08. Practical_NeuralNets.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/WRr2e7mKCUY\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1046e86a0>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# see the actual derivation of these equations \n",
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"WRr2e7mKCUY\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Implementation of Neural Networks\n",
    "\n",
    "We define a new objective function as:\n",
    "\n",
    "$$ J(\\mathbf{W})=-[\\mathbf{y}^{(i)}\\ln[\\mathbf{a}^{(L)}]^{(i)}+(1-\\mathbf{y}^{(i)})\\ln(1-[\\mathbf{a}^{(L)}]^{(i)}) ]$$\n",
    "\n",
    "Notice that this is highly similar to the log-likelihood we derived for logistic regression.\n",
    "\n",
    "Such that the new update for the final layer becomes:\n",
    "\n",
    "$$ \\left[\\frac{\\partial J(\\mathbf{W})}{\\mathbf{z}^{(L)}}\\right]^{(i)} = ([\\mathbf{a}^{(L+1)}]^{(i)}- \\mathbf{y}^{(i)}) $$\n",
    "\n",
    "$$ \\left[\\frac{\\partial J(\\mathbf{W})}{\\mathbf{z}^{(2)}}\\right]^{(i)} = ([\\mathbf{a}^{(3)}]^{(i)}- \\mathbf{y}^{(i)})$$\n",
    "\n",
    "And this is straight forward to convert to vectorized math for the sensitivity:\n",
    "\n",
    "$$ \\mathbf{V}^{(2)} = \\mathbf{A}^{(3)}-\\mathbf{Y} $$\n",
    "\n",
    "You can verify this via the derivation here: ![CrossEntropyDerivation](PDF_Slides/CrossEntropy.pdf)\n",
    "\n",
    "Another option is to choose the softmax, which is defined as:\n",
    "\n",
    "$$  a_j^{(L+1)} = \\frac{\\exp(z_j^{(L)})}{\\sum_i \\exp(z_i^{(L)})}  $$\n",
    "\n",
    "However, it has an identical update equation as the sigmoid final layer using cross entropy. We will stick with cross entropy in order to keep the consistency to previous feedforward code. However, please note that that sigmoid activation functions are more susceptible to gradient instability. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example adapted from https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch12/ch12.ipynb\n",
    "# Original Author: Sebastian Raschka\n",
    "\n",
    "# This is the optional book we use in the course, excellent intuitions and straightforward programming examples\n",
    "# please note, however, that this code has been manipulated to reflect our assumptions and notation.\n",
    "import numpy as np\n",
    "from scipy.special import expit\n",
    "import pandas as pd\n",
    "import sys\n",
    "\n",
    "# start with a simple base classifier, which can't be fit or predicted\n",
    "# it only has internal classes to be used by classes that will subclass it\n",
    "class TwoLayerPerceptronBase(object):\n",
    "    def __init__(self, n_hidden=30,\n",
    "                 C=0.0, epochs=500, eta=0.001, random_state=None):\n",
    "        np.random.seed(random_state)\n",
    "        self.n_hidden = n_hidden\n",
    "        self.l2_C = C\n",
    "        self.epochs = epochs\n",
    "        self.eta = eta\n",
    "        \n",
    "    @staticmethod\n",
    "    def _encode_labels(y):\n",
    "        \"\"\"Encode labels into one-hot representation\"\"\"\n",
    "        onehot = pd.get_dummies(y).values.T\n",
    "            \n",
    "        return onehot\n",
    "\n",
    "    def _initialize_weights(self):\n",
    "        \"\"\"Initialize weights with small random numbers.\"\"\"\n",
    "        W1_num_elems = (self.n_features_ + 1)*self.n_hidden\n",
    "        W1 = np.random.uniform(-1.0, 1.0,size=W1_num_elems)\n",
    "        W1 = W1.reshape(self.n_hidden, self.n_features_ + 1) # reshape to be W\n",
    "        \n",
    "        W2_num_elems = (self.n_hidden + 1)*self.n_output_\n",
    "        W2 = np.random.uniform(-1.0, 1.0, size=W2_num_elems)\n",
    "        W2 = W2.reshape(self.n_output_, self.n_hidden + 1)\n",
    "        return W1, W2\n",
    "    \n",
    "    @staticmethod\n",
    "    def _sigmoid(z):\n",
    "        \"\"\"Use scipy.special.expit to avoid overflow\"\"\"\n",
    "        # 1.0 / (1.0 + np.exp(-z))\n",
    "        return expit(z)\n",
    "    \n",
    "    @staticmethod\n",
    "    def _add_bias_unit(X, how='column'):\n",
    "        \"\"\"Add bias unit (column or row of 1s) to array at index 0\"\"\"\n",
    "        if how == 'column':\n",
    "            ones = np.ones((X.shape[0], 1))\n",
    "            X_new = np.hstack((ones, X))\n",
    "        elif how == 'row':\n",
    "            ones = np.ones((1, X.shape[1]))\n",
    "            X_new = np.vstack((ones, X))\n",
    "        return X_new\n",
    "    \n",
    "    @staticmethod\n",
    "    def _L2_reg(lambda_, W1, W2):\n",
    "        \"\"\"Compute L2-regularization cost\"\"\"\n",
    "        # only compute for non-bias terms\n",
    "        return (lambda_/2.0) * np.sqrt(np.mean(W1[:, 1:] ** 2) + np.mean(W2[:, 1:] ** 2))\n",
    "    \n",
    "    def _cost(self,A3,Y_enc,W1,W2):\n",
    "        '''Get the objective function value'''\n",
    "        cost = np.mean((Y_enc-A3)**2)\n",
    "        L2_term = self._L2_reg(self.l2_C, W1, W2)\n",
    "        return cost + L2_term\n",
    "    \n",
    "    def _feedforward(self, X, W1, W2):\n",
    "        \"\"\"Compute feedforward step\n",
    "        \"\"\"\n",
    "        A1 = self._add_bias_unit(X, how='column')\n",
    "        A1 = A1.T\n",
    "        Z1 = W1 @ A1\n",
    "        A2 = self._sigmoid(Z1)\n",
    "        A2 = self._add_bias_unit(A2, how='row')\n",
    "        Z2 = W2 @ A2\n",
    "        A3 = self._sigmoid(Z2)\n",
    "        return A1, Z1, A2, Z2, A3\n",
    "    \n",
    "    def _get_gradient(self, A1, A2, A3, Z1, Z2, Y_enc, W1, W2):\n",
    "        \"\"\" Compute gradient step using backpropagation.\n",
    "        \"\"\"\n",
    "        # vectorized backpropagation\n",
    "        V2 = -2*(Y_enc-A3)*A3*(1-A3)  # last layer sensitivity\n",
    "        V1 = A2*(1-A2)*(W2.T @ V2) # back prop the sensitivity \n",
    "        \n",
    "        grad2 = V2 @ A2.T # no bias on final layer\n",
    "        grad1 = V1[1:,:] @ A1.T # dont back prop sensitivity of bias\n",
    "        \n",
    "        \n",
    "        # regularize weights that are not bias terms\n",
    "        grad1[:, 1:] += W1[:, 1:] * self.l2_C\n",
    "        grad2[:, 1:] += W2[:, 1:] * self.l2_C\n",
    "\n",
    "        return grad1, grad2\n",
    "    \n",
    "    def predict(self, X):\n",
    "        \"\"\"Predict class labels\"\"\"\n",
    "        _, _, _, _, A3 = self._feedforward(X, self.W1, self.W2)\n",
    "        y_pred = np.argmax(A3, axis=0)\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "# just start with the vectorized version and minibatch\n",
    "class TLPMiniBatch(TwoLayerPerceptronBase):\n",
    "    def __init__(self, alpha=0.0, decrease_const=0.0, shuffle=True, \n",
    "                 minibatches=1, **kwds):        \n",
    "        # need to add to the original initializer \n",
    "        self.alpha = alpha\n",
    "        self.decrease_const = decrease_const\n",
    "        self.shuffle = shuffle\n",
    "        self.minibatches = minibatches\n",
    "        # but keep other keywords\n",
    "        super().__init__(**kwds)\n",
    "        \n",
    "    \n",
    "    def fit(self, X, y, print_progress=False):\n",
    "        \"\"\" Learn weights from training data. With mini-batch\"\"\"\n",
    "        X_data, y_data = X.copy(), y.copy()\n",
    "        Y_enc = self._encode_labels(y)\n",
    "        \n",
    "        # init weights and setup matrices\n",
    "        self.n_features_ = X_data.shape[1]\n",
    "        self.n_output_ = Y_enc.shape[0]\n",
    "        self.W1, self.W2 = self._initialize_weights()\n",
    "\n",
    "        delta_W1_prev = np.zeros(self.W1.shape)\n",
    "        delta_W2_prev = np.zeros(self.W2.shape)\n",
    "\n",
    "        self.cost_ = []\n",
    "        self.score_ = []\n",
    "        # get starting acc\n",
    "        self.score_.append(accuracy_score(y_data,self.predict(X_data)))\n",
    "        for i in range(self.epochs):\n",
    "\n",
    "            # adaptive learning rate\n",
    "            self.eta /= (1 + self.decrease_const*i)\n",
    "\n",
    "            if print_progress>0 and (i+1)%print_progress==0:\n",
    "                sys.stderr.write('\\rEpoch: %d/%d' % (i+1, self.epochs))\n",
    "                sys.stderr.flush()\n",
    "\n",
    "            if self.shuffle:\n",
    "                idx_shuffle = np.random.permutation(y_data.shape[0])\n",
    "                X_data, Y_enc, y_data = X_data[idx_shuffle], Y_enc[:, idx_shuffle], y_data[idx_shuffle]\n",
    "\n",
    "            mini = np.array_split(range(y_data.shape[0]), self.minibatches)\n",
    "            mini_cost = []\n",
    "            for idx in mini:\n",
    "\n",
    "                # feedforward\n",
    "                A1, Z1, A2, Z2, A3 = self._feedforward(X_data[idx],\n",
    "                                                       self.W1,\n",
    "                                                       self.W2)\n",
    "                \n",
    "                cost = self._cost(A3,Y_enc[:, idx],self.W1,self.W2)\n",
    "                mini_cost.append(cost) # this appends cost of mini-batch only\n",
    "\n",
    "                # compute gradient via backpropagation\n",
    "                grad1, grad2 = self._get_gradient(A1=A1, A2=A2, A3=A3, Z1=Z1, Z2=Z2, \n",
    "                                                  Y_enc=Y_enc[:, idx],\n",
    "                                                  W1=self.W1,W2=self.W2)\n",
    "\n",
    "                # momentum calculations\n",
    "                delta_W1, delta_W2 = self.eta * grad1, self.eta * grad2\n",
    "                self.W1 -= (delta_W1 + (self.alpha * delta_W1_prev))\n",
    "                self.W2 -= (delta_W2 + (self.alpha * delta_W2_prev))\n",
    "                delta_W1_prev, delta_W2_prev = delta_W1, delta_W2\n",
    "\n",
    "            self.cost_.append(mini_cost)\n",
    "            self.score_.append(accuracy_score(y_data,self.predict(X_data)))\n",
    "            \n",
    "        return self\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [End review]\n",
    "___\n",
    "\n",
    "## Start of new material"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# to implement the new style of objective function, \n",
    "# we just need to update the final layer calculation of the gradient\n",
    "class TLPMiniBatchCrossEntropy(TLPMiniBatch):\n",
    "    def _cost(self,A3,Y_enc,W1,W2):\n",
    "        '''Get the objective function value'''\n",
    "        cost = -np.mean(np.nan_to_num((Y_enc*np.log(A3)+(1-Y_enc)*np.log(1-A3))))\n",
    "        L2_term = self._L2_reg(self.l2_C, W1, W2)\n",
    "        return cost + L2_term\n",
    "    \n",
    "    def _get_gradient(self, A1, A2, A3, Z1, Z2, Y_enc, W1, W2):\n",
    "        \"\"\" Compute gradient step using backpropagation.\n",
    "        \"\"\"\n",
    "        # vectorized backpropagation\n",
    "        V2 = (A3-Y_enc) # <- this is only line that changed\n",
    "        V1 = A2*(1-A2)*(W2.T @ V2)\n",
    "        \n",
    "        grad2 = V2 @ A2.T\n",
    "        grad1 = V1[1:,:] @ A1.T\n",
    "        \n",
    "        # regularize weights that are not bias terms\n",
    "        grad1[:, 1:] += W1[:, 1:] * self.l2_C\n",
    "        grad2[:, 1:] += W2[:, 1:] * self.l2_C\n",
    "\n",
    "        return grad1, grad2\n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rows: 60000, columns: 784\n",
      "Rows: 10000, columns: 784\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# more diver fashion MNIST data\n",
    "# Let's use Raschka's implementation for using the mnist dataset:\n",
    "# https://github.com/rasbt/python-machine-learning-book/blob/master/code/ch12/ch12.ipynb\n",
    "import os\n",
    "import struct\n",
    "import numpy as np\n",
    "# from sklearn.preprocessing import RobustScaler\n",
    " \n",
    "def load_mnist(path, kind='fashion_train'):\n",
    "    \"\"\"Load MNIST data from `path`\"\"\"\n",
    "    labels_path = os.path.join(path, '%s-labels-idx1-ubyte' % kind)\n",
    "    images_path = os.path.join(path, '%s-images-idx3-ubyte' % kind)\n",
    "        \n",
    "    with open(labels_path, 'rb') as lbpath:\n",
    "        magic, n = struct.unpack('>II', lbpath.read(8))\n",
    "        labels = np.fromfile(lbpath, dtype=np.uint8)\n",
    "\n",
    "    with open(images_path, 'rb') as imgpath:\n",
    "        magic, num, rows, cols = struct.unpack(\">IIII\", imgpath.read(16))\n",
    "        images = np.fromfile(imgpath, dtype=np.uint8).reshape(len(labels), 784)\n",
    " \n",
    "    return images, labels\n",
    "\n",
    "X_train, y_train = load_mnist('data/', kind='fashion_train')\n",
    "print('Rows: %d, columns: %d' % (X_train.shape[0], X_train.shape[1]))\n",
    "\n",
    "X_test, y_test = load_mnist('data/', kind='fashion_t10k')\n",
    "print('Rows: %d, columns: %d' % (X_test.shape[0], X_test.shape[1]))\n",
    "\n",
    "X_train = X_train/255.0 - 0.5\n",
    "X_test = X_test/255.0 - 0.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 20/20"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 37.7 s, sys: 10.3 s, total: 48 s\n",
      "Wall time: 27.7 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 20/20"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 37.1 s, sys: 10 s, total: 47.1 s\n",
      "Wall time: 26.7 s\n",
      "Done\n"
     ]
    }
   ],
   "source": [
    "vals = { 'n_hidden':30, \n",
    "         'C':0.1, 'epochs':20, 'eta':0.001, \n",
    "         'alpha':0.001, 'decrease_const':1e-5, 'minibatches':50,\n",
    "         'shuffle':True,'random_state':1}\n",
    "\n",
    "nn_quad = TLPMiniBatch(**vals)\n",
    "\n",
    "nn_cross = TLPMiniBatchCrossEntropy(**vals)\n",
    "\n",
    "%time nn_cross.fit(X_train, y_train, print_progress=1)\n",
    "%time nn_quad.fit(X_train, y_train, print_progress=1)\n",
    "print(\"Done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "def print_result(nn,X_train,y_train,X_test,y_test,title=\"\",color=\"red\"):\n",
    "    \n",
    "    print(\"=================\")\n",
    "    print(title,\":\")\n",
    "    yhat = nn.predict(X_train)\n",
    "    print('Resubstitution acc:',accuracy_score(y_train,yhat))\n",
    "    \n",
    "    yhat = nn.predict(X_test)\n",
    "    print('Validation acc:',accuracy_score(y_test,yhat))\n",
    "    \n",
    "    if hasattr(nn,'val_score_'):\n",
    "        plt.plot(range(len(nn.val_score_)), nn.val_score_, color=color,label=title)\n",
    "        plt.ylabel('Validation Accuracy')\n",
    "    else:\n",
    "        plt.plot(range(len(nn.score_)), nn.score_, color=color,label=title)\n",
    "        plt.ylabel('Resub Accuracy')\n",
    "        \n",
    "    plt.xlabel('Epochs')\n",
    "    plt.tight_layout()\n",
    "    plt.legend(loc='best')\n",
    "    plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=================\n",
      "Cross Entropy Loss :\n",
      "Resubstitution acc: 0.846633333333\n",
      "Validation acc: 0.827\n",
      "=================\n",
      "Quadratic Loss :\n",
      "Resubstitution acc: 0.812033333333\n",
      "Validation acc: 0.8003\n"
     ]
    },
    {
     "data": {
      "image/png": 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Cystzdsk1veE0LEwhNdV5PejXv66hZ0+7q0UUG9vyLX7S+BSiY5AE5WeGQ4eIeuYZwj74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\n8MEH2bVrF3q9ngMHDpz2mBs2bODFF19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YoAAAXiKgAABeIqAAAF4ioAAAXiKgAABeegLS\niTdewyzChAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1149d9208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_result(nn_cross,X_train,y_train,X_test,y_test,title=\"Cross Entropy Loss\",color=\"red\")\n",
    "print_result(nn_quad,X_train,y_train,X_test,y_test,title=\"Quadratic Loss\",color=\"blue\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Back to Slides]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO: add some mechanism to look at the distribution of gradient weight values\n",
    "#   over training iterations, for each layer (motivates Glorot initialization)\n",
    "class TLPDropout(TLPMiniBatchCrossEntropy):\n",
    "    def __init__(self, dropout=0.25, **kwds):        \n",
    "        # need to add to the original initializer \n",
    "        self.dropout = dropout\n",
    "\n",
    "        # but keep other keywords\n",
    "        super().__init__(**kwds)\n",
    "        \n",
    "    def fit(self, X, y, print_progress=0, XY_test=None):\n",
    "        \"\"\" Learn weights from training data. With mini-batch\"\"\"\n",
    "        X_data, y_data = X.copy(), y.copy()\n",
    "        Y_enc = self._encode_labels(y)\n",
    "        \n",
    "        # init weights and setup matrices\n",
    "        self.n_features_ = X_data.shape[1]\n",
    "        self.n_output_ = Y_enc.shape[0]\n",
    "        self.W1, self.W2 = self._initialize_weights()\n",
    "\n",
    "        delta_W1_prev = np.zeros(self.W1.shape)\n",
    "        delta_W2_prev = np.zeros(self.W2.shape)\n",
    "\n",
    "        self.cost_ = []\n",
    "        self.score_ = []\n",
    "        self.score_.append(accuracy_score(y_data,self.predict(X_data)))\n",
    "        if XY_test is not None:\n",
    "            X_test = XY_test[0].copy()\n",
    "            y_test = XY_test[1].copy()\n",
    "            self.val_score_ = []\n",
    "            self.val_score_.append(accuracy_score(y_test,self.predict(X_test)))\n",
    "        for i in range(self.epochs):\n",
    "\n",
    "            # adaptive learning rate\n",
    "            self.eta /= (1 + self.decrease_const*i)\n",
    "\n",
    "            if print_progress>0 and (i+1)%print_progress==0:\n",
    "                sys.stderr.write('\\rEpoch: %d/%d' % (i+1, self.epochs))\n",
    "                sys.stderr.flush()\n",
    "\n",
    "            if self.shuffle:\n",
    "                idx_shuffle = np.random.permutation(y_data.shape[0])\n",
    "                X_data, Y_enc, y_data = X_data[idx_shuffle], Y_enc[:, idx_shuffle], y_data[idx_shuffle]\n",
    "\n",
    "            mini = np.array_split(range(y_data.shape[0]), self.minibatches)\n",
    "            mini_cost = []\n",
    "            \n",
    "            # adding dropout neurons\n",
    "            W1 = self.W1.copy()\n",
    "            W2 = self.W2.copy()\n",
    "            \n",
    "            if self.dropout>0.0:\n",
    "                \n",
    "                # randomly select half of the neurons\n",
    "                idx_dropout = np.random.permutation(W1.shape[0])\n",
    "                #idx_other_half = idx_dropout[:int(W1.shape[0]*self.dropout)]\n",
    "                idx_dropout = idx_dropout[int(W1.shape[0]*self.dropout):] #drop half\n",
    "                    \n",
    "                idx_dropout = np.sort(idx_dropout)\n",
    "                idx_W2_withbias = np.hstack(([0],(idx_dropout+1)))\n",
    "                W1 = W1[idx_dropout,:]# get rid of rows\n",
    "                W2 = W2[:,idx_W2_withbias]# get rid of extra columns\n",
    "                delta_W1_prev_dropout = delta_W1_prev[idx_dropout,:]\n",
    "                delta_W2_prev_dropout = delta_W2_prev[:,idx_W2_withbias]\n",
    "            else:\n",
    "                delta_W1_prev_dropout = delta_W1_prev\n",
    "                delta_W2_prev_dropout = delta_W2_prev\n",
    "                \n",
    "            \n",
    "            for idx in mini:\n",
    "\n",
    "                # feedforward\n",
    "                A1, Z1, A2, Z2, A3 = self._feedforward(X_data[idx],\n",
    "                                                       W1,\n",
    "                                                       W2)\n",
    "                \n",
    "                cost = self._cost(A3,Y_enc[:, idx],W1,W2)\n",
    "                mini_cost.append(cost) # this appends cost of mini-batch only\n",
    "\n",
    "                # compute gradient via backpropagation\n",
    "                grad1, grad2 = self._get_gradient(A1=A1, A2=A2, A3=A3, Z1=Z1, Z2=Z2,\n",
    "                                                  Y_enc=Y_enc[:, idx],\n",
    "                                                  W1=W1,W2=W2)\n",
    "\n",
    "                delta_W1, delta_W2 = self.eta * grad1, self.eta * grad2\n",
    "                W1 -= (delta_W1 + (self.alpha * delta_W1_prev_dropout))\n",
    "                W2 -= (delta_W2 + (self.alpha * delta_W2_prev_dropout))\n",
    "                delta_W1_prev_dropout, delta_W2_prev_dropout = delta_W1, delta_W2\n",
    "\n",
    "            if self.dropout>0.0:\n",
    "                # now append the learned weights back into the original matrices\n",
    "                self.W1[idx_dropout,:] = W1\n",
    "                self.W2[:,idx_W2_withbias] = W2\n",
    "                delta_W1_prev[idx_dropout,:] = delta_W1_prev_dropout\n",
    "                delta_W2_prev[:,idx_W2_withbias] = delta_W2_prev_dropout\n",
    "            else:\n",
    "                # don't eliminate any neurons\n",
    "                self.W1 = W1\n",
    "                self.W2 = W2\n",
    "                delta_W1_prev = delta_W1_prev_dropout\n",
    "                delta_W2_prev = delta_W2_prev_dropout\n",
    "                \n",
    "            self.score_.append(accuracy_score(y_data,self.predict(X_data)))\n",
    "            self.cost_.append(mini_cost) # only uses dropped samples, so more noise\n",
    "            if XY_test is not None:\n",
    "                self.val_score_.append(accuracy_score(y_test,self.predict(X_test)))\n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 30/30"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 57.1 s, sys: 15.1 s, total: 1min 12s\n",
      "Wall time: 40.5 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 30/30"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 55.6 s, sys: 14.8 s, total: 1min 10s\n",
      "Wall time: 39.3 s\n",
      "=================\n",
      "No Regularization :\n",
      "Resubstitution acc: 0.819883333333\n",
      "Validation acc: 0.8017\n",
      "=================\n",
      "With Dropout :\n",
      "Resubstitution acc: 0.832733333333\n",
      "Validation acc: 0.8184\n"
     ]
    },
    {
     "data": {
      "image/png": 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+/R7cdJOVZcuyiY62XfJ9Z7uVZ336Keh0LohUCCFco9p1kqhrjhzRMWNGIBs2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\nQQkhhPBI0qCEEEJ4JGlQQgghPNL/ASakwBdaTTtOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1149bbe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vals = {'n_hidden':30, \n",
    "         'C':0.0, 'epochs':30, 'eta':0.001, \n",
    "         'alpha':0.0, 'decrease_const':1e-5, 'minibatches':15,\n",
    "        'shuffle':True,'random_state':1}\n",
    "\n",
    "# USING NO REGULARIZATION OR DROPOUT OR ANYTHING\n",
    "nn_noreg = TLPDropout(**vals, dropout=0.0)\n",
    "\n",
    "# ADDING ONLY DROPOUT\n",
    "nn_drop = TLPDropout(**vals, dropout=0.2)\n",
    "\n",
    "%time nn_noreg.fit(X_train, y_train, print_progress=True, XY_test=(X_test,y_test))\n",
    "%time nn_drop.fit(X_train, y_train, print_progress=True, XY_test=(X_test,y_test))\n",
    "\n",
    "print_result(nn_noreg,X_train,y_train,X_test,y_test,title=\"No Regularization\",color=\"red\")\n",
    "print_result(nn_drop,X_train,y_train,X_test,y_test,title=\"With Dropout\",color=\"blue\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of dropout typically is only appropriate for much larger networks, with many more hidden layers than what I have provided here. As such, the performance is actually about the same as without dropout.\n",
    "___"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TLPGaussianInitial(TLPDropout):             \n",
    "    def _initialize_weights(self):\n",
    "        \"\"\"Initialize weights with small random numbers.\"\"\"\n",
    "        W1 = np.random.randn(self.n_hidden, self.n_features_ + 1)\n",
    "        W1[:,1:] = W1[:,1:]/np.sqrt(self.n_features_+1) # don't saturate the neuron\n",
    "        W1[:,:1] = 0 # common practice to start with zero bias\n",
    "        \n",
    "        W2 = np.random.randn(self.n_output_, self.n_hidden + 1)\n",
    "        W2[:,1:] = W2[:,1:]/np.sqrt(self.n_hidden+1) # don't saturate the neuron\n",
    "        W2[:,:1] = 0 # common practice to start with zero bias\n",
    "        return W1, W2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 10/10"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 19 s, sys: 5.56 s, total: 24.6 s\n",
      "Wall time: 14.1 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 10/10"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 19.2 s, sys: 5.5 s, total: 24.7 s\n",
      "Wall time: 13.9 s\n",
      "=================\n",
      "Uniform :\n",
      "Resubstitution acc: 0.8245\n",
      "Validation acc: 0.8075\n",
      "=================\n",
      "Gaussian/$\\sqrt{n_i}$ :\n",
      "Resubstitution acc: 0.846633333333\n",
      "Validation acc: 0.833\n"
     ]
    },
    {
     "data": {
      "image/png": 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k5eUBsGzZMsxms0c1dEav13f7GK0UBYq/UvkBBfTPnk3/Hjqur/RkWwQzaYc2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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113147ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vals = {'n_hidden':30, \n",
    "         'C':0.01, 'epochs':10, 'eta':0.001, \n",
    "         'alpha':0.001, 'decrease_const':1e-5, 'minibatches':50,\n",
    "         'shuffle':True,'random_state':1}\n",
    "\n",
    "nn_uniform = TLPMiniBatchCrossEntropy(**vals)\n",
    "nn_gauss = TLPGaussianInitial(**vals, dropout=False)\n",
    "\n",
    "%time nn_uniform.fit(X_train, y_train, print_progress=1)\n",
    "%time nn_gauss.fit(X_train, y_train, print_progress=1)\n",
    "\n",
    "print_result(nn_uniform,X_train,y_train,X_test,y_test,title=\"Uniform\",color=\"red\")\n",
    "print_result(nn_gauss,X_train,y_train,X_test,y_test,title=\"Gaussian/$\\sqrt{n_i}$\",color=\"blue\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 75/75"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3min 52s, sys: 39.5 s, total: 4min 31s\n",
      "Wall time: 2min 25s\n",
      "=================\n",
      "Long Run :\n",
      "Resubstitution acc: 0.904\n",
      "Validation acc: 0.8759\n"
     ]
    },
    {
     "data": {
      "image/png": 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Mm4bG3/zGq1mIiHobjxSogQMHoqysDJWVlbDZbCgoKEBSUpLLNkajET/++CMA4Ny5czhz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\nBYqIiBSJBYqIiBTp/wMnL9HMOF2WcAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11317b2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# just for fun, let's look at the output of what happens when we let our system loose\n",
    "# these values have been hand tuned\n",
    "vals = {'n_hidden':50, \n",
    "         'C':1e-2, 'epochs':75, 'eta':0.001, \n",
    "         'alpha':1e-4, 'decrease_const':1e-9, 'minibatches':600,\n",
    "         'shuffle':True,'random_state':1, 'dropout':0.0}\n",
    "nn_long_sigmoid = TLPGaussianInitial(**vals)\n",
    "\n",
    "%time nn_long_sigmoid.fit(X_train, y_train, print_progress=1, XY_test=(X_test,y_test))\n",
    "print_result(nn_long_sigmoid,X_train,y_train,X_test,y_test,title=\"Long Run\",color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## [Back To Slides]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rectified Linear Units\n",
    "Now lets look at another type of activation function. The rectified linear unit (ReLu) is an interesting choice to use because of its simplicity. Moreover, we will learn that its backpropagated derivative has some characteristics that are advantageous. \n",
    "\n",
    "We define the ReLu neuron as:\n",
    "\n",
    "$$\n",
    "    \\phi(\\mathbf{z}^{(i)})=\\left\\{\n",
    "                \\begin{array}{ll}\n",
    "                \\mathbf{z}^{(i)}  \\text{,  if }\\mathbf{z}^{(i)}>0 \\\\\n",
    "                \\mathbf{0} \\text{,      else } \\\\\n",
    "                \\end{array}\n",
    "              \\right.\n",
    "$$\n",
    "\n",
    "Which has a very simple derivative:\n",
    "$$\n",
    "    \\frac{\\partial\\phi(\\mathbf{z}^{(i)})}{\\partial\\mathbf{z}^{(i)}}=\\left\\{\n",
    "                \\begin{array}{ll}\n",
    "                \\mathbf{1} \\text{,  if }\\mathbf{z}^{(i)}>0 \\\\\n",
    "                \\mathbf{0} \\text{,      else } \\\\\n",
    "                \\end{array}\n",
    "              \\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Epoch: 64/75/Users/eclarson/anaconda/envs/MLEnv/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: divide by zero encountered in log\n",
      "/Users/eclarson/anaconda/envs/MLEnv/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: invalid value encountered in multiply\n",
      "Epoch: 75/75"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3min 54s, sys: 39.9 s, total: 4min 34s\n",
      "Wall time: 2min 28s\n",
      "{'n_hidden': 50, 'eta': 0.001, 'epochs': 75, 'random_state': 1, 'shuffle': True, 'decrease_const': 1e-09, 'minibatches': 600, 'alpha': 0.0001, 'dropout': 0.0, 'C': 0.01}\n"
     ]
    }
   ],
   "source": [
    "class TLPReLu(TLPGaussianInitial):\n",
    "    def _initialize_weights(self):\n",
    "        \"\"\"Initialize weights with small random numbers.\"\"\"\n",
    "        # suggested relu/sigmoid bounds\n",
    "        #Xavier Glorot, Yoshua Bengio ; \n",
    "        #  Understanding the difficulty of training deep feedforward neural networks\n",
    "        #  Conference on Artificial Intelligence and Statistics, PMLR 9:249-256, 2010.\n",
    "        init_bound = np.sqrt(6. / (self.n_hidden + self.n_features_ + 1))\n",
    "        W1 = np.random.uniform(-init_bound, init_bound,(self.n_hidden, self.n_features_ + 1))\n",
    "        W1[:,:1] = 0\n",
    "        \n",
    "        # reduce the final layer magnitude in order to balance the size of the gradients\n",
    "        # between \n",
    "        init_bound = np.sqrt(0.5 / (self.n_output_ + self.n_hidden + 1))\n",
    "        W2 = np.random.uniform(-init_bound, init_bound,(self.n_output_, self.n_hidden + 1)) \n",
    "        W2[:,:1] = 0\n",
    "        \n",
    "        return W1, W2\n",
    "    \n",
    "    @staticmethod\n",
    "    def _relu(Z):\n",
    "        return np.maximum(0,Z.copy())\n",
    "        \n",
    "    def _feedforward(self, X, W1, W2):\n",
    "        \"\"\"Compute feedforward step\n",
    "        \"\"\"\n",
    "        # A1->W1->ReLu->A2->W2->Sigmoid\n",
    "        A1 = self._add_bias_unit(X.T, how='row')\n",
    "        Z1 = W1 @ A1\n",
    "        A2 = self._relu(Z1)\n",
    "        A2 = self._add_bias_unit(A2, how='row')\n",
    "        Z2 = W2 @ A2\n",
    "        A3 = self._sigmoid(Z2) # never use relu as last layer for classification (yuck!)\n",
    "        return A1, Z1, A2, Z2, A3\n",
    "    \n",
    "    def _get_gradient(self, A1, A2, A3, Z1, Z2, Y_enc, W1, W2):\n",
    "        \"\"\" Compute gradient step using backpropagation.\n",
    "        \"\"\"\n",
    "        # vectorized backpropagation\n",
    "        V2 = (A3-Y_enc) \n",
    "        \n",
    "        # V3[Z2<=0] = 0 # can change to be relu back prop on this layer too!\n",
    "        \n",
    "        # old update: V1 = A2*(1-A2)*(W2.T @ V2)\n",
    "        # the derivative of sigmoid was A2(1-A2), but now that is relu\n",
    "        # so we change it to:\n",
    "        Z1_with_bias = self._add_bias_unit(Z1,how='row')\n",
    "        V1 = (W2.T @ V2) \n",
    "        V1[Z1_with_bias<=0] = 0\n",
    "        # relu derivative only zeros out certain values! easy!\n",
    "        \n",
    "        grad2 = V2 @ A2.T\n",
    "        grad1 = V1[1:,:] @ A1.T\n",
    "        \n",
    "        \n",
    "        # regularize weights that are not bias terms\n",
    "        grad1[:, 1:] += (W1[:, 1:] * self.l2_C)\n",
    "        grad2[:, 1:] += (W2[:, 1:] * self.l2_C)\n",
    "\n",
    "        return grad1, grad2\n",
    "    \n",
    "nn_long_relu = TLPReLu(**vals) # same as previous parameter values\n",
    "%time nn_long_relu.fit(X_train, y_train, print_progress=True, XY_test=(X_test,y_test))\n",
    "print(vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=================\n",
      "ReLu :\n",
      "Resubstitution acc: 0.937516666667\n",
      "Validation acc: 0.8857\n",
      "=================\n",
      "Sigmoid :\n",
      "Resubstitution acc: 0.904\n",
      "Validation acc: 0.8759\n"
     ]
    },
    {
     "data": {
      "image/png": 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VgSosLOSll17ivPPOo6SkhJEjR7Jx40Zyc3M7Ol+HC2oGSfjQpYtP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\n3nnnndafA8ToGpTVamXmzJksWrSIO++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      "text/plain": [
       "<matplotlib.figure.Figure at 0x109877f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_result(nn_long_relu, X_train, y_train, X_test, y_test, title=\"ReLu\",color=\"blue\")\n",
    "print_result(nn_long_sigmoid, X_train, y_train, X_test, y_test, title=\"Sigmoid\",color=\"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sklearn Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.19.0\n",
      "CPU times: user 1min 52s, sys: 13.4 s, total: 2min 5s\n",
      "Wall time: 1min 7s\n",
      "Validation Acc: 0.8811\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/eclarson/anaconda/envs/MLEnv/lib/python3.5/site-packages/sklearn/neural_network/multilayer_perceptron.py:564: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (75) reached and the optimization hasn't converged yet.\n",
      "  % self.max_iter, ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn import __version__ as sklearn_version\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "print(sklearn_version)\n",
    "# these values have been hand tuned\n",
    "clf = MLPClassifier(hidden_layer_sizes=(50, ), \n",
    "                    activation='logistic', \n",
    "                    solver='sgd', \n",
    "                    alpha=1e-4, # L2 penalty\n",
    "                    batch_size='auto', # min of 200, num_samples\n",
    "                    learning_rate='constant', \n",
    "                    learning_rate_init=0.1, # only SGD\n",
    "                    power_t=0.5,    # only SGD\n",
    "                    max_iter=75, \n",
    "                    shuffle=True, \n",
    "                    random_state=1, \n",
    "                    tol=1e-9, # for stopping\n",
    "                    verbose=False, \n",
    "                    warm_start=False, \n",
    "                    momentum=0.9, # only SGD\n",
    "                    nesterovs_momentum=True, # only SGD\n",
    "                    early_stopping=False, \n",
    "                    validation_fraction=0.1, # only if early_stop is true\n",
    "                    beta_1=0.9, # adam decay rate of moment\n",
    "                    beta_2=0.999, # adam decay rate of moment\n",
    "                    epsilon=1e-08) # adam numerical stabilizer\n",
    "\n",
    "%time clf.fit(X_train,y_train)\n",
    "yhat = clf.predict(X_test)\n",
    "print('Validation Acc:',accuracy_score(yhat,y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 56.8 s, sys: 7.06 s, total: 1min 3s\n",
      "Wall time: 34.4 s\n",
      "Validation Acc: 0.8768\n"
     ]
    }
   ],
   "source": [
    "# but with this implementation we can also easily change Neurons\n",
    "clf = MLPClassifier(hidden_layer_sizes=(50, ), \n",
    "                    activation='relu', # type of non-linearity, every layer\n",
    "                    solver='sgd', \n",
    "                    alpha=1e-4, # L2 penalty\n",
    "                    batch_size= 'auto', # min of 200, num_samples\n",
    "                    learning_rate='constant', # adapt learning? only for sgd\n",
    "                    learning_rate_init=0.1, # only SGD\n",
    "                    power_t=0.0,    # only SGD with inverse scaling of learning rate\n",
    "                    max_iter=75, # stopping criteria\n",
    "                    shuffle=True, \n",
    "                    random_state=1, \n",
    "                    tol=0, # for stopping\n",
    "                    verbose=False, \n",
    "                    warm_start=False, \n",
    "                    momentum=0.9, # only SGD\n",
    "                    nesterovs_momentum=False, # only SGD\n",
    "                    early_stopping=False, \n",
    "                    validation_fraction=0.0, # only if early_stop is true\n",
    "                    beta_1=0.9, # adam decay rate of moment\n",
    "                    beta_2=0.999, # adam decay rate of moment\n",
    "                    epsilon=1e-08) # adam numerical stabilizer\n",
    "\n",
    "%time clf.fit(X_train,y_train)\n",
    "yhat = clf.predict(X_test)\n",
    "print('Validation Acc:',accuracy_score(yhat,y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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