\n",
    "    nn_matrix = NeuralNetVectorized(2,2,2,lambdas,K)\n",
    "    \n",
    "    #gradient with loop implementation\n",
    "    grad_W1_loop, grad_W2_loop, grad_b1_loop, grad_b2_loop, _ = nn_loop.bprop(train_data[:,:-1],train_data[:,-1])\n",
    "    \n",
    "    #gradient with matrix multiplications implementation\n",
    "    nn_matrix.fprop(train_data[:,:-1])\n",
    "    grad_W1_mat, grad_W2_mat, grad_b1_mat, grad_b2_mat = nn_matrix.bprop(train_data[:,:-1],train_data[:,-1])\n",
    "    \n",
    "    #print comparison of all gradients\n",
    "    print('Différence entre les deux gradients pour W1, W2, b1, b2 lorsque la taille du lot est ', K)\n",
    "    print(grad_W1_loop / grad_W1_mat)\n",
    "\n",
    "    print(grad_W2_loop / grad_W2_mat)\n",
    "\n",
    "    print(grad_b1_loop / grad_b1_mat)\n",
    "\n",
    "    print(grad_b2_loop / grad_b2_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remaque que les parametre calculé par descente de gradient avec les deux modèles on un ratio de 1 (i.e.: ils sont egale)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Comparaison du temps de calcul pour une époque quand K=100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fetch MNIST dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7ff86babfc50>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff8a3b0b5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata('mnist-original')\n",
    "#mnist = fetch_mldata('mnist-original', data_home='/u/dift3395/sklearn_data')\n",
    "\n",
    "plt.imshow(mnist.data[21455,:].reshape(28, 28), interpolation=\"nearest\", cmap='Greys')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diviser le dataset MNIST en ensembles train, valid et test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(70000, 784)\n"
     ]
    }
   ],
   "source": [
    "indices = np.random.permutation(len(mnist['target']))\n",
    "\n",
    "print(mnist['data'].shape)\n",
    "\n",
    "X_train = mnist['data'][indices][:50000]/255.\n",
    "X_valid = mnist['data'][indices][50000:60000]/255.\n",
    "X_test = mnist['data'][indices][60000:]/255.\n",
    "y_train = mnist['target'][indices][:50000]\n",
    "y_valid = mnist['target'][indices][50000:60000]\n",
    "y_test = mnist['target'][indices][60000:]\n",
    "\n",
    "#from keras.utils import np_utils\n",
    "#y_train = np_utils.to_categorical(y_train)\n",
    "#y_valid = np_utils.to_categorical(y_valid)\n",
    "#y_test = np_utils.to_categorical(y_test)\n",
    "\n",
    "#concatenate data and target into one np.array\n",
    "train = np.concatenate((X_train, np.reshape(y_train, (50000,1))), axis=1)\n",
    "valid = np.concatenate((X_valid, np.reshape(y_valid, (10000,1))), axis=1)\n",
    "test = np.concatenate((X_test, np.reshape(y_test, (10000,1))), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- 18.6254301071167 seconds ---\n",
      "--- 1.6593289375305176 seconds ---\n"
     ]
    }
   ],
   "source": [
    "#initializing neural networks\n",
    "nn_loop = NeuralNet_loop(784,20,10,lambdas,100)\n",
    "nn_matrix = NeuralNetVectorized(784,20,10,lambdas,100)\n",
    "\n",
    "#train both neural networks\n",
    "import time\n",
    "start_time = time.time()\n",
    "nn_loop.train(train,1,0.05)\n",
    "print(\"--- %s seconds ---\" % (time.time() - start_time))\n",
    "\n",
    "start_time = time.time()\n",
    "nn_matrix.train(train,1,0.05)\n",
    "print(\"--- %s seconds ---\" % (time.time() - start_time))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On voit que l'implementation avec le calcul matriciel du gradient est plus rapide par un facteur 10 que l'implementation avec boucle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Calcul de taux d'erreur de classification sur MNIST"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modification de la classe NeuralNetworkVectorized pour calculer les valeurs recherchées à chaque époque de la phase l'entraînement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class NeuralNetVectorized2:\n",
    "    \n",
    "    def __init__(self, n_input, n_hidden, n_out, lambdas, K=1):\n",
    "        \n",
    "        self.n_in = n_input\n",
    "        self.n_h = n_hidden\n",
    "        self.n_o = n_out\n",
    "        self.lambdas = lambdas\n",
    "        self.K = K\n",
    "        \n",
    "        low_bound = -1 / np.sqrt([self.n_in, self.n_h])\n",
    "        up_bound = 1 / np.sqrt([self.n_in, self.n_h])\n",
    "        \n",
    "        # Initialize the parameters\n",
    "        np.random.seed(123)\n",
    "        self.W1 = np.random.uniform(low_bound[0], up_bound[0], size=(self.n_h, self.n_in))  # d_h x d\n",
    "        self.W2 = np.random.uniform(low_bound[1], up_bound[1], size=(self.n_o, self.n_h))  # m x d_h\n",
    "        self.b1 = np.zeros(self.n_h)  # dimension d_h\n",
    "        self.b2 = np.zeros(self.n_o) # dimension m\n",
    "    \n",
    "    def fprop(self, X):\n",
    "        '''\n",
    "        Computes activations for every layer\n",
    "        X: input data set\n",
    "        '''\n",
    "        self.ha = self.W1.dot(X.T) + self.b1.reshape(self.n_h, 1)\n",
    "        self.hs = relu(self.ha)\n",
    "        self.oa = self.W2.dot(self.hs) + self.b2.reshape(self.n_o, 1)\n",
    "        self.os = np.transpose(softmax(self.oa.T))\n",
    "            \n",
    "    def bprop(self, X, Y):\n",
    "        '''\n",
    "        Computes the gradients, must be executed after fprop\n",
    "        X: Input data set\n",
    "        Y: targets\n",
    "        '''\n",
    "        n = X.shape[0]\n",
    "                      \n",
    "        grad_oa = self.os - onehot_matrix(self.n_o, Y)\n",
    "        grad_b2 = np.sum(grad_oa, axis =1) # m x n\n",
    "        grad_W2 = np.dot(grad_oa, self.hs.T) # sum of gradients grad_W2 for each example\n",
    "        grad_hs = self.W2.T.dot(grad_oa) # d_h x n\n",
    "        grad_ha = grad_hs * (self.ha > 0) # d_h x n\n",
    "        grad_W1 = np.dot(grad_ha, X) # sum of gradients grad_W1 for each example\n",
    "        grad_b1 = np.sum(grad_ha, axis =1) # d_h x n\n",
    "        \n",
    "        return grad_W1 / n, grad_W2 / n, grad_b1 / n, grad_b2 / n #returns average of the gradient\n",
    "    \n",
    "    def compute_loss(self, Y):\n",
    "        ind = [i for i in range(Y.shape[0])]\n",
    "        loss = self.os[Y.astype(int),ind]\n",
    "        return np.mean(-np.log(loss))\n",
    "    \n",
    "    def train(self, train_data, valid_data, test_data, max_iter, eta=0.05):\n",
    "        \n",
    "        n_batches = int(np.ceil(train_data.shape[0]/self.K)) # number of batches\n",
    "        \n",
    "        for i in range(max_iter):\n",
    "            for j in range(0,train_data.shape[0],self.K):\n",
    "                batch = train_data[j:j+self.K]\n",
    "                \n",
    "                self.fprop(batch[:,:-1])\n",
    "                grad_W1_mean, grad_W2_mean, grad_b1_mean, grad_b2_mean = self.bprop(batch[:,:-1], batch[:,-1]) \n",
    "                \n",
    "                n = len(batch)\n",
    "                \n",
    "                #regularization\n",
    "                penality_grad_W1 = self.lambdas[0][0] * np.sign(self.W1) + 2 * self.lambdas[0][1] * self.W1\n",
    "                penality_grad_W2 = self.lambdas[1][0] * np.sign(self.W2) + 2 * self.lambdas[1][1] * self.W2\n",
    "                \n",
    "                self.W1 = self.W1 - eta * (grad_W1_mean + penality_grad_W1)\n",
    "                self.W2 = self.W2 - eta * (grad_W2_mean + penality_grad_W2)\n",
    "                self.b1 = self.b1 - eta * grad_b1_mean\n",
    "                self.b2 = self.b2 - eta * grad_b2_mean\n",
    "                    \n",
    "            self.write_in_file(i,train_data, valid_data, test_data)\n",
    "                    \n",
    "    def compute_predictions(self, test_data):\n",
    "        self.fprop(test_data)\n",
    "        pred = self.os\n",
    "        return pred\n",
    "    \n",
    "    def write_in_file(self,epoque,train_data,valid_data,test_data):\n",
    "        train_prob = self.compute_predictions(train_data[:,:-1])\n",
    "        train_classe_pred = np.argmax(train_prob, axis = 0)  \n",
    "        valid_prob = self.compute_predictions(valid_data[:,:-1])\n",
    "        valid_classe_pred = np.argmax(valid_prob, axis = 0)\n",
    "        test_prob = self.compute_predictions(test_data[:,:-1])\n",
    "        test_classe_pred = np.argmax(test_prob, axis = 0)\n",
    "        classif_erreur_train = 100*float(sum(sum([train_classe_pred != train_data[:,-1]])))/train_data.shape[0]\n",
    "        classif_erreur_valid = 100*float(sum(sum([valid_classe_pred != valid_data[:,-1]])))/valid_data.shape[0]\n",
    "        classif_erreur_test = 100*float(sum(sum([test_classe_pred != test_data[:,-1]])))/test_data.shape[0]\n",
    "        self.fprop(train_data[:,:-1])\n",
    "        loss_train = self.compute_loss(train_data[:,-1])\n",
    "        self.fprop(valid_data[:,:-1])\n",
    "        loss_valid = self.compute_loss(valid_data[:,-1])\n",
    "        self.fprop(test_data[:,:-1])\n",
    "        loss_test = self.compute_loss(test_data[:,-1])\n",
    "        \n",
    "        # Enregistre dans le fichier les résultats a chaque epoque.\n",
    "        # file : les résultat sont écrit de facon compréhensible\n",
    "        # fileforgraph pour realiser les graphiques\n",
    "        if epoque==0: # Ecrase le fichier s'il existe\n",
    "            file=open(\"Question_9.txt\",\"w\")\n",
    "            file_forgraph=open(\"Question_9_forgraph.txt\",\"w\")\n",
    "        else: # ecrit en bas du fichier\n",
    "            file = open(\"Question_9.txt\", \"a\")\n",
    "            file_forgraph=open(\"Question_9_forgraph.txt\",\"a\")\n",
    "        toprint= 'Epoque %d,ERREUR - train : %f, valid : %f, test :%f,\\\n",
    "        COUT MOYEN train : %f, valid : %f, test: %f'\\\n",
    "        % (epoque+1,classif_erreur_train,classif_erreur_valid,classif_erreur_test,\\\n",
    "        loss_train, loss_valid, loss_test)\n",
    "        \n",
    "        toprint_forgraph  = '%d %f %f %f %f %f %f' % (epoque+1,classif_erreur_train,classif_erreur_valid,\n",
    "                                                      classif_erreur_test,loss_train, loss_valid, loss_test)\n",
    "        # Ecriture dans les fichiers\n",
    "        file.write(toprint)\n",
    "        file_forgraph.write(toprint_forgraph)\n",
    "        \n",
    "        file.close()\n",
    "        file_forgraph.close()\n",
    "        #Afficher les résultats pour la recherche des meilleur parametre\n",
    "        print ('Epoque : %d Erreur sur le valid : %f' % (epoque+1,classif_erreur_valid))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Question 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoque : 1 Erreur sur le valid : 4.700000\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-33-170dbfe3c53f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m                     [0.00, 0.00]])\n\u001b[1;32m      3\u001b[0m \u001b[0mnn_mnist\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mNeuralNetVectorized2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m784\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m256\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlambdas\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mnn_mnist\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrain\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalid\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtest\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0meta\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.25\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-30-3306c0bf931d>\u001b[0m in \u001b[0;36mtrain\u001b[0;34m(self, train_data, valid_data, test_data, max_iter, eta)\u001b[0m\n\u001b[1;32m     60\u001b[0m                 \u001b[0mbatch\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_data\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mK\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     61\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 62\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     63\u001b[0m                 \u001b[0mgrad_W1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_W2_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b1_mean\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrad_b2_mean\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbprop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-30-3306c0bf931d>\u001b[0m in \u001b[0;36mfprop\u001b[0;34m(self, X)\u001b[0m\n\u001b[1;32m     24\u001b[0m         \u001b[0mX\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0minput\u001b[0m \u001b[0mdata\u001b[0m \u001b[0mset\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m         '''\n\u001b[0;32m---> 26\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mha\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mW1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mb1\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_h\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrelu\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mha\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mW2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mb2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_o\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "lambdas = np.array([[0.0, 0.0],\n",
    "                    [0.00, 0.00]])\n",
    "nn_mnist = NeuralNetVectorized2(784,256,10,lambdas,50)\n",
    "nn_mnist.train(train, valid, test, 20,eta=0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cc+y+aKiIiDSI/fbzB/l47yOOvv32W0pLS9lnn30q3WdmtGjRAvD9KH7zm98w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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff86bad27b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iIZy0xvB6OqJhLjAKOC1K9YVE9JwAgyuTcDhWl62O9qVERER2CfGwCVsJ0ADk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\nmUka1f9bIQomo4Ej3H1R1u5ZhCkh4v2+J/BZogk0JS86AZ1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff86ba0f908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Graphique de l'erreur de classification et du cout sur mnist a partir des \n",
    "import matplotlib.pyplot as plt\n",
    "data=np.loadtxt(open('Question_9_forgraph.txt','r'))\n",
    "epoque=data[:,0]\n",
    "erreur_train=data[:,1]\n",
    "erreur_valid=data[:,2]\n",
    "erreur_test=data[:,3]\n",
    "cout_train=data[:,4]\n",
    "cout_valid=data[:,5]\n",
    "cout_test=data[:,6]\n",
    "plt.plot(epoque, erreur_train,label='train')\n",
    "plt.plot(epoque, erreur_valid, label='valid')\n",
    "plt.plot(epoque, erreur_test,label='test')\n",
    "plt.legend()\n",
    "plt.xlabel('epoque')\n",
    "plt.ylabel('erreur en %')\n",
    "plt.title('Taux d erreur de Classification')\n",
    "plt.show()\n",
    "plt.plot(epoque, cout_train,label='train')\n",
    "plt.plot(epoque, cout_valid, label='valid')\n",
    "plt.plot(epoque, cout_test,label='test')\n",
    "plt.legend()\n",
    "plt.xlabel('epoque')\n",
    "plt.ylabel('cout')\n",
    "plt.title('Cout')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec la meilleure configuration obtenue pour les hyperparametres (256 neurones dans la couche cachee, lambdas = 0, taille de lot = 50, learning rate = 0.25) voit que l erreur de classification de l ensemble de validation diminue beaucoup les 15 premieres epoques puis se stabilise un peu au dessus de 2%. Cela semble optimal d arreter l entrainement apres environ 20 epoques selon l erreur sur l ensemble de validation. L erreur sur l ensemble de test pour cette configuration des hyperparametres est legerement inferieure a celle de validation et est 1.97%. Mais il y a probablement un facteur aleatoire du a la selection random des indices des ensembles train, valid et test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}