exercises_1_all_code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np # Scientific library for numerical programming.\n",
    "import matplotlib.pyplot as plt # Plotting library.\n",
    "import matplotlib\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def onehot(t, num_classes):\n",
    "    out = np.zeros((t.shape[0], num_classes))\n",
    "    for row, col in enumerate(t):\n",
    "        out[row, col] = 1\n",
    "    return out\n",
    "\n",
    "data = np.load('mnist.npz')\n",
    "num_classes = 10\n",
    "x_train = data['X_train'][:2000]\n",
    "targets_train = data['y_train'][:2000]\n",
    "targets_train = onehot(targets_train, num_classes)\n",
    "\n",
    "x_valid = data['X_valid'][:500]\n",
    "targets_valid = data['y_valid'][:500]\n",
    "targets_valid = onehot(targets_valid, num_classes)\n",
    "\n",
    "x_test = data['X_test'][:500]\n",
    "targets_test = data['y_test'][:500]\n",
    "targets_test = onehot(targets_test, num_classes)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pl8v1yNXJ3T9+IQQREREkJCTcZnYKDAyUExZjYmJITk7GZDLJRTlzc3NxOBxM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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085a5c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idx = 0\n",
    "canvas = np.zeros((28*10, 10*28))\n",
    "for i in range(10):\n",
    "    for j in range(10):\n",
    "        canvas[i*28:(i+1)*28, j*28:(j+1)*28] = x_train[idx].reshape((28, 28))\n",
    "        idx += 1\n",
    "plt.figure(figsize=(7, 7))\n",
    "plt.imshow(canvas, cmap='gray')\n",
    "plt.title('MNIST handwritten digits')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "One-of-k                                  | Label\n",
      "--------------------------------------------------\n",
      "[ 0.  0.  0.  0.  0.  1.  0.  0.  0.  0.] | 5\n",
      "[ 1.  0.  0.  0.  0.  0.  0.  0.  0.  0.] | 0\n",
      "[ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.] | 4\n",
      "[ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.] | 1\n",
      "[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  1.] | 9\n",
      "[ 0.  0.  1.  0.  0.  0.  0.  0.  0.  0.] | 2\n",
      "[ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.] | 1\n",
      "[ 0.  0.  0.  1.  0.  0.  0.  0.  0.  0.] | 3\n",
      "[ 0.  1.  0.  0.  0.  0.  0.  0.  0.  0.] | 1\n",
      "[ 0.  0.  0.  0.  1.  0.  0.  0.  0.  0.] | 4\n"
     ]
    }
   ],
   "source": [
    "print \"One-of-k\" + \" \"*34  + \"| Label\"\n",
    "print \"-\"*50\n",
    "for i in range(10):\n",
    "   print targets_train[i], \"|\",  targets_train[i].argmax(axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LinearLayer():\n",
    "    def __init__(self, num_inputs, num_units, scale=0.01):\n",
    "        self.num_units = num_units\n",
    "        self.num_inputs = num_inputs\n",
    "        self.W = np.random.random((num_inputs, num_units)) * scale\n",
    "        self.b = np.zeros(num_units)\n",
    "\n",
    "    def __str__(self): \n",
    "        return \"LinearLayer(%i, %i)\" % (self.num_inputs, self.num_units)\n",
    "\n",
    "    def fprop(self, x, *args):\n",
    "        self.x = x\n",
    "        self.a = np.dot(x, self.W) + self.b\n",
    "        return self.a\n",
    "        \n",
    "    def bprop(self, delta_in):\n",
    "        x_t = np.transpose(self.x)\n",
    "        self.grad_W = np.dot(x_t, delta_in)\n",
    "        self.grad_b = delta_in.sum(axis=0)\n",
    "        W_T = np.transpose(self.W)\n",
    "        self.delta_out = np.dot(delta_in,W_T)\n",
    "        return self.delta_out\n",
    "        \n",
    "    def update_params(self, lr):\n",
    "        self.W = self.W - self.grad_W*lr\n",
    "        self.b = self.b - self.grad_b*lr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JpN8BzwNNgHvMbKykX8fyO4CrgfskvU9YEnKRu8iz4+23w+jp1VfrdXBOvSKTMHNJvYFv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\nCNGaMmXBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108589bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def linear(x):\n",
    "    return x\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def tanh(x):\n",
    "    return (np.exp(x)-np.exp(-x)) / (np.exp(x)+np.exp(-x))\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def softplus(x):\n",
    "    return np.log(np.exp(x) + 1)\n",
    "\n",
    "x = np.linspace(-10,10,100)\n",
    "\n",
    "plt.subplot(321)\n",
    "plt.plot(linear(x))\n",
    "plt.title('linear activation')\n",
    "plt.subplot(322)\n",
    "plt.plot(sigmoid(x))\n",
    "plt.title('sigmoid activation')\n",
    "plt.subplot(323)\n",
    "plt.plot(tanh(x))\n",
    "plt.title('tanh activation')\n",
    "plt.subplot(324)\n",
    "plt.plot(relu(x))\n",
    "plt.title('relu activation')\n",
    "plt.subplot(325)\n",
    "plt.plot(softplus(x))\n",
    "plt.title('softplus activation')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SigmoidActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"Sigmoid()\"\n",
    "    \n",
    "    def fprop(self, x, train=True):\n",
    "        self.a = 1.0 / (1+np.exp(-x))\n",
    "        return self.a\n",
    "        \n",
    "    def bprop(self, delta_in):\n",
    "        delta_out = self.a * (1 - self.a)*delta_in\n",
    "        return delta_out\n",
    "        \n",
    "    def update_params(self, lr):\n",
    "        pass\n",
    "    \n",
    "class TanhActivationLayer():\n",
    "    def __str__(self):\n",
    "        return \"Tanh()\"\n",
    "\n",
    "    def fprop(self, x, train=True):\n",
    "        self.a = np.tanh(x)\n",
    "        return self.a\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        return (1-self.a**2)*delta_in\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass\n",
    "\n",
    "class ReluActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"ReLU()\"\n",
    "\n",
    "    def fprop(self, x, train=True):\n",
    "        self.a = np.maximum(0, x)\n",
    "        return self.a\n",
    "        \n",
    "    def bprop(self, delta_in):\n",
    "        return delta_in * (self.a > 0).astype(self.a.dtype)\n",
    "        \n",
    "    def update_params(self, lr):\n",
    "        pass\n",
    "    \n",
    "class SoftplusActivationLayer():\n",
    "    def __str__(self):\n",
    "        return \"Softplus()\"\n",
    "\n",
    "    def fprop(self, x, train=True):\n",
    "        self.g = np.exp(x) + 1\n",
    "        self.a = np.log(g)\n",
    "        return self.a\n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        return delta_in * 1-g**(-1)\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SoftmaxActivationLayer():\n",
    "    def __str__(self): \n",
    "        return \"Softmax()\"\n",
    "    \n",
    "    def fprop(self, x, train=True):\n",
    "        x_exp = np.exp(x)\n",
    "        normalizer = x_exp.sum(axis=-1, keepdims=True)\n",
    "        self.a = x_exp / normalizer\n",
    "        return self.a\n",
    "        \n",
    "    def bprop(self, delta_in):\n",
    "        return delta_in\n",
    "        \n",
    "    def update_params(self, lr):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class MeanSquaredLoss():\n",
    "    def __str__(self): \n",
    "        return \"MeanSquaredLoss()\"\n",
    "    \n",
    "    def fprop(self, x, t):\n",
    "        num_batches = x.shape[0]\n",
    "        cost = 0.5 * (x-t)**2   # samples, num_outputs\n",
    "        cost = cost.sum()  # sum over output and batches\n",
    "        return cost / num_batches  # divide by batchsize\n",
    "               \n",
    "    def bprop(self, y, t):\n",
    "        num_batches = x.shape[0]\n",
    "        delta_out = (1./num_batches) * (y-t)\n",
    "        return delta_out\n",
    "        \n",
    "    def update_params(self):\n",
    "        pass\n",
    "\n",
    "class CrossEntropyLoss():\n",
    "    def __str__(self): \n",
    "        return \"CrossEntropyLoss()\"\n",
    "    \n",
    "    def fprop(self, x, t):\n",
    "        tol = 1e-8\n",
    "        num_batches = x.shape[0]\n",
    "        cost = np.sum(-t * np.log(x + tol), axis=-1)\n",
    "        return cost / num_batches  # divide by batchsize\n",
    "        \n",
    "    def bprop(self, y, t):\n",
    "        num_batches = y.shape[0]\n",
    "        delta_out = (1./num_batches) * (y-t)\n",
    "        return delta_out\n",
    "        \n",
    "    def update_params(self):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_samples, num_inputs = x_train.shape\n",
    "num_hidden_units = 100\n",
    "num_classes = 10\n",
    "\n",
    "l_hid_pre1 = LinearLayer(num_inputs, num_hidden_units) \n",
    "l_hid_act1 = ReluActivationLayer()\n",
    "l_hid_pre2 = LinearLayer(num_hidden_units, num_classes)\n",
    "l_hid_act2 = SoftmaxActivationLayer()\n",
    "\n",
    "LossLayer = CrossEntropyLoss()\n",
    "\n",
    "def forward(x):\n",
    "    out_hid_pre1 = l_hid_pre1.fprop(x)\n",
    "    out_hid_act1 = l_hid_act1.fprop(out_hid_pre1)\n",
    "    out_hid_pre2 = l_hid_pre2.fprop(out_hid_act1)\n",
    "    y_probs = l_hid_act2.fprop(out_hid_pre2)\n",
    "    return y_probs\n",
    "\n",
    "def backward(y_probs, targets):\n",
    "    delta1 = LossLayer.bprop(y_probs, targets)\n",
    "    delta2 = l_hid_act2.bprop(delta1)\n",
    "    delta3 = l_hid_pre2.bprop(delta2)\n",
    "    delta4 = l_hid_act1.bprop(delta3)\n",
    "    delta5 = l_hid_pre1.bprop(delta4)\n",
    "    \n",
    "def update(learning_rate):\n",
    "    l_hid_pre1.update_params(learning_rate)\n",
    "    l_hid_pre2.update_params(learning_rate)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 : Train Loss 1.139633e-03 , Train acc 0.095500,  Valid acc 0.106000 \n",
      "Epoch 2 : Train Loss 1.115221e-03 , Train acc 0.102000,  Valid acc 0.108000 \n",
      "Epoch 3 : Train Loss 1.027921e-03 , Train acc 0.388500,  Valid acc 0.382000 \n",
      "Epoch 4 : Train Loss 8.332726e-04 , Train acc 0.613500,  Valid acc 0.608000 \n",
      "Epoch 5 : Train Loss 6.226057e-04 , Train acc 0.698500,  Valid acc 0.682000 \n",
      "Epoch 6 : Train Loss 4.900818e-04 , Train acc 0.769500,  Valid acc 0.722000 \n",
      "Epoch 7 : Train Loss 4.071604e-04 , Train acc 0.803000,  Valid acc 0.756000 \n",
      "Epoch 8 : Train Loss 3.499901e-04 , Train acc 0.824500,  Valid acc 0.768000 \n",
      "Epoch 9 : Train Loss 3.085080e-04 , Train acc 0.843000,  Valid acc 0.792000 \n",
      "Epoch 10 : Train Loss 2.774449e-04 , Train acc 0.859500,  Valid acc 0.810000 \n"
     ]
    }
   ],
   "source": [
    "from confusionmatrix import ConfusionMatrix\n",
    "batch_size = 100\n",
    "num_epochs = 10\n",
    "learning_rate = 0.1\n",
    "num_samples = x_train.shape[0]\n",
    "num_batches = num_samples // batch_size\n",
    "\n",
    "\n",
    "train_acc, train_loss = [], []\n",
    "valid_acc, valid_loss = [], []\n",
    "test_acc, test_loss = [], []\n",
    "batch_loss = []\n",
    "for epoch in range(num_epochs):\n",
    "    #Forward->Backprob->Update params\n",
    "    for i in range(num_batches):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        target_batch = targets_train[idx]\n",
    "        y_probs = forward(x_batch)\n",
    "        batch_loss_cur = LossLayer.fprop(y_probs, target_batch)\n",
    "        batch_loss += [batch_loss_cur]\n",
    "        backward(y_probs, target_batch)\n",
    "        update(learning_rate)\n",
    "\n",
    "    #Measure performance\n",
    "    confusion_train = ConfusionMatrix(num_classes)\n",
    "    confusion_valid = ConfusionMatrix(num_classes)\n",
    "    confusion_test = ConfusionMatrix(num_classes)\n",
    "    \n",
    "    y_train_probs = forward(x_train)\n",
    "    train_loss_cur = LossLayer.fprop(y_train_probs, targets_train)\n",
    "    confusion_train.batch_add(targets_train.argmax(-1), y_train_probs.argmax(-1))\n",
    "    train_acc_cur = confusion_train.accuracy()\n",
    "    train_acc += [train_acc_cur]\n",
    "    train_loss += [train_loss_cur.mean()]\n",
    "\n",
    "    y_valid_probs = forward(x_valid)\n",
    "    valid_loss_cur = LossLayer.fprop(y_valid_probs, targets_valid)\n",
    "    confusion_valid.batch_add(targets_valid.argmax(-1), y_valid_probs.argmax(-1))\n",
    "    valid_acc_cur = confusion_valid.accuracy()\n",
    "    valid_acc += [valid_acc_cur]\n",
    "    valid_loss += [valid_loss_cur.mean()]\n",
    "    \n",
    "    y_test_probs = forward(x_test)\n",
    "    test_loss_cur = LossLayer.fprop(y_test_probs, targets_test)\n",
    "    confusion_test.batch_add(targets_test.argmax(-1), y_test_probs.argmax(-1))\n",
    "    test_acc_cur = confusion_test.accuracy()\n",
    "    test_acc += [test_acc_cur]\n",
    "    test_loss += [test_loss_cur.mean()]\n",
    "    \n",
    "    print \"Epoch %i : Train Loss %e , Train acc %f,  Valid acc %f \" \\\n",
    "    % (epoch+1, np.mean(train_loss_cur), train_acc_cur, valid_acc_cur)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ----------------------------------\n",
      " 0 | 38  0  0  0  0  4  0  0  0  0 |42\n",
      " 1 |  0 66  0  0  0  0  0  0  1  0 |67\n",
      " 2 |  0  0 49  1  0  0  0  3  2  0 |55\n",
      " 3 |  0  0  1 33  0  7  0  3  1  0 |45\n",
      " 4 |  0  0  0  0 40  0  3  0  0 12 |55\n",
      " 5 |  1  0  0  3  0 37  3  1  1  4 |50\n",
      " 6 |  2  0  4  0  3  2 32  0  0  0 |43\n",
      " 7 |  0  2  0  0  0  0  0 37  2  8 |49\n",
      " 8 |  0  0  1  1  1  4  1  1 29  2 |40\n",
      " 9 |  0  1  1  1  8  0  0  2  3 38 |54\n",
      "  ----------------------------------\n",
      "     41 69 56 39 52 54 39 47 39 64\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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gwAB7HsCYEGNdRE1Q3HUXLKhxE706NeSlaYnWDmBMiPJ62AhTBMXFQdymTwiv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\nTL4TyZ/X2UqvFho+fDhlypS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FYmIiNWrUoF+/fvTp04eSJUsG94OfBZte0hgTMOuHn3fD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1085a5a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vf4/1Wb77Lnv5krotlwGlDTAvbXt+sm9j05TWyt0XJa8XAa2qkkmRusisatVe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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115d210d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print confusion_test\n",
    "plt.plot(range(num_epochs), train_acc, label='training')\n",
    "plt.plot(range(num_epochs), valid_acc, label='validation')\n",
    "plt.plot(range(num_epochs), test_acc, label='testing')\n",
    "plt.title('Training Accuracy on MNIST')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(loc=4)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(np.mean(batch_loss,axis=1))\n",
    "plt.title('Training Losses on MNIST')\n",
    "plt.xlabel('Updates')\n",
    "plt.ylabel('Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class DropoutLayer():\n",
    "    def __str__(self): \n",
    "        return \"Dropout(%f)\" % self.p\n",
    "\n",
    "    def __init__(self, p=0.5):\n",
    "        self.p = p\n",
    "\n",
    "    def fprop(self, x, train=True):\n",
    "        if train:\n",
    "            mask = np.random.random(x.shape) > (1-self.p)\n",
    "            scale = 1.0 / (1-self.p)            \n",
    "            self.a = x*mask*scale\n",
    "            return self.a \n",
    "        else:\n",
    "            return x \n",
    "\n",
    "    def bprop(self, delta_in):\n",
    "        delta_out = delta_in*self.a\n",
    "        return delta_out\n",
    "\n",
    "    def update_params(self, lr):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_samples, num_inputs = x_train.shape\n",
    "num_hidden_units = 100\n",
    "num_classes = 10\n",
    "\n",
    "l_hid_pre1 = LinearLayer(num_inputs, num_hidden_units)\n",
    "l_hid_act1 = ReluActivationLayer()\n",
    "l_hid_pre2 = LinearLayer(num_hidden_units, num_classes)\n",
    "l_hid_act2 = SoftmaxActivationLayer()\n",
    "\n",
    "LossLayer = CrossEntropyLoss()\n",
    "\n",
    "def forward(x):\n",
    "    out_hid_pre1 = l_hid_pre1.fprop(x)\n",
    "    out_hid_act1 = l_hid_act1.fprop(out_hid_pre1)\n",
    "    out_hid_pre2 = l_hid_pre2.fprop(out_hid_act1)\n",
    "    y_probs = l_hid_act2.fprop(out_hid_pre2)\n",
    "    return y_probs\n",
    "\n",
    "def forward_eval(x):\n",
    "    out_hid_pre1 = l_hid_pre1.fprop(x)\n",
    "    out_hid_act1 = l_hid_act1.fprop(out_hid_pre1)\n",
    "    out_hid_pre2 = l_hid_pre2.fprop(out_hid_act1)\n",
    "    y_probs = l_hid_act2.fprop(out_hid_pre2)\n",
    "    return y_probs\n",
    "\n",
    "def backward(y_probs, targets):\n",
    "    delta1 = LossLayer.bprop(y_probs, targets)\n",
    "    delta2 = l_hid_act2.bprop(delta1)\n",
    "    delta3 = l_hid_pre2.bprop(delta2)\n",
    "    delta4 = l_hid_act1.bprop(delta3)\n",
    "    delta5 = l_hid_pre1.bprop(delta4)\n",
    "    \n",
    "def update(learning_rate):\n",
    "    l_hid_pre1.update_params(learning_rate)\n",
    "    l_hid_pre2.update_params(learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "num_samples, num_inputs = x_train.shape\n",
    "num_hidden_units = 100\n",
    "num_classes = 10\n",
    "\n",
    "l_hid_pre1 = LinearLayer(num_inputs, num_hidden_units)\n",
    "l_hid_act1 = ReluActivationLayer()\n",
    "l_hid_dro1 = DropoutLayer()\n",
    "l_hid_pre2 = LinearLayer(num_hidden_units, num_classes)\n",
    "l_hid_act2 = SoftmaxActivationLayer()\n",
    "\n",
    "LossLayer = CrossEntropyLoss()\n",
    "\n",
    "def forward(x):\n",
    "    out_hid_pre1 = l_hid_pre1.fprop(x)\n",
    "    out_hid_act1 = l_hid_act1.fprop(out_hid_pre1)\n",
    "    out_hid_dro1 = l_hid_dro1.fprop(out_hid_act1)\n",
    "    out_hid_pre2 = l_hid_pre2.fprop(out_hid_dro1)\n",
    "    y_probs = l_hid_act2.fprop(out_hid_pre2)\n",
    "    return y_probs\n",
    "\n",
    "def forward_eval(x):\n",
    "    out_hid_pre1 = l_hid_pre1.fprop(x)\n",
    "    out_hid_act1 = l_hid_act1.fprop(out_hid_pre1)\n",
    "    out_hid_dro1 = l_hid_dro1.fprop(out_hid_act1, train = False)\n",
    "    out_hid_pre2 = l_hid_pre2.fprop(out_hid_dro1)\n",
    "    y_probs = l_hid_act2.fprop(out_hid_pre2)\n",
    "    return y_probs\n",
    "\n",
    "def backward(y_probs, targets):\n",
    "    delta1 = LossLayer.bprop(y_probs, targets)\n",
    "    delta2 = l_hid_act2.bprop(delta1)\n",
    "    delta3 = l_hid_pre2.bprop(delta2)\n",
    "    delta4 = l_hid_dro1.bprop(delta3)\n",
    "    delta5 = l_hid_act1.bprop(delta4)\n",
    "    delta6 = l_hid_pre1.bprop(delta5)\n",
    "    \n",
    "def update(learning_rate):\n",
    "    l_hid_pre1.update_params(learning_rate)\n",
    "    l_hid_pre2.update_params(learning_rate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 : Train loss,acc: 0.011443, 0.098500; Valid loss,acc: 0.000229, 0.099100; Test loss,acc: 0.000229, 0.098000.\n",
      "Epoch 2 : Train loss,acc: 0.011396, 0.101000; Valid loss,acc: 0.000228, 0.099100; Test loss,acc: 0.000228, 0.098000.\n",
      "Epoch 3 : Train loss,acc: 0.011389, 0.114000; Valid loss,acc: 0.000227, 0.099100; Test loss,acc: 0.000227, 0.098100.\n",
      "Epoch 4 : Train loss,acc: 0.011301, 0.120000; Valid loss,acc: 0.000225, 0.099900; Test loss,acc: 0.000225, 0.099500.\n",
      "Epoch 5 : Train loss,acc: 0.011183, 0.145500; Valid loss,acc: 0.000222, 0.116600; Test loss,acc: 0.000223, 0.112000.\n",
      "Epoch 6 : Train loss,acc: 0.010932, 0.186000; Valid loss,acc: 0.000218, 0.196300; Test loss,acc: 0.000218, 0.188600.\n",
      "Epoch 7 : Train loss,acc: 0.010577, 0.248500; Valid loss,acc: 0.000210, 0.349400; Test loss,acc: 0.000210, 0.325900.\n",
      "Epoch 8 : Train loss,acc: 0.009879, 0.323000; Valid loss,acc: 0.000197, 0.525300; Test loss,acc: 0.000197, 0.503800.\n",
      "Epoch 9 : Train loss,acc: 0.009152, 0.408500; Valid loss,acc: 0.000178, 0.660400; Test loss,acc: 0.000179, 0.649500.\n",
      "Epoch 10 : Train loss,acc: 0.008460, 0.429000; Valid loss,acc: 0.000156, 0.680200; Test loss,acc: 0.000157, 0.666300.\n",
      "Epoch 11 : Train loss,acc: 0.007729, 0.479500; Valid loss,acc: 0.000135, 0.713300; Test loss,acc: 0.000136, 0.695700.\n",
      "Epoch 12 : Train loss,acc: 0.006841, 0.519000; Valid loss,acc: 0.000117, 0.754800; Test loss,acc: 0.000119, 0.733000.\n",
      "Epoch 13 : Train loss,acc: 0.006056, 0.548000; Valid loss,acc: 0.000106, 0.734200; Test loss,acc: 0.000108, 0.707000.\n",
      "Epoch 14 : Train loss,acc: 0.005730, 0.573000; Valid loss,acc: 0.000096, 0.739000; Test loss,acc: 0.000099, 0.719000.\n",
      "Epoch 15 : Train loss,acc: 0.005456, 0.589000; Valid loss,acc: 0.000091, 0.740900; Test loss,acc: 0.000094, 0.722200.\n",
      "Epoch 16 : Train loss,acc: 0.004850, 0.616000; Valid loss,acc: 0.000085, 0.750600; Test loss,acc: 0.000088, 0.726000.\n",
      "Epoch 17 : Train loss,acc: 0.004688, 0.643000; Valid loss,acc: 0.000081, 0.752600; Test loss,acc: 0.000084, 0.734400.\n",
      "Epoch 18 : Train loss,acc: 0.004759, 0.660500; Valid loss,acc: 0.000077, 0.772000; Test loss,acc: 0.000081, 0.747600.\n",
      "Epoch 19 : Train loss,acc: 0.004570, 0.671500; Valid loss,acc: 0.000071, 0.786500; Test loss,acc: 0.000074, 0.769000.\n",
      "Epoch 20 : Train loss,acc: 0.004067, 0.676500; Valid loss,acc: 0.000070, 0.787200; Test loss,acc: 0.000074, 0.763000.\n",
      "Epoch 21 : Train loss,acc: 0.003914, 0.697000; Valid loss,acc: 0.000067, 0.800100; Test loss,acc: 0.000070, 0.779300.\n",
      "Epoch 22 : Train loss,acc: 0.003510, 0.711000; Valid loss,acc: 0.000063, 0.818300; Test loss,acc: 0.000066, 0.801600.\n",
      "Epoch 23 : Train loss,acc: 0.003370, 0.722000; Valid loss,acc: 0.000060, 0.821900; Test loss,acc: 0.000063, 0.806000.\n",
      "Epoch 24 : Train loss,acc: 0.004097, 0.734500; Valid loss,acc: 0.000058, 0.829300; Test loss,acc: 0.000061, 0.814000.\n",
      "Epoch 25 : Train loss,acc: 0.003570, 0.741500; Valid loss,acc: 0.000058, 0.827800; Test loss,acc: 0.000061, 0.811800.\n",
      "Epoch 26 : Train loss,acc: 0.003567, 0.756000; Valid loss,acc: 0.000055, 0.841100; Test loss,acc: 0.000058, 0.829600.\n",
      "Epoch 27 : Train loss,acc: 0.003146, 0.751500; Valid loss,acc: 0.000054, 0.844400; Test loss,acc: 0.000057, 0.830700.\n",
      "Epoch 28 : Train loss,acc: 0.002744, 0.757000; Valid loss,acc: 0.000053, 0.848200; Test loss,acc: 0.000055, 0.835700.\n",
      "Epoch 29 : Train loss,acc: 0.002925, 0.761500; Valid loss,acc: 0.000053, 0.844100; Test loss,acc: 0.000055, 0.832600.\n",
      "Epoch 30 : Train loss,acc: 0.002757, 0.780500; Valid loss,acc: 0.000052, 0.845000; Test loss,acc: 0.000055, 0.831400.\n",
      "Epoch 31 : Train loss,acc: 0.002875, 0.787000; Valid loss,acc: 0.000052, 0.844200; Test loss,acc: 0.000055, 0.827200.\n",
      "Epoch 32 : Train loss,acc: 0.003150, 0.775000; Valid loss,acc: 0.000053, 0.839900; Test loss,acc: 0.000056, 0.825400.\n",
      "Epoch 33 : Train loss,acc: 0.002898, 0.794000; Valid loss,acc: 0.000049, 0.855700; Test loss,acc: 0.000052, 0.842400.\n",
      "Epoch 34 : Train loss,acc: 0.002951, 0.778500; Valid loss,acc: 0.000048, 0.861700; Test loss,acc: 0.000051, 0.847600.\n",
      "Epoch 35 : Train loss,acc: 0.002464, 0.800000; Valid loss,acc: 0.000048, 0.860400; Test loss,acc: 0.000051, 0.846700.\n",
      "Epoch 36 : Train loss,acc: 0.002650, 0.791000; Valid loss,acc: 0.000047, 0.863700; Test loss,acc: 0.000050, 0.849800.\n",
      "Epoch 37 : Train loss,acc: 0.002783, 0.805000; Valid loss,acc: 0.000047, 0.861200; Test loss,acc: 0.000050, 0.849500.\n",
      "Epoch 38 : Train loss,acc: 0.002390, 0.817000; Valid loss,acc: 0.000046, 0.863500; Test loss,acc: 0.000049, 0.850300.\n",
      "Epoch 39 : Train loss,acc: 0.002639, 0.810000; Valid loss,acc: 0.000046, 0.864900; Test loss,acc: 0.000049, 0.850000.\n",
      "Epoch 40 : Train loss,acc: 0.002477, 0.816000; Valid loss,acc: 0.000047, 0.854100; Test loss,acc: 0.000050, 0.841900.\n",
      "Epoch 41 : Train loss,acc: 0.002365, 0.809500; Valid loss,acc: 0.000045, 0.866100; Test loss,acc: 0.000048, 0.853400.\n",
      "Epoch 42 : Train loss,acc: 0.002477, 0.807000; Valid loss,acc: 0.000044, 0.871800; Test loss,acc: 0.000047, 0.859900.\n",
      "Epoch 43 : Train loss,acc: 0.002573, 0.811500; Valid loss,acc: 0.000044, 0.876500; Test loss,acc: 0.000046, 0.864000.\n",
      "Epoch 44 : Train loss,acc: 0.002279, 0.820500; Valid loss,acc: 0.000044, 0.871000; Test loss,acc: 0.000046, 0.857600.\n",
      "Epoch 45 : Train loss,acc: 0.002358, 0.837500; Valid loss,acc: 0.000044, 0.868800; Test loss,acc: 0.000046, 0.858300.\n",
      "Epoch 46 : Train loss,acc: 0.002243, 0.825500; Valid loss,acc: 0.000042, 0.876500; Test loss,acc: 0.000045, 0.865200.\n",
      "Epoch 47 : Train loss,acc: 0.002373, 0.830000; Valid loss,acc: 0.000042, 0.879600; Test loss,acc: 0.000044, 0.869300.\n",
      "Epoch 48 : Train loss,acc: 0.002146, 0.831000; Valid loss,acc: 0.000041, 0.881000; Test loss,acc: 0.000044, 0.871400.\n",
      "Epoch 49 : Train loss,acc: 0.002058, 0.847500; Valid loss,acc: 0.000042, 0.875500; Test loss,acc: 0.000044, 0.864500.\n",
      "Epoch 50 : Train loss,acc: 0.002666, 0.826000; Valid loss,acc: 0.000043, 0.869700; Test loss,acc: 0.000046, 0.856200.\n",
      "Epoch 51 : Train loss,acc: 0.002051, 0.828500; Valid loss,acc: 0.000041, 0.879700; Test loss,acc: 0.000044, 0.868300.\n",
      "Epoch 52 : Train loss,acc: 0.002218, 0.839000; Valid loss,acc: 0.000041, 0.880400; Test loss,acc: 0.000044, 0.867300.\n",
      "Epoch 53 : Train loss,acc: 0.002295, 0.838000; Valid loss,acc: 0.000041, 0.877000; Test loss,acc: 0.000044, 0.865500.\n",
      "Epoch 54 : Train loss,acc: 0.002261, 0.848000; Valid loss,acc: 0.000041, 0.877000; Test loss,acc: 0.000044, 0.864900.\n",
      "Epoch 55 : Train loss,acc: 0.002116, 0.843000; Valid loss,acc: 0.000040, 0.880900; Test loss,acc: 0.000043, 0.869700.\n",
      "Epoch 56 : Train loss,acc: 0.002164, 0.841500; Valid loss,acc: 0.000040, 0.881100; Test loss,acc: 0.000043, 0.870400.\n",
      "Epoch 57 : Train loss,acc: 0.001945, 0.845000; Valid loss,acc: 0.000039, 0.884400; Test loss,acc: 0.000042, 0.873500.\n",
      "Epoch 58 : Train loss,acc: 0.001758, 0.843500; Valid loss,acc: 0.000040, 0.883400; Test loss,acc: 0.000043, 0.871100.\n",
      "Epoch 59 : Train loss,acc: 0.001913, 0.850500; Valid loss,acc: 0.000040, 0.881300; Test loss,acc: 0.000043, 0.869100.\n",
      "Epoch 60 : Train loss,acc: 0.002259, 0.841500; Valid loss,acc: 0.000040, 0.882600; Test loss,acc: 0.000042, 0.874200.\n",
      "Epoch 61 : Train loss,acc: 0.001823, 0.850000; Valid loss,acc: 0.000039, 0.885500; Test loss,acc: 0.000042, 0.876500.\n",
      "Epoch 62 : Train loss,acc: 0.001994, 0.855000; Valid loss,acc: 0.000040, 0.882100; Test loss,acc: 0.000042, 0.873500.\n",
      "Epoch 63 : Train loss,acc: 0.001784, 0.849000; Valid loss,acc: 0.000039, 0.886400; Test loss,acc: 0.000041, 0.878500.\n",
      "Epoch 64 : Train loss,acc: 0.001873, 0.858000; Valid loss,acc: 0.000039, 0.885100; Test loss,acc: 0.000042, 0.876100.\n",
      "Epoch 65 : Train loss,acc: 0.001940, 0.859000; Valid loss,acc: 0.000039, 0.885000; Test loss,acc: 0.000041, 0.876200.\n",
      "Epoch 66 : Train loss,acc: 0.001917, 0.856500; Valid loss,acc: 0.000039, 0.882800; Test loss,acc: 0.000042, 0.873500.\n",
      "Epoch 67 : Train loss,acc: 0.001880, 0.871500; Valid loss,acc: 0.000038, 0.887600; Test loss,acc: 0.000041, 0.878900.\n",
      "Epoch 68 : Train loss,acc: 0.002109, 0.859500; Valid loss,acc: 0.000039, 0.884100; Test loss,acc: 0.000042, 0.874000.\n",
      "Epoch 69 : Train loss,acc: 0.001897, 0.861500; Valid loss,acc: 0.000038, 0.886400; Test loss,acc: 0.000041, 0.878300.\n",
      "Epoch 70 : Train loss,acc: 0.001775, 0.865000; Valid loss,acc: 0.000038, 0.889400; Test loss,acc: 0.000041, 0.879400.\n",
      "Epoch 71 : Train loss,acc: 0.001770, 0.874000; Valid loss,acc: 0.000039, 0.883500; Test loss,acc: 0.000042, 0.873300.\n",
      "Epoch 72 : Train loss,acc: 0.001795, 0.866000; Valid loss,acc: 0.000038, 0.886700; Test loss,acc: 0.000041, 0.876400.\n",
      "Epoch 73 : Train loss,acc: 0.001681, 0.861000; Valid loss,acc: 0.000037, 0.891100; Test loss,acc: 0.000040, 0.881800.\n",
      "Epoch 74 : Train loss,acc: 0.001949, 0.859000; Valid loss,acc: 0.000037, 0.890300; Test loss,acc: 0.000041, 0.879900.\n",
      "Epoch 75 : Train loss,acc: 0.001687, 0.854000; Valid loss,acc: 0.000037, 0.890400; Test loss,acc: 0.000040, 0.883300.\n",
      "Epoch 76 : Train loss,acc: 0.001673, 0.856500; Valid loss,acc: 0.000037, 0.889800; Test loss,acc: 0.000040, 0.881500.\n",
      "Epoch 77 : Train loss,acc: 0.001554, 0.855500; Valid loss,acc: 0.000037, 0.890400; Test loss,acc: 0.000040, 0.881800.\n",
      "Epoch 78 : Train loss,acc: 0.001774, 0.874500; Valid loss,acc: 0.000037, 0.891400; Test loss,acc: 0.000039, 0.882900.\n",
      "Epoch 79 : Train loss,acc: 0.001731, 0.875000; Valid loss,acc: 0.000037, 0.891700; Test loss,acc: 0.000040, 0.883400.\n",
      "Epoch 80 : Train loss,acc: 0.001663, 0.877500; Valid loss,acc: 0.000036, 0.894600; Test loss,acc: 0.000039, 0.885900.\n",
      "Epoch 81 : Train loss,acc: 0.001971, 0.870000; Valid loss,acc: 0.000037, 0.889800; Test loss,acc: 0.000040, 0.884900.\n",
      "Epoch 82 : Train loss,acc: 0.001908, 0.872500; Valid loss,acc: 0.000036, 0.893200; Test loss,acc: 0.000039, 0.886300.\n",
      "Epoch 83 : Train loss,acc: 0.001908, 0.873000; Valid loss,acc: 0.000036, 0.894400; Test loss,acc: 0.000039, 0.884300.\n",
      "Epoch 84 : Train loss,acc: 0.001572, 0.870500; Valid loss,acc: 0.000037, 0.892700; Test loss,acc: 0.000039, 0.886300.\n",
      "Epoch 85 : Train loss,acc: 0.001817, 0.877000; Valid loss,acc: 0.000037, 0.890400; Test loss,acc: 0.000040, 0.881200.\n",
      "Epoch 86 : Train loss,acc: 0.001452, 0.875000; Valid loss,acc: 0.000036, 0.894000; Test loss,acc: 0.000039, 0.887200.\n",
      "Epoch 87 : Train loss,acc: 0.001740, 0.871500; Valid loss,acc: 0.000036, 0.893300; Test loss,acc: 0.000040, 0.884900.\n",
      "Epoch 88 : Train loss,acc: 0.001425, 0.871000; Valid loss,acc: 0.000035, 0.895200; Test loss,acc: 0.000038, 0.889100.\n",
      "Epoch 89 : Train loss,acc: 0.001812, 0.877000; Valid loss,acc: 0.000035, 0.895700; Test loss,acc: 0.000038, 0.890100.\n",
      "Epoch 90 : Train loss,acc: 0.001188, 0.878000; Valid loss,acc: 0.000035, 0.896500; Test loss,acc: 0.000038, 0.889800.\n",
      "Epoch 91 : Train loss,acc: 0.001617, 0.877000; Valid loss,acc: 0.000036, 0.894200; Test loss,acc: 0.000039, 0.888000.\n",
      "Epoch 92 : Train loss,acc: 0.001614, 0.874000; Valid loss,acc: 0.000036, 0.893000; Test loss,acc: 0.000039, 0.883700.\n",
      "Epoch 93 : Train loss,acc: 0.001699, 0.874500; Valid loss,acc: 0.000035, 0.897700; Test loss,acc: 0.000039, 0.886700.\n",
      "Epoch 94 : Train loss,acc: 0.001231, 0.879500; Valid loss,acc: 0.000035, 0.898000; Test loss,acc: 0.000038, 0.889500.\n",
      "Epoch 95 : Train loss,acc: 0.001635, 0.878000; Valid loss,acc: 0.000035, 0.896900; Test loss,acc: 0.000039, 0.887900.\n",
      "Epoch 96 : Train loss,acc: 0.001436, 0.884000; Valid loss,acc: 0.000035, 0.897700; Test loss,acc: 0.000038, 0.891100.\n",
      "Epoch 97 : Train loss,acc: 0.001466, 0.884500; Valid loss,acc: 0.000035, 0.898000; Test loss,acc: 0.000038, 0.891100.\n",
      "Epoch 98 : Train loss,acc: 0.001474, 0.880500; Valid loss,acc: 0.000035, 0.895900; Test loss,acc: 0.000038, 0.888300.\n",
      "Epoch 99 : Train loss,acc: 0.001266, 0.884500; Valid loss,acc: 0.000035, 0.897300; Test loss,acc: 0.000038, 0.890900.\n",
      "Epoch 100 : Train loss,acc: 0.001666, 0.876500; Valid loss,acc: 0.000036, 0.894600; Test loss,acc: 0.000039, 0.888800.\n"
     ]
    }
   ],
   "source": [
    "from confusionmatrix import ConfusionMatrix\n",
    "batch_size = 200\n",
    "num_epochs = 100\n",
    "learning_rate = 0.1\n",
    "num_samples = x_train.shape[0]\n",
    "num_batches = num_samples // batch_size\n",
    "\n",
    "x_valid = data['X_valid']\n",
    "targets_valid = data['y_valid']\n",
    "targets_valid = onehot(targets_valid, num_classes)\n",
    "\n",
    "x_test = data['X_test']\n",
    "targets_test = data['y_test']\n",
    "targets_test = onehot(targets_test, num_classes)\n",
    "\n",
    "acc, losses = [], []\n",
    "test_acc, test_loss = [], []\n",
    "valid_acc, valid_loss = [], []\n",
    "for epoch in range(num_epochs):\n",
    "    confusion = ConfusionMatrix(num_classes)\n",
    "    for i in range(num_batches):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        target_batch = targets_train[idx]\n",
    "        y_probs = forward(x_batch)\n",
    "        loss = LossLayer.fprop(y_probs, target_batch)\n",
    "        losses += [loss]\n",
    "        backward(y_probs, target_batch)\n",
    "        update(learning_rate)\n",
    "        confusion.batch_add(target_batch.argmax(-1), y_probs.argmax(-1))\n",
    "    \n",
    "    confusion_valid = ConfusionMatrix(num_classes)\n",
    "    y_valid_probs = forward_eval(x_valid)\n",
    "    loss_valid = LossLayer.fprop(y_valid_probs, targets_valid)\n",
    "    valid_loss += [loss_valid]\n",
    "    confusion_valid.batch_add(targets_valid.argmax(-1), y_valid_probs.argmax(-1))\n",
    "    valid_curr_acc = confusion_valid.accuracy()\n",
    "    valid_acc += [valid_curr_acc]\n",
    "\n",
    "    confusion_test = ConfusionMatrix(num_classes)\n",
    "    y_test_probs = forward_eval(x_test)\n",
    "    loss_test = LossLayer.fprop(y_test_probs, targets_test)\n",
    "    test_loss += [loss_test]\n",
    "    confusion_test.batch_add(targets_test.argmax(-1), y_test_probs.argmax(-1))\n",
    "    test_curr_acc = confusion_test.accuracy()\n",
    "    test_acc += [test_curr_acc]\n",
    "    \n",
    "    curr_acc = confusion.accuracy()\n",
    "    print \"Epoch %i : Train loss,acc: %f, %f; Valid loss,acc: %f, %f; Test loss,acc: %f, %f.\" % (epoch+1, np.mean(loss), curr_acc, np.mean(loss_valid), valid_curr_acc, np.mean(loss_test), test_curr_acc)\n",
    "    acc += [curr_acc]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  --------------------------------------------\n",
      " 0 | 184   0   1   1   0   3   1   1   0   0 |191\n",
      " 1 |   0 205   3   1   1   2   1   1   5   1 |220\n",
      " 2 |   1   3 174   2   4   2   4   2   5   1 |198\n",
      " 3 |   3   0   2 158   2  17   1   2   4   2 |191\n",
      " 4 |   1   2   1   0 190   2   4   3   1  10 |214\n",
      " 5 |   4   1   3  16   3 134   4   1  10   4 |180\n",
      " 6 |   3   1   1   0   5   2 186   0   2   0 |200\n",
      " 7 |   0   5   1   1   5   0   0 206   0   6 |224\n",
      " 8 |   1   2   3   4   2   9   3   1 141   6 |172\n",
      " 9 |   2   1   2   3   8   4   0  12   3 175 |210\n",
      "  --------------------------------------------\n",
      "     199 220 191 186 220 175 204 229 171 205\n",
      "\n",
      "  -------------------------------------------------\n",
      " 0 |  939    0   11    5    0   23    8    1    2    2 |991\n",
      " 1 |    0 1029    6    3    0   10    3    2    9    2 |1064\n",
      " 2 |    3    7  902   12   16    3   12    7   23    5 |990\n",
      " 3 |    3    2   30  823    1  127    2    6   25   11 |1030\n",
      " 4 |    2    7    5    1  895    1    3    2    1   66 |983\n",
      " 5 |    6    2   13   35   10  810   14    7    8   10 |915\n",
      " 6 |    8    1   29    0   20   23  884    0    2    0 |967\n",
      " 7 |    5    9   19    7    7    2    0 1004    1   36 |1090\n",
      " 8 |    2   26   22   26    5   60    7    5  816   40 |1009\n",
      " 9 |    7    3    7   16   32    7    0   43    2  844 |961\n",
      "  -------------------------------------------------\n",
      "     975 1086 1044 928 986 1066 933 1077 889 1016\n",
      "\n",
      "  --------------------------------------------------\n",
      " 0 |  947    0    9    2    1   12    8    1    0    0 |980\n",
      " 1 |    0 1109    6    3    0    4    3    0   10    0 |1135\n",
      " 2 |   11    5  933   11   18    2   15   10   25    2 |1032\n",
      " 3 |    6    0   24  805    2  133    2   19   13    6 |1010\n",
      " 4 |    3    3    6    0  900    3   11    3    2   51 |982\n",
      " 5 |   12    1    7   25   14  784   15    5   19   10 |892\n",
      " 6 |   16    4   23    2   26   28  858    0    1    0 |958\n",
      " 7 |    1   17   38    4    8    1    0  915    3   41 |1028\n",
      " 8 |    5   10   23   28   12   87   20    8  745   36 |974\n",
      " 9 |    5    3   11   13   29   20    0   34    2  892 |1009\n",
      "  --------------------------------------------------\n",
      "     1006 1152 1080 893 1010 1074 932 995 820 1038\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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T0LuhLRnXrrWPyCtXwmuv2TGV7lgs3g2MsTWBr7+GH37I33Wxf7/dvvf66/M3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\nrb6elgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115eacf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print confusion\n",
    "print confusion_valid\n",
    "print confusion_test\n",
    "plt.plot(range(num_epochs), acc, label='training')\n",
    "plt.plot(range(num_epochs), valid_acc, label='validation')\n",
    "plt.plot(range(num_epochs), test_acc, label='testing')\n",
    "plt.title('Training Accuracy on MNIST')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(loc=4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import theano\n",
    "import theano.tensor as T # Theano subpackage where many useful symbols are included."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import lasagne\n",
    "from lasagne.layers import InputLayer, DenseLayer, get_output, get_all_params\n",
    "from lasagne.init import Normal, Constant\n",
    "from lasagne.nonlinearities import rectify, softmax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "batch_size = 100\n",
    "num_class = 10\n",
    "learning_rate = 0.1\n",
    "\n",
    "data = np.load('mnist.npz')\n",
    "num_classes = 10\n",
    "x_train = data['X_train'].astype('float32')\n",
    "targets_train = data['y_train'].astype('int32')\n",
    "\n",
    "x_valid = data['X_valid'].astype('float32')\n",
    "targets_valid = data['y_valid'].astype('int32')\n",
    "\n",
    "x_test = data['X_test'].astype('float32')\n",
    "targets_test = data['y_test'].astype('int32')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "l_in = InputLayer(shape=(batch_size, x_train.shape[1]))\n",
    "l_hid = DenseLayer(incoming=l_in, num_units=100, nonlinearity=rectify)\n",
    "l_out = DenseLayer(incoming=l_hid, num_units=num_class, nonlinearity=softmax)\n",
    "#l_hid = DenseLayer(incoming=l_in, num_units=100, W=Normal(1,0), b=Constant(0.), nonlinearity=rectify)\n",
    "#l_out = DenseLayer(incoming=l_hid, num_units=10, W=Normal(1,0), b=Constant(0.), nonlinearity=softmax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from lasagne.objectives import categorical_crossentropy\n",
    "from lasagne.updates import sgd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sym_x = T.matrix('sym_x') # a symbolic variable taking on the value of a input batch.\n",
    "sym_t = T.ivector('sym_t') # a symbolic variable taking on the value of the target batch.\n",
    "\n",
    "# Get network output\n",
    "train_out = lasagne.layers.get_output(l_out, sym_x, deterministic=False)\n",
    "eval_out = lasagne.layers.get_output(l_out, sym_x, deterministic=True)\n",
    "\n",
    "\n",
    "# Get list of all trainable parameters in the network.\n",
    "all_params = lasagne.layers.get_all_params(l_out, trainable=True)\n",
    "\n",
    "cost = T.nnet.categorical_crossentropy(train_out+1e-8, sym_t).mean()\n",
    "# Let Theano do its magic and get all the gradients we need for training\n",
    "all_grads = T.grad(cost, all_params)\n",
    "\n",
    "\n",
    "# Set the update function for parameters \n",
    "# you might wan't to experiment with more advanded update schemes like rmsprob, adadelta etc.\n",
    "updates = lasagne.updates.sgd(all_grads, all_params, learning_rate=learning_rate)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "f_eval = theano.function([sym_x],\n",
    "                     eval_out, on_unused_input='warn')\n",
    "\n",
    "f_train = theano.function([sym_x, sym_t],\n",
    "                          [cost],\n",
    "                          updates=updates, on_unused_input='warn')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('l_in', (45, 784))\n",
      "('l_hid', (45, 100))\n",
      "('l_out', (45, 10))\n"
     ]
    }
   ],
   "source": [
    "    #Test the forward pass\n",
    "x = np.random.normal(0,1, (45, 28*28)).astype('float32') #dummy data\n",
    "\n",
    "model = lasagne.layers.get_output(l_in, sym_x)\n",
    "out = model.eval({sym_x:x}) #this could also include mask etc if used\n",
    "print(\"l_in\", out.shape)\n",
    "\n",
    "\n",
    "model = lasagne.layers.get_output(l_hid, sym_x)\n",
    "out = model.eval({sym_x:x}) #this could also include mask etc if used\n",
    "print(\"l_hid\", out.shape)\n",
    "\n",
    "\n",
    "model = lasagne.layers.get_output(l_out, sym_x)\n",
    "out = model.eval({sym_x:x}) #this could also include mask etc if used\n",
    "print(\"l_out\", out.shape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1 : Train Loss 2.339797e+00 , Train acc 0.909280,  Valid acc 0.921100 \n",
      "Epoch 2 : Train Loss 1.336328e+00 , Train acc 0.932020,  Valid acc 0.939300 \n",
      "Epoch 3 : Train Loss 1.074890e+00 , Train acc 0.944860,  Valid acc 0.948300 \n",
      "Epoch 4 : Train Loss 9.037619e-01 , Train acc 0.953280,  Valid acc 0.955500 \n",
      "Epoch 5 : Train Loss 7.817803e-01 , Train acc 0.960000,  Valid acc 0.959500 \n",
      "Epoch 6 : Train Loss 6.893804e-01 , Train acc 0.965040,  Valid acc 0.962000 \n",
      "Epoch 7 : Train Loss 6.165814e-01 , Train acc 0.968560,  Valid acc 0.964700 \n",
      "Epoch 8 : Train Loss 5.579831e-01 , Train acc 0.971660,  Valid acc 0.967600 \n",
      "Epoch 9 : Train Loss 5.092940e-01 , Train acc 0.974320,  Valid acc 0.969800 \n",
      "Epoch 10 : Train Loss 4.682522e-01 , Train acc 0.976380,  Valid acc 0.970800 \n"
     ]
    }
   ],
   "source": [
    "from confusionmatrix import ConfusionMatrix\n",
    "batch_size = 100\n",
    "num_epochs = 10\n",
    "learning_rate = 0.1\n",
    "num_samples_train = x_train.shape[0]\n",
    "num_batches_train = num_samples_train // batch_size\n",
    "num_samples_valid = x_valid.shape[0]\n",
    "num_batches_valid = num_samples_valid // batch_size\n",
    "\n",
    "train_acc, train_loss = [], []\n",
    "valid_acc, valid_loss = [], []\n",
    "test_acc, test_loss = [], []\n",
    "cur_loss = 0\n",
    "loss = []\n",
    "for epoch in range(num_epochs):\n",
    "    #Forward->Backprob->Update params\n",
    "    cur_loss = 0\n",
    "    for i in range(num_batches_train):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        target_batch = targets_train[idx]    \n",
    "        batch_loss = f_train(x_batch,target_batch) #this will do the complete backprob pass\n",
    "        cur_loss += batch_loss[0]\n",
    "    loss += [cur_loss/batch_size]\n",
    "    \n",
    "    confusion_valid = ConfusionMatrix(num_classes)\n",
    "    confusion_train = ConfusionMatrix(num_classes)\n",
    "\n",
    "    for i in range(num_batches_train):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_train[idx]\n",
    "        targets_batch = targets_train[idx]\n",
    "        net_out = f_eval(x_batch)   \n",
    "        preds = np.argmax(net_out, axis=-1) \n",
    "        confusion_train.batch_add(targets_batch, preds)\n",
    "\n",
    "    confusion_valid = ConfusionMatrix(num_classes)\n",
    "    for i in range(num_batches_valid):\n",
    "        idx = range(i*batch_size, (i+1)*batch_size)\n",
    "        x_batch = x_valid[idx]\n",
    "        targets_batch = targets_valid[idx]\n",
    "        net_out = f_eval(x_batch)   \n",
    "        preds = np.argmax(net_out, axis=-1) \n",
    "        \n",
    "        confusion_valid.batch_add(targets_batch, preds)\n",
    "    \n",
    "    train_acc_cur = confusion_train.accuracy()\n",
    "    valid_acc_cur = confusion_valid.accuracy()\n",
    "\n",
    "    \n",
    "    print \"Epoch %i : Train Loss %e , Train acc %f,  Valid acc %f \" \\\n",
    "    % (epoch+1, loss[-1], train_acc_cur, valid_acc_cur)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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