Programming Exercise 4 - Neural Network Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Exercise 4: Neural Networks Learning\n",
    "\n",
    "> In this exercise, you will implement the backpropagation algorithm for neural networks and apply it to the task of hand-written digit recognition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Neural Networks\n",
    "\n",
    "### 1.1 Visualizing the data\n",
    "\n",
    "> There are 5000 training examples in ex4data1.mat, where each training example is a 20 pixel by 20 pixel grayscale image of the digit. Each pixel is represented by a floating point number indicating the grayscale intensity at that location."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "mat = scipy.io.loadmat('data/ex4data1.mat')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = 10\n",
    "cols = 10\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "indexes = np.random.choice(5000, rows*cols)\n",
    "count = 0\n",
    "for i in range(0,rows):\n",
    "    for j in range(0,cols):\n",
    "        ax1 = fig.add_subplot(rows, cols, count+1)\n",
    "        ax1.imshow(mat['X'][indexes[count]].reshape((20,20), order='F'), cmap='gray')\n",
    "        ax1.set_axis_off()\n",
    "        count+=1\n",
    "plt.subplots_adjust(wspace=.1, hspace=.1, left=0, right=1, bottom=0, top=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Model representation\n",
    "\n",
    "<img src=\"neural_network.png\">\n",
    "\n",
    "* $a_i^{(j)}$ = activation of unit $i$ in layer $j$\n",
    "\n",
    "* $\\Theta^{(j)}$ = matrix of weights controlling function mapping from layer $j$ to layer $j+1$. It's dimension is $s_{j+1}\\times(s_j+1)$ where $s_j$ is the number of units in layer $j$ and $s_{j+1}$ is the number of units in layer $j+1$.\n",
    "\n",
    "* $z^{(j+1)} = \\Theta^{(j)}a^{(j)}$\n",
    "\n",
    "* $h_\\Theta(x) = a^{(j+1)} = g(z^{(j+1)}) $\n",
    "\n",
    "\n",
    "\n",
    "Our neural network has:\n",
    "* $3$ layers: an input layer, a hidden layer and an output layer\n",
    "* $400$ input layer units (because the images are of size $20 \\times 20$\n",
    "* $25$ units in the second layer\n",
    "* $10$ output units (corresponding to the 10 digit classes)\n",
    "* $\\Theta^{(1)}$ and $\\Theta^{(2)}$ are provided\n",
    "    * $\\Theta^{(1)}$ has dimension $25 \\times 401$\n",
    "    * $\\Theta^{(2)}$ has dimension $10 \\times 26$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_layer_size = 400\n",
    "hidden_layer_size = 25\n",
    "num_labels = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 401), (10, 26))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat_weights = scipy.io.loadmat('data/ex4weights.mat')\n",
    "mat_weights['Theta1'].shape, mat_weights['Theta2'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unroll parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "nn_params = np.hstack((mat_weights['Theta1'].ravel(order='F'), \n",
    "                       mat_weights['Theta2'].ravel(order='F')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Feedforward and cost function\n",
    "\n",
    "Cost function without regularization\n",
    "\n",
    "$$ J(\\theta) = \\frac{1}{m} \\sum_{i=1}^m \\sum_{k=1}^K [-y_k^{(i)} log((h_\\theta(x^{(i)}))_k) - (1-y_k^{(i)})log(1-(h_\\theta(x^{(i)}))_k)]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def sigmoid(z):\n",
    "    z = np.array(z)\n",
    "    return 1 / (1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y):\n",
    "    \n",
    "    theta1 = np.reshape(nn_params[:hidden_layer_size * (input_layer_size+1)], newshape=(hidden_layer_size, input_layer_size+1), order='F')\n",
    "    theta2 = np.reshape(nn_params[hidden_layer_size * (input_layer_size+1):], newshape=(num_labels, hidden_layer_size+1), order='F')\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    J = 0\n",
    "    \n",
    "    K = num_labels\n",
    "    X = np.hstack((np.ones((m,1)),X)) #add bias unit\n",
    "\n",
    "    for i in range(m):\n",
    "        a1 = X[i]\n",
    "        \n",
    "        z2 = a1.dot(theta1.T)\n",
    "        a2 = sigmoid(z2)\n",
    "        a2 = np.hstack([1, a2]) ##add bias unit\n",
    "        \n",
    "        z3 = a2.dot(theta2.T)\n",
    "        a3 = sigmoid(z3)\n",
    "        \n",
    "        h = a3\n",
    "        \n",
    "        yk = np.zeros((K,1)) ##y is as K-dimensional vector\n",
    "        yk[y[i,0]-1, 0] = 1\n",
    "        \n",
    "        j = (-yk.T.dot(np.log(h).T) - (1-yk).T.dot(np.log(1-h).T))\n",
    "        J = J + (j/m)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at parameters (loaded from ex4weights): [ 0.28762917] \n",
      "(this value should be about 0.287629)\n"
     ]
    }
   ],
   "source": [
    "J = nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, mat['X'], mat['y'])\n",
    "print('Cost at parameters (loaded from ex4weights): {0} \\n(this value should be about 0.287629)'.format(J))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Regularized cost function\n",
    "\n",
    "Cost function with regularization for neural network of the example:\n",
    "\n",
    "$$ J(\\theta) = \\frac{1}{m} \\sum_{i=1}^m \\sum_{k=1}^K [-y_k^{(i)} log((h_\\theta(x^{(i)}))_k) - (1-y_k^{(i)})log(1-(h_\\theta(x^{(i)}))_k)] + \\frac{\\lambda}{2m}[\\sum_{j=1}^{25} \\sum_{k=1}^{400} (\\Theta_{j,k}^{(1)})^2 + \\sum_{j=1}^{10} \\sum_{k=1}^{25} (\\Theta_{j,k}^{(2)})^2] $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r):\n",
    "    \n",
    "    theta1 = np.reshape(nn_params[:hidden_layer_size * (input_layer_size+1)], newshape=(hidden_layer_size, input_layer_size+1), order='F')\n",
    "    theta2 = np.reshape(nn_params[hidden_layer_size * (input_layer_size+1):], newshape=(num_labels, hidden_layer_size+1), order='F')\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    J = 0\n",
    "    \n",
    "    K = num_labels\n",
    "    X = np.hstack((np.ones((m,1)),X)) #add bias unit\n",
    "\n",
    "    for i in range(m):\n",
    "        a1 = X[i]\n",
    "        \n",
    "        z2 = a1.dot(theta1.T)\n",
    "        a2 = sigmoid(z2)\n",
    "        a2 = np.hstack([1, a2]) ##add bias unit\n",
    "        \n",
    "        z3 = a2.dot(theta2.T)\n",
    "        a3 = sigmoid(z3)\n",
    "        \n",
    "        h = a3\n",
    "        \n",
    "        yk = np.zeros((K,1)) ##y is as K-dimensional vector\n",
    "        yk[y[i,0]-1, 0] = 1\n",
    "        \n",
    "        j = (-yk.T.dot(np.log(h).T) - (1-yk).T.dot(np.log(1-h).T)) ##sum of K\n",
    "        J = J + (j/m) #sum of i\n",
    "        \n",
    "    sum1 = np.sum(np.sum(theta1[:, 1:] ** 2))\n",
    "    sum2 = np.sum(np.sum(theta2[:, 1:] ** 2))\n",
    "    J = J + (lambda_r / (2*m)) * (sum1 + sum2)\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at parameters (loaded from ex4weights): [ 0.38376986] \n",
      "(this value should be about 0.383770)\n"
     ]
    }
   ],
   "source": [
    "lambda_r = 1\n",
    "\n",
    "J = nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, mat['X'], mat['y'], lambda_r)\n",
    "print('Cost at parameters (loaded from ex4weights): {0} \\n(this value should be about 0.383770)'.format(J))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Backpropagation\n",
    "\n",
    "> In this part of the exercise, you will implement the backpropagation algorithm to compute the gradient for the neural network cost function.\n",
    "\n",
    "### 2.1 Sigmoid gradient\n",
    "\n",
    "$$g'(z) = \\frac{d}{dz}g(z) = g(z)(1-g(z))$$ \n",
    "\n",
    "where $g(z) = sigmoid(z) = \\frac{1}{1+e^{-z}}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_gradient(z):\n",
    "    return sigmoid(z) * (1-sigmoid(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Random initialization\n",
    "> When training neural networks, it is important to randomly initialize the pa- rameters for symmetry breaking. One effective strategy for random initialization is to randomly select values for $\\Theta^{(l)}$ uniformly in the range $[−\\epsilon_{init}, \\epsilon_{init}]$. You should use $\\epsilon_{init} = 0.12$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon_init = 0.12\n",
    "initial_theta1 = np.random.uniform(low=-epsilon_init, high=epsilon_init, size=(hidden_layer_size, input_layer_size+1))\n",
    "initial_theta2 = np.random.uniform(low=-epsilon_init, high=epsilon_init, size=(num_labels, hidden_layer_size+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Backpropagation\n",
    "\n",
    "> Given a training example $(x^{(t)},y^{(t)})$, we will first run a \"forward pass\" to compute all the activations throughout the network, including the output value of the hypothesis $h_\\Theta(x)$. Then, for each node $j$ in layer $l$, we would like to compute an \"error term\" $\\delta_j^{(l)}$ that measures how much that node was \"responsible\" for any errors in our output.\n",
    "\n",
    "<img src=\"backpropagation.png\">\n",
    "\n",
    "Algorithm:\n",
    "\n",
    "1) Set the input layer's values $(a^{(1)})$ to the t-th training example $x^{(t)}$.\n",
    "Perform a feedforward pass, computing the activations ($z^{(2)}, a^{(2)}, z^{(3)}, a^{(3)}$) for layers 2 and 3.\n",
    "\n",
    "2) For each output unit $k$ in layer $3$ (the output layer), set \n",
    "\n",
    "$$ \\delta_k^{(3)} = (a_k^{(3)} - y_k)$$\n",
    "\n",
    "3) For the hidden layer $l = 2$, set\n",
    "\n",
    "$$ \\delta_k^{(2)} = (\\Theta^{(2)})^T \\delta^{(3)} .* g'(z^{(2)})$$ \n",
    "\n",
    "4) Accumulate the gradient from this example using the following formula. Note that you should skip or remove $\\delta_0^{(2)}$\n",
    "\n",
    "$$ \\Delta^{(l)} = \\Delta^{(l)} + \\delta^{(l+1)}(a^{(l)})^T$$\n",
    "\n",
    "5) Obtain the (unregularized) gradient for the neural network cost func-\n",
    "tion by dividing the accumulated gradients by $\\frac{1}{m}$:\n",
    "\n",
    "$$ D_{ij}^{(l)} = \\frac{1}{m}\\Delta_{ij}^{(l)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r):\n",
    "    \n",
    "    theta1 = np.reshape(nn_params[:hidden_layer_size * (input_layer_size+1)], newshape=(hidden_layer_size, input_layer_size+1), order='F')\n",
    "    theta2 = np.reshape(nn_params[hidden_layer_size * (input_layer_size+1):], newshape=(num_labels, hidden_layer_size+1), order='F')\n",
    "    \n",
    "    m = X.shape[0]\n",
    "    J = 0\n",
    "    \n",
    "    K = num_labels\n",
    "    X = np.hstack((np.ones((m,1)),X)) #add bias unit\n",
    "\n",
    "    capital_delta1 = np.zeros(theta1.shape)\n",
    "    capital_delta2 = np.zeros(theta2.shape)\n",
    "    \n",
    "    for i in range(m):\n",
    "        a1 = X[i]\n",
    "        \n",
    "        z2 = a1.dot(theta1.T)\n",
    "        a2 = sigmoid(z2)\n",
    "        a2 = np.hstack([1, a2]) ##add bias unit\n",
    "        \n",
    "        z3 = a2.dot(theta2.T)\n",
    "        a3 = sigmoid(z3)\n",
    "        \n",
    "        h = a3\n",
    "        \n",
    "        yk = np.zeros((K,1)) ##y is as K-dimensional vector\n",
    "        yk[y[i,0]-1, 0] = 1\n",
    "        \n",
    "        j = (-yk.T.dot(np.log(h).T) - (1-yk).T.dot(np.log(1-h).T)) ##sum of K\n",
    "        J = J + (j/m) #sum of i\n",
    "        \n",
    "        delta3 = a3 - yk.T\n",
    "        \n",
    "        z2 = np.hstack([1, z2])\n",
    "        delta2 = theta2.T.dot(delta3.T) * (sigmoid_gradient(z2).reshape(-1,1))\n",
    "        \n",
    "        capital_delta1 = capital_delta1 + (delta2[1:,:].dot(a1.reshape(1,-1)))\n",
    "        capital_delta2 = capital_delta2 + (delta3.T.dot(a2.reshape(1,-1)))\n",
    "        \n",
    "    sum1 = np.sum(np.sum(theta1[:, 1:] ** 2))\n",
    "    sum2 = np.sum(np.sum(theta2[:, 1:] ** 2))\n",
    "    J = J + (lambda_r / (2*m)) * (sum1 + sum2)\n",
    "    \n",
    "    theta1_grad = (1/m) * (capital_delta1 + lambda_r * theta1) #with regularization\n",
    "    theta1_grad[:,0] = ((1/m) * capital_delta1)[:,0]\n",
    "    \n",
    "    theta2_grad = (1/m) * (capital_delta2 + lambda_r * theta2) #with regularization\n",
    "    theta2_grad[:,0] = ((1/m) * capital_delta2)[:,0]\n",
    "    \n",
    "    grad = np.hstack((theta1_grad.ravel(order='F'), theta2_grad.ravel(order='F')))\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Gradient Checking\n",
    "\n",
    "> In your neural network, you are minimizing the cost function $J(\\Theta)$. To perform gradient checking on your parameters, you can imagine “unrolling” the parameters $\\Theta^{(1)}, \\Theta^{(2)}$ into a long vector $\\theta$. By doing so, you can think of the cost function being $J(\\theta)$ instead and use the following gradient checking procedure. Suppose you have a function $f_i(\\theta)$ that purportedly computes $\\frac{\\partial}{\\partial \\theta_i} J(\\theta)$; you’d like to check if $f_i$ is outputting correct derivative values. If $\\theta^{(i+)}$ is the same $\\theta$, except its i-th element has been incremented by $\\epsilon$. You can now numerically verify $f_i(\\theta)$’s correctness by checking, for each $i$, that: $f_i(\\theta) \t\\approx \\frac{J(\\theta^{(i+)} - J(\\theta^{(i-)}}{2\\epsilon}$. The degree to which these two values should approximate each other will depend on the details of $J$. But assuming $\\epsilon = 10^{−4}$, you’ll usually find that the left- and right-hand sides of the above will agree to at least 4 significant digits (and often many more)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_numerical_gradient(theta, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r):\n",
    "    e = 0.0001\n",
    "    num_grad = np.zeros(theta.shape)\n",
    "    perturb = np.zeros(theta.shape)\n",
    "    for p in range(len(theta)):\n",
    "        perturb[p] = e\n",
    "        loss1, _ = nn_cost_function(theta-perturb, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r)\n",
    "        loss2, _ = nn_cost_function(theta+perturb, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r)\n",
    "        num_grad[p] = (loss2-loss1)/(2*e)\n",
    "        perturb[p] = 0\n",
    "    return num_grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def debug_initialize_weights(fan_out, fan_in):\n",
    "    W = np.zeros((fan_out, 1+fan_in))\n",
    "    W = np.reshape(range(len(W.ravel(order='F'))), W.shape)/10\n",
    "    return W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_nn_gradients(lambda_r=0):\n",
    "    input_layer_size = 3\n",
    "    hidden_layer_size = 5\n",
    "    num_labels = 3\n",
    "    m = 5\n",
    "    \n",
    "    theta1 = debug_initialize_weights(hidden_layer_size, input_layer_size)\n",
    "    theta2 = debug_initialize_weights(num_labels, hidden_layer_size)\n",
    "    \n",
    "    X = debug_initialize_weights(m, input_layer_size-1)\n",
    "    y = 1 + np.mod(range(m), num_labels).reshape(-1, 1)\n",
    "    \n",
    "    nn_params = np.hstack((theta1.ravel(order='F'), theta2.ravel(order='F')))\n",
    "    \n",
    "    cost, grad = nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r)\n",
    "    num_grad = compute_numerical_gradient(nn_params, input_layer_size, hidden_layer_size, num_labels, X, y, lambda_r)\n",
    "    \n",
    "    print('The columns should be very similar...')\n",
    "    for i, j in zip(num_grad, grad):\n",
    "        print(i,j)\n",
    "        \n",
    "    diff = np.linalg.norm(num_grad-grad)/np.linalg.norm(num_grad+grad)\n",
    "    if diff < 0.000000010:\n",
    "        print('\\nBackpropagation is correct')\n",
    "    else:\n",
    "        print('\\nBackpropagation is incorrect')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The columns should be very similar...\n",
      "0.350810279111 0.350810278248\n",
      "0.235352218816 0.235352218829\n",
      "0.145297910761 0.145297911142\n",
      "0.0931519991454 0.0931519992319\n",
      "0.0603206957006 0.0603206959969\n",
      "0.193739801544 0.193739801851\n",
      "0.0873538309687 0.0873538307836\n",
      "0.0297739735089 0.029773974437\n",
      "0.0105903644609 0.0105903645745\n",
      "0.00404766653972 0.0040476658802\n",
      "0.228820831349 0.228820829676\n",
      "0.110889052669 0.110889052667\n",
      "0.0443037659892 0.0443037655512\n",
      "0.0199055643968 0.0199055644977\n",
      "0.0100797357039 0.0100797354799\n",
      "0.263901857176 0.2639018575\n",
      "0.134424273925 0.134424274549\n",
      "0.0588335566487 0.0588335566654\n",
      "0.0292207642172 0.0292207644209\n",
      "0.0161118053743 0.0161118050796\n",
      "0.396222246097 0.396222246265\n",
      "0.588733996851 0.58873399685\n",
      "0.799466367374 0.799466367039\n",
      "0.249842282916 0.249842282957\n",
      "0.349065613472 0.349065613487\n",
      "0.484656985673 0.484656985951\n",
      "0.343211700198 0.343211700294\n",
      "0.469290171488 0.469290171492\n",
      "0.648764112379 0.648764112678\n",
      "0.380299384979 0.380299385093\n",
      "0.526333519888 0.526333519887\n",
      "0.720856438514 0.720856438357\n",
      "0.393027787062 0.393027787199\n",
      "0.553043481188 0.553043481221\n",
      "0.755454640409 0.755454640119\n",
      "0.39678989241 0.396789892552\n",
      "0.56741786941 0.567417869423\n",
      "0.774136082491 0.774136082163\n",
      "\n",
      "Backpropagation is correct\n"
     ]
    }
   ],
   "source": [
    "check_nn_gradients()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The columns should be very similar...\n",
      "0.350810279119 0.350810278248\n",
      "0.235352218816 0.235352218829\n",
      "0.145297910752 0.145297911142\n",
      "0.0931519991454 0.0931519992319\n",
      "0.0603206956917 0.0603206959969\n",
      "0.253739801543 0.253739801851\n",
      "0.387353830966 0.387353830784\n",
      "0.569773973496 0.569773974437\n",
      "0.790590364446 0.790590364574\n",
      "1.02404766654 1.02404766588\n",
      "0.348820831348 0.348820829676\n",
      "0.470889052675 0.470889052667\n",
      "0.644303766002 0.644303765551\n",
      "0.85990556439 0.859905564498\n",
      "1.09007973572 1.09007973548\n",
      "0.443901857174 0.4439018575\n",
      "0.55442427394 0.554424274549\n",
      "0.718833556643 0.718833556665\n",
      "0.92922076421 0.929220764421\n",
      "1.15611180538 1.15611180508\n",
      "0.396222246088 0.396222246265\n",
      "0.58873399686 0.58873399685\n",
      "0.799466367383 0.799466367039\n",
      "0.309842282924 0.309842282957\n",
      "0.769065613486 0.769065613487\n",
      "1.26465698566 1.26465698595\n",
      "0.463211700197 0.463211700294\n",
      "0.949290171484 0.949290171492\n",
      "1.48876411238 1.48876411268\n",
      "0.560299384986 0.560299385093\n",
      "1.06633351988 1.06633351989\n",
      "1.62085643851 1.62085643836\n",
      "0.63302778706 0.633027787199\n",
      "1.15304348119 1.15304348122\n",
      "1.71545464042 1.71545464012\n",
      "0.696789892416 0.696789892552\n",
      "1.2274178694 1.22741786942\n",
      "1.79413608247 1.79413608216\n",
      "\n",
      "Backpropagation is correct\n",
      "Cost at parameters (loaded from ex4weights): [ 0.57605125] \n",
      "(this value should be about 0.576051)\n"
     ]
    }
   ],
   "source": [
    "lambda_r = 3\n",
    "check_nn_gradients(lambda_r)\n",
    "J, grad = nn_cost_function(nn_params, input_layer_size, hidden_layer_size, num_labels, mat['X'], mat['y'], lambda_r)\n",
    "print('Cost at parameters (loaded from ex4weights): {0} \\n(this value should be about 0.576051)'.format(J))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 Learning Parameters - Training the Neural Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt\n",
    "lambda_r = 1\n",
    "opt_results = opt.minimize(nn_cost_function, nn_params, args=(input_layer_size, \n",
    "                                                              hidden_layer_size, \n",
    "                                                              num_labels, \n",
    "                                                              mat['X'], \n",
    "                                                              mat['y'], \n",
    "                                                              lambda_r), \n",
    "                            method='L-BFGS-B', jac=True, options={'maxiter':50})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: array([ 0.31722116])\n",
       " hess_inv: <10285x10285 LbfgsInvHessProduct with dtype=float64>\n",
       "      jac: array([  2.31088680e-04,  -9.15347261e-05,  -6.81873625e-05, ...,\n",
       "        -4.79810736e-05,  -2.89538852e-05,   2.21663569e-05])\n",
       "  message: b'STOP: TOTAL NO. of ITERATIONS REACHED LIMIT'\n",
       "     nfev: 55\n",
       "      nit: 50\n",
       "   status: 1\n",
       "  success: False\n",
       "        x: array([-0.06388654, -0.13010792,  0.50133758, ..., -2.95836945,\n",
       "       -2.87425683, -1.74870182])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta1 = np.reshape(opt_results['x'][:hidden_layer_size * (input_layer_size+1)], newshape=(hidden_layer_size, input_layer_size+1), order='F')\n",
    "theta2 = np.reshape(opt_results['x'][hidden_layer_size * (input_layer_size+1):], newshape=(num_labels, hidden_layer_size+1), order='F')    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_nn(theta1, theta2, X):\n",
    "    m, n = X.shape\n",
    "    a1 = np.hstack((np.ones((m,1)),X)) #with a0\n",
    "    \n",
    "    z2 = a1.dot(theta1.T)\n",
    "    a2 = sigmoid(z2)\n",
    "    \n",
    "    z3 = np.hstack((np.ones((m,1)),a2)).dot(theta2.T) #with a0\n",
    "    a3 = sigmoid(z3)\n",
    "    h = np.argmax(a3, axis=1)+1 #get label with largest h(x)\n",
    "    \n",
    "    return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Train accuracy: 99.24'"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = predict_nn(theta1, theta2, mat['X'])\n",
    "accuracy = np.mean(y_pred == mat['y'].T)\n",
    "f'Train accuracy: {accuracy * 100}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.5.1 Similar Code using Scikit-Learn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MLPClassifier(activation='logistic', alpha=1, batch_size='auto', beta_1=0.9,\n",
       "       beta_2=0.999, early_stopping=False, epsilon=1e-08,\n",
       "       hidden_layer_sizes=(25,), learning_rate='constant',\n",
       "       learning_rate_init=0.001, max_iter=50, momentum=0.9,\n",
       "       n_iter_no_change=10, nesterovs_momentum=True, power_t=0.5,\n",
       "       random_state=None, shuffle=True, solver='lbfgs', tol=0.0001,\n",
       "       validation_fraction=0.1, verbose=False, warm_start=False)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.neural_network import MLPClassifier\n",
    "nn = MLPClassifier(hidden_layer_sizes=(hidden_layer_size,), activation='logistic', solver='lbfgs', alpha=1, max_iter=50)\n",
    "nn.fit(mat['X'], mat['y'].T[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98040000000000005"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn.score(mat['X'], mat['y'].T[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Visualizing the hidden layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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c+7Qi629KuwWe9Nr5/HJNZ+7cuakdbb3sZ732pky3WuCM6zo6Rni9tPPreo/alzeh62Kt9pFnFMYYY6r4RWGMMabKgLHHcirM6ZbWXqbdk5lfdRcma/3Syqf2S8olaunkdzNTrU67+RmcXup3tbtTVKUrfi8/W6fwnN5TOtDCRexzWmp1qs9rZ9bLiCwpTZ06tcS6w5n3jd/bifRE1PbJKT3vn+4Up+2VY0Wn7JSseD+OO+641I67cJmVNyLbYxlTstDv5lhReaBVSyP/Tu3jvC6O34ULF6Z2lCq4A1kt4rQfc0ezjk3KtpoZlfeOvwG176IUw7EY0ZrVmnKfnivt5LSi0iobkbPZ8vO0/jslJUpUs2fPTu1q9eufffbZEtOurLvFab/lM6vZIiw9GWOM6Qp+URhjjKnSb9KTJnPjrlROd7njMyJP8zhVVQmD9Wm525aSQ0ROuKY7p+nk4LRRdxNTTuAUv7dJyWqyCh0iTMwX0SwDMNFaRJayuBtbnU10RGlCREpblAJ1VyzPl9JJJ84wTpc1YR5lFBYTonym50d3iiah5BjgNajMQZeSynN0AVFW4PlF5LFTk+fUmdUE+1kL1vDeU4bS66cst3jx4hLzOYzI13/EEUeUWJMncvc0n5uIiJNOOqnEHBcqPfHv6K7rpJ9qSRr5eew/PlMRWf7iWHrooYdSu8mTJ5eYstSll16a2vHeLFq0KB1j/Wueh7oMKZUx1uet1SJYnlEYY4yp4heFMcaYKn5RGGOMqTJg7LHU5ahJqobGHYi0r9EqFpGthtzZyl3LEdk2qeshhOsXupZBbbmTwvdN6BoH9UXqp3retBbSjsgskhHZesc1GN0pyuu79dZb0zFaBZsslxH5ntIW2c3+UnjeamnmGgAzcmpfUqPn9amezR3iuvuVa1pcN9D7Qb2c7XqbdbgnOH6WLFlSYt3pzrUIri/ouXPtipl1uZs9Imv448aNS8c4Zqj76z3hekjT2ldE+zuztT37nTq/roVwTZDP6Je+9KXUbtKkSSXm+oJmh9iwYUOPnx0RceGFF5aYv2WaqZpZCXRNtRM8ozDGGFPFLwpjjDFVBrz0pJIBp/Wsnau7IDnF5TGVqCgn6C5wTrVrlkzKXGp57Cac1nLqymIpEfmauGNTi8jw8zjd1Sk8p7W6U5T3hzKAyma9tQo3UZMXKGtpH3E6zn7QndlMGEjbq9ZDphSl9dtppeVYVNsn/90kQ3WKSny8p7xmrU/N+3booYeWmIk2I/I1Uh4+6qijUjtKfrozm7uJ+ZxrDXLuLua960Y/Ed5H/p6o9ZsSGrMfqCWZ1lY+iyotcmxphgOOsyb5NCLfU35+p1KvZxTGGGOq+EVhjDGmyoCRnginRzqN5y5rugXUGcGaCpzyqcOAzhjN/U53BafgWh9Ap+F9AXf4qquBx+hA0b7kzm/+je7O5f1QKZDyHKe76nqiNKGf0Rt0Ks1ranKjRGRZgJKZ7hZmX1Da0D6nNKF1t5u+S3feb0kHmEp0vB+UMzRRIc+dsq06u5gdgNKTXiPlJpWKOAYpuXBne0R+1lW+6iZ8zul0UqmI44ztVA5nskjea01GyjGn2RTo9GRiQd2FTmmRv136HDgpoDHGmK7gF4UxxpgqflEYY4ypMiDXKIjuAKUOTp1Pd1wvX768xNQK1SZJm5quNVBLp35aq/fdV9R2mzPbK/VJ1YSpV/Ka1NbHv1MdvWlnrLZrd5dsp/B7eF/Unktdnsf02nkdXI/RbJ3U7Gs1rqnZq85fy/K5JaHOr3WeuW7HfqrZnXkPVDtnf+pzw2eMayX6GVtip3pP8Dp439TWzPvI3ww9T14vr0nXWfh52kdNn6+ZAjg+a79dreIZhTHGmCp+URhjjKmyVV9JAsYYY3498YzCGGNMFb8ojDHGVPGLwhhjTBW/KIwxxlTxi8IYY0wVvyiMMcZU6dOd2V//+td77cXlzk7uBFabb1PhF+5SjMg7H3U3bNN3dYPvfe97PaYKveKKK3rdR7x27uTU3dJN16T/vZbVlN/Vbav1VVdd1eMXf/vb3+4zTzevif3QasGk2md0g29961uNH/jNb35zwHnfOba2VDGrnvjOd77TYz/99V//db/3kT5v3HGtO7O3ZJ9deOGFjWPJMwpjjDFV/KIwxhhTZcAnBVQ4LWPRIU2KxWIiTOi11157pXZMOqhJvJikjckIta5yfyQFrEF5TRPPEfYf+4hJBSNygRSFCfDYX5rojMdalXD6iiapTo/VZJOmJIP6d61e75YsYtQOPHc+H1qUp6mdFstqKqgTkccSj9WScPalfNUKlK9r95Dnrb8f/AyVw1st+tXt8eMZhTHGmCp+URhjjKniF4UxxpgqA3KNoknv1H//6le/KjG1z4iIN998s8RcUxg6dGhqx0LmWoyGOiKL1mjhEuqG1Pq33nrr1K6bFlt+p34ui8/suOOOJdYiUCzixEIq2o7FnVj0PiLfA94bXdfgdzUVw4nonwJHrbajhq7jkmOHaz8Rec2I40MLHA2E9RqFWjfHCO9hRNbZd9pppxJz/EXka95+++3TsZdffrnEHGeq4bMPGeu6SX+s87S6jsVr/+STT1I7jhe9Jj6bXP+pFXPiMd0e0Ooaj2cUxhhjqvhFYYwxpsqAlJ5qUGKipKTTfVo8Fy5cWGLaZiOypESJJSLilFNOKfFXv/rVEu+xxx6N3/XSSy+VuGaT7ISmesMqWey9994l5lT1tddeS+123nnnEm+33XYlHjlyZGq3aNGiEqv0tO222/Z4HnpOnP7WpsmUEnoLz6E2xVZ5hHDs7Lvvvo1/w/MeMWJEOsY+o1ygEibH0aefflrivrRfq62Z18Wa8mrTpJRC2ZG1ryMilixZUuKbbropHRs8eHCJ161b19J31aQevZZuoTW8eQ61uvEcMxMnTiyx1rx/+OGHG7+L/6a0zecwIv821rJPWHoyxhjTFfyiMMYYU2XASE+c4m7cuLHE6kTiMUoYKnVw2jdq1KgS05ERkafT++yzTzr2xhtvlPgHP/hBiadMmZLacTo4fvz4EuuUsrZLul14fSrXcErK61Onyo033lhiSmZHHHFEakf56uOPP07HZs6cWWJKAnpOlAF47rrLXR1X3UJlAI6rIUOGlPj1119v/Ds6UFSCo5vnnnvuScd47ZQcKLVEROy5554l5th7++23Uzt1yfQWyiX6fFCO5VhSNw6ddrwu7XfKa7vvvns6xud08eLFJVapd8OGDSXmmFb5WXeFtwtlGV6HutV4DvxOff75d48//niJVZ6jDPzKK6+kY+wj3rdBgwY1njulO5WaKHHW8IzCGGNMFb8ojDHGVPGLwhhjTJU+XaOoZYSk7ZV62y677JLa3XbbbSWmJWz//fdP7bgL8rzzzivxH/3RH6V2P/zhD0s8derUdOxv//ZvS/zBBx+UWG201PmoIaqtr7eZLrnGQe1S+5J9tnTp0hJzF3VEXkc4+uijSzxp0qTG79U1hNNOO63E7AfVn59++ukScy1DNdhWqNmMW9WV169fX2Ku6axcuTK1o/7Mc+UagqJrXewLWo11veeAAw4oMXV5vW+6rtMJtElyrU/7if/mOta4ceNSO675cE1F1zy4DkO7cUTW9LluRM0+Il8/bbQ6NtUyujlq44pjRLNAcL2Ka5Rc04nI/czP098T9tGhhx6aji1YsKDEzIT93nvvpXZcr2Gs7VrFMwpjjDFV/KIwxhhTpU+lJ07tdIcg5QjKB8uWLUvtOF2fPn16iXX3Kne9rl69usRPPvlkakebn1ojuUOZMpLu7uaUklKP7kBuJelbbTdxk3VU+/Luu+8uMafm3LEdEXHCCSeUeNiwYSWm1TEiT5P1GjhtfvDBB0tMKSsiT5kpzeh3tWJprBVvaapzrveMlmbaWceOHZva0YpKyYPXE5ElOC38xGvkMU2cuGLFih6vg5bwiO4kD2Qf8h4ySWZEllko5bzwwguN7Q4//PASq2X1lltuKbHKKrz3lOteffXV1I7HKCEq7e7yryWopJRdq4nOMaeyOX8PKNOOGTMmteP9njBhQjpGyY+Sl44l9hnlP5XN9LlowjMKY4wxVfyiMMYYU6XfdmZrjWvKJ8xLrzuzjzzyyBJTGqKbJCLvhuWUWaUs7iJV+YquAjpedFcqpRm6o5h0L6KeDG8TnNbqNJFwqqlSBGUVOshYEyIiYvjw4SVukvQicjLB22+/PR3j51Omef755xvPiZ+nNcxbkVXYR+oI4pSeUsLy5ctTO7qKeD8p1el31dx4lO7UPUO5iZIoXUQRWVrkZ2hdk06kJ5Untd+avotyGyW0OXPmpHZ8TulM/MY3vpHa7bbbbiVmzZiILHtRslJphvCY7pbvbRLOJrlJJWB+D5MeKhxblMOPO+641I6/Q1dffXU6RjdYrXY4d7bTTac1QFrtI88ojDHGVPGLwhhjTBW/KIwxxlTptzUKrd1Kux71yT/90z9N7ah10/al6wvUcfl5qp1zJ+7Xv/71dGzevHklpn6qhX24pkKNUrNHqvVyc+g6Dq+Jmqlmn6Rezl2yukZy8803l5gas66tcIep6uN33XVXibmDdu3atakd7wHXSrgLtRNUe+e/uV6h2TW5xkCLpVoquV7DXfdq+1yzZk2Jb7311nSMGXb5XWpp1HWPTagdWK+5FfQzuNuetlS9frbj+FWL6KOPPlpiWtBPP/301I7jR7+LaznHH398iXWdssmyS90/ov1MCDW9njvxtQAYnz/2i+7y5xjkc6PnzetVGzZ/E/i86bopba/8G81g4TUKY4wxXcEvCmOMMVUGTOEiSlGUdmjhjMjTuauuuqrEBx54YGrHXZ+c7qocRLvs97///cbz4zR21apVjed+8MEHl1inqK1MhTl1rSX741RYJaVjjz22xNwpzsR8+ndXXnllibXwDmv4HnLIIekYd1nX7LGsPU1rqhbvUUljc2h7XhOlSZWeaMtlcjraDyMipk2bVmLWV1fZhHIB7YgR2bbJdmpF5b8ppWrBK02S1wmUFylPqhTBMcgxp7Ioz5e2X30GLr744hLfcMMN6Rg//yc/+UmJ1R47efLkEvOZoDU9or6Dvyf0+eTY4u51yowRzRZiTYhIy+pFF11UYi0oxvOmBBeRpW3+FuoYYWJPynOa9LHVeuyeURhjjKniF4Uxxpgq/SY91aZ5nLLpDlLuiqztdL7++utLzDoT6lahA0fPiZIEpQuVXzj1pOSidQPaTQqo10fJgcnC1PFA1xOdNbrrmPILp8yax//ss88usfYfpQomI+QO5Igsz7Gf9f6qHLM5VCppkq5YJyAi33dKFvr37Be6xGo7wlXepExD2VIlFbp56KTRcdnbHccReSxRftAkcdxJzbGtUu+Xv/zlEg8dOrTEWt+bjihmT4jIDji6zVRSuv/++6MnWsl80A4cCxy/Kt/wmaAUq642JuWkNK5JD/kMqIx51FFHlXju3LklpsSs0Cmq49uuJ2OMMV3BLwpjjDFV/KIwxhhTpd/WKGrWNWpqqnVz9yY1Xt3dyB2N1O/UikatVe16jzzySIkfeOCBEqs1csqUKSV+5plnSqzFXbTO8ObQNQ3q4iNGjCix6sDsW9o9uUM4Ihdqoq4+ceLE1I7rQlormpoz+0V3gFK3Zqw7szut6bsJ9hljtfwyCzE1Z11foI2UGrOuefz4xz8usa5NcYzx2nWnPvuP95QFjSLatxD3BNc9uF6hhYsI1020wBTXxbgOo8/UmWeeWeLRo0enYzfeeGOJeR90xzr7hn2mddp7C9duuG7ANc+I/IxxnUTHCC3itNuqRfyxxx4rse5K55oRx6bWH2cGAP7m1bID1/CMwhhjTBW/KIwxxlQZMPZYTvM4Lfu7v/u71I7TtCZLbUQunkL7mdbp/d73vlfiSy65JB1jkQ/KL5deemlqR6mG0kktqV8TTZa8iCwpcSem2vCYlI47z/V8aBHllJY1jyNyUSO9BvYRp7iaWJCyG79rw4YNqV27u2n1fGgVpsyjfcnd0rQI1pLdsdAOk7pFRBx00EEl1trklOe4K13lG0qLtaJV3YDPG79L7c/z588vMce5tmPfUJ485phjUjsWAFNZmRITn2dtx+/mMe0g0xzLAAAgAElEQVSzdu2y+pvEf3PMqlxKyYsFndRGyx3wlNCZbDIi4k/+5E9KzGwAEVli5+8kpeiIbOvmc6591KqM6RmFMcaYKn5RGGOMqeIXhTHGmCr9tkahaSeog1O3Vv2dmRuphf7+7/9+4+dTP6WuF5G1as2kyAyMTH+h6RuYYoBWOWqDEa1l/ayl8KB+z/6aNWtWanfnnXeWmBZfPR9eE1MPaMZeFmZSazDXHmi903Qh7Fuu96j+3Mo6Tg2mH+F6QC0dCq28Tz31VGrHtSDq1JpBlNqvXjuti1wn0tQU1LA3btxYYi1U1Ekf6d/wflDPVks3Lby0FOuzctNNN5WYha7UTk0brcKss8wgrf3J9Saui3VS0InQlq+ft+OOO5ZYdX6eA89b1yi4dvXiiy+WmM9eRP6N0t9Jjltm5lWLPNOj8F7p89vqmqBnFMYYY6r4RWGMMaZKn0pPtJvpNI9TLBb4UJmH00HKCZy2RzRnYOSux4hs49Sdspw6cncsd2JHZLmJ1j29xnZROyvtlJTMvvvd76Z27BdO03Uayyn0E088UeI77rgjtaNFTwv70JZHmymzqUbkHabsF52etzIVpoyicgPvO2VLvXbuHua91Z3h7HNKIHpv2eennnpqOkbLJO3EWuucfcbv0mwC3diZzeeKn6/PAGVb2nzVSspMCOeff36JdQzz/rAmvX43M9XqmOBn8P7rd7VbM1v/vinDrsp4zHDA55/3OiLLQZTxVJ7j2NLvouTMHf+U+/R8KWN2monYMwpjjDFV/KIwxhhTpU+lJ05zVFKiNMCauEykFZETAVL2qO06ppzwla98JbXjTtH77rsvHeM0b8aMGT1+XkR2aVGa0XPqLew/Skp0i0RkB8Ty5ctLrG4m9jndUZqIjEkVuQNZv4uFkPQz+G9Ok3XHdCtQetGpNM+H8hKdPRHZecUEdOrmoQuI91OLDvE89JwoR/B79ZwosfD5UKmpE9dTrbY4nV2a4YD3lFKl9tNll11WYkpoWpSHUq860Xi/6PzRQlp0ILFv25WalJoMyowQ2v+8RspnWsearif2n9YVZ6I+dWmyLzh+NLkfn6umOKL13eueURhjjKniF4UxxpgqflEYY4yp0m87sxXqftxRe8YZZ6R21CGpE3OtISJiyZIlJaZNTdcNnnvuuRKrHkj7IjNGatZPrmXQuqe6cG81VO6q5PdQs43Iu4ZpEWUxk4isT7KYve4gpzataxS0zrK/1D7KdR3uSO5tnyjsc9oO1WLJPuJuWhavj8jWao4P/Txeh1p2uZa2cuXKEqulm+dOy2pvd6v3BM+fu+N1zA4aNKjEvG/6vFEjrxWC4rOt6yGEY1N1dK5LdMMq3ATvKce5rq9y3YVrggrHD23HulbFbLK645rnQQuxWnH5+8B7rXbYVp8/zyiMMcZU8YvCGGNMlQEjPdEuRtmC9ryIbK3kDu6PPvootWMCt9tvv73EKguwri13OkZkKyPh9DkiTx35+d2WDCg9cXqv01NKGpTn1GZIqxzbqU2QhYyYKDEi7zblfdOCK7y/tE9qH7UrJdT+nv2l50MZgEn7NCkgpUpO4VV+pNRJuSYiT/cpU6rNmnZl9mtfSk8qqdHiySJYutOdzwCPqURFm6nuAuc94jVrESzKXCqndhPKMuwjlW84Rpos7BF53PNZmTBhQmrH51nlOZ4TLef6u8ZnuNXd1zU8ozDGGFPFLwpjjDFVBoz0xKk2p3I6feO0nlNclag4XaVjSadynOLqMe64pHSiu1J5Hnqsm1Du4FRTazqMHj26xHTPqKzA66VMozVAeIzJ3/Q8OJ1WNwWdWZSHeuta0b/neOG5aY1n9iV3/7OWcURz7WqO14gsozB5nn43x6XeD45t9t+WdPbo56ukRrmEtST0WaF0SelT60+wLzTZISUXXr9KoZoAb0vBc+AzrjIP/8067TrmKDvSyaXXw3GgLk0mA2W/aLve1uZQPKMwxhhTxS8KY4wxVfyiMMYYU2XArFHQwkVtUHd2Uk+lzqdrA9T9qN/p7mt+Ri1LJ7Vv1XGpNdd2QfYWng+vSbVergfw+vR8mgqkqC24VkilKeOpavv87m7rp6Qpi6vuFGcmT7bjLu2IZrut1rvm/eAaUUTzWolm/KyNxb5C7z3PkeekzyV3JFPP1zrtfP5Um+dY4vNWq/fdV/B8dM2kaR1L4RjhNdWuR2tc0+Jey07d7YwHnlEYY4yp4heFMcaYKlttiV2fxhhj/t/BMwpjjDFV/KIwxhhTxS8KY4wxVfyiMMYYU8UvCmOMMVX6dMPdLbfc0muLVVNCuU7dW/3l+jrrrLN63FF13XXX9bsNrdM+6fYmsfPPP7/HD7z66qv7vY8U9llfbpa7/PLLG79s1qxZA66f+ovZs2f32E9XXHFFr/uI956bBnUcNG3A1f9eGz/8rm7/dl111VWNX+wZhTHGmCp+URhjjKkyYHI9NVGbvjE3jsIcKcx7UsuPolM55uhpyiHU09/9OlLLxdSqlKL1FQj7bCD0V1OuHb0GjjH2C+s0ROQcTrU8O92sxdHXsM9qecyYF6l2jbXP+HXqG14vS8cqHCP8fdIaKFoPhjDPFHPOaX0UHuuGRO8ZhTHGmCp+URhjjKniF4UxxpgqA2aNgjoatctajQjmzldtcIcddigx1yW0ji01aNZT0POgdq3f1VSvoabZd5NaH9WunX/HY5off+PGjSXeY4890jH2Ga9Xc/SzrgFrfOu5d1ObZj/ougF1Zd7nrbfeOrXbfvvtS8w+WrduXWrHz9c67+wX1hPQGhm1uux9ha4bcF2GY0nXsXiMOvq7776b2rFWhfY1/47nofVf+He12trdpFZnZptttikxa8FobQ/W5uC913as2cEa2RH5eeNvl65r8LtYr6bT9VXPKIwxxlTxi8IYY0yVfpOeVGLg1I7ShJaL5BS3ZmscNGhQiTm92m+//VI7TvM4hYyIWLlyZY+fp1NhTkU5/eV1RHS3PCGn/joVpjTGafq4ceNSO06T2ZevvvpqarfTTjuVWKeqb775Zol57TUZgNPubpdF5XSclkG9t9ttt12J2UeUhiIiFi1aVOLBgweXWO8lpbYlS5akY0OHDi0xx5uOj7322qvH61AZr2YL7zYqD21iw4YN6d/sX44X/Xtei0q97Cf2Ta0U6pYsq8vfKH6nng/L6lJGeu2111K7nXfeucQcf1p+l2NOpSeOz9oubY6RVrcR1PCMwhhjTBW/KIwxxlQZMK4nOms4rf3kk09SuzFjxpR4n332KbFOzzkV5rSMElJExNtvv11inSo2OVl0Os0pNKeUKoep1NAunApzOqkOGf6bstTw4cNTO8og119/fYl333331G7IkCElXrNmTTrG6/34449LvHr16sbPaJJ9Inovz1Fu2mWXXUo8derU1I4y0iuvvFLi9evXp3bz5s0r8WOPPVZiXo9+vo5ZOsXoRpk/f35qR9mCkp46zdS91glNu3W1/ykTfvTRR42fR6lx2LBhJWY/azt9ZulU5G5llZ/fe++9EtNFpTJUk2zWCewvlWv4Pe+//36J6TaKiLjxxhtL/NJLL5X4iCOOSO04DvhMRUTMnDmzxHTk6TnxOeC5a1+q46oJzyiMMcZU8YvCGGNMFb8ojDHGVOnTNYpaFkPawGjbnDZtWmpHLY6apO6GpRVt7dq1JX755ZdTO1r52C4i4oMPPigx9W5q+xFZu+U6QLd313LNg/3Hc4vI/cx1kaeffjq1e/DBB0tM7Xjs2LGpXc0aSE2fu0N33XXX1I73Q22RpLfWT2rq1Ig1u+YDDzxQ4sWLF5dYbdtcE+Nn6DUsX768x7+JiNh///1L/NZbb5VYd9PyGaBGr33ZKrVdt7xOjivtJz4fXHuZOHFiasd1lLPOOqvE9957b2pHC+yyZcvSMa6NcS3nxRdfTO2Yubf2jPV2lz9t5lzH0n7l87d06dIS6xjhb9fRRx9d4kmTJjV+r64hnHbaaSVmP+i6Ip91rmXwOtrBMwpjjDFV/KIwxhhTpU+lp1pdYVomP/e5z5VYLW+07/GYTtE4FXvuuedKzF2PEdlqqPZV2vAoLfC/63nQjqq7gWuFWjZR221JWYWfxaml/h13l+uOYcpGnP4+8sgjqR2nu3pOlOsoWen95bSbFlvKjBFZ6ugElU42QbtpRL6Hq1atKvGoUaNSO/Yz+0glTO6u1YSBtGDz8/Ta2Y5jUeWVVsZRRF164f2gbKv9z36jpKSyEcf666+/XmK19l5zzTUl5o7miCzpsi/UlksrPS21SitW65o1uMk6qr9Jd999d4l57/X6TjjhhBLTQqy/E7Tb6vPGPqJ0TCkrImLBggUl5jYC/S7NMtGEZxTGGGOq+EVhjDGmyoDZmU0HCKfdKvNQoqIcNH369NSOksstt9xS4ocffji1O+6440o8fvz4dIwSGHeL6+5GulLoHtJ6A61AuUCdXHQ5cEeq1tzl9x522GElpiSgn3/RRReVWF1P7HN14NDlRZeYOj4oF1A6UblP5Zh2Yf8zuaHulubOcSaapIwQkcdlU+K7iIhzzjmnxLfeems6xvPgbmTdTcvvoiTAcdgpKkNRPqH8qjvYeX/YT3rfODbvueeeEqtsxPvz/PPPp2N0vLGvtT45E+PxOjQTQivSE/tFd4oT3puaJMzMD3RuReRnhTuu9beLGSJuv/32dIyfzzGtfclz4ucx8WSE61EYY4zpEn5RGGOMqeIXhTHGmCr9tkZR08aov6vFjBo2bY1qGeQOWK5lfOUrX0ntTj/99BKrFkrNnVkwDzzwwNSOOie1VV1jaNXWuAm14VHvpe2Q+n9E1t9POumkEh966KGpHa+X56q7o++7774Sf+1rX0vHmnRgtalSB6fGrOfeqma6Ce1Tfi8tnHfddVdqx/vZtM4S0Zw99cwzz0zt1HpM2M/cZaxrWNy9zn7Qvqxp6U1ov/J+cw1K7z138t52220l1vUAavi8xn333Te14xoFd2lH5LUYWr7feOON1I7XwutotQhPE1yD0e/hM65rRrS60tarfXnzzTeXmLZe3veInIFW7xvHMe+bZpXg88a1kj333DM6wTMKY4wxVfyiMMYYU6XfkgLW4FRb5RfufKQtlHKVfgYlFy1MQ5lGk+txJy4Tto0ePTq1405jTsl1et4uKqtwqslj2o4J22q1q88999wScyf7ihUrUjvKB7SBRkQ8+eSTJeYOeC24csghh5RYC7qQdhO5aXtO/Sn5aC1sUis2s3DhwhKzX3X3Os9Di/U8/vjjJaZMUSsSxPGskkpvk91FZImUO7/VPs4EdXzeVFZlf1A2OvHEE1M72tbVrk3rJ22hWueeEhHHt0p0rdTTriUq5e8B5S+VlI499tgSMymgJuHk31155ZUlpp04It8DPjcReZd1zR7LcUuZWsdmq2PJMwpjjDFV/KIwxhhTZcAkBSScumo7TlcpJ1A+iIh46qmnStxUoyAiT6F1VzDlE07/OR2PyFNK7tpWSajdetB67ewXTr/1cylRcfqrNcHHjRtXYjo5+N8jslx3//33p2NNbil1V1AG4r3SPmpXVlF5j/eGfaS77jl2eL1///d/n9oddNBBJX733XdLrLtpKU3eeeed6RhdVcccc0yJta44JUzubG/XLdcKvFe8HzpG2I5uK60Tw3On3MQ+i8iuslNPPTUdo1uK36vOuJoDqV34m6SSEp+jCRMmlFhlbsqJdH9pckjuiqb0p7Lo2WefXWKtj86xwCwCulOezyV/HzRjQqt1xT2jMMYYU8UvCmOMMVX8ojDGGFNlwOzMpkWPawpaaIOWtSFDhpRYrXZsx0ycajWkxq07s6lxU0dUXZyfT41cLYTtono9tcamXdX6d7TDUUePyH1O7fPRRx9N7Q4++OASaz832Qt1lyv7nVq37kptt8646vf8Xq45aR/RDkyNXjXcph35qo2zwM+IESMaP4MWU73WpiIy2pfdqMXOMczP19rLLNBEvVyzwtIyzn5nbfKIPF7U0vnSSy+VmNl5a2t77AvV29vd5a/tORZ4TzUTMfuSv0kzZ85M7fjsMHOE1h9nwSTdlU47Op8p1mWPyLveGevaoWbnbsIzCmOMMVX8ojDGGFOl33Zmq3zDaR/rwrJgUESe/nIXrlrWuJuTyeF0ykxpS2tPcwrI6Zta0Tg1pqVOpZ52UVmF107LYK04DG2hKq2xoA6vQXdm8zPUXkyZgTbBmoWY97e36O5bns+YMWNKrBIIp9y8Z7pznxIIYyaajMj3Q2UpTvdpneVO5Igsj/Heq9TUrqSyOfhcaqJCWsT5DBx++OGp3TPPPFNi3ntagyOyPVatuLx33GWtxXZ479hPKtW20k+1QmH8jeI10QIbkQtV8bdGJUMm59ttt91KrH3JPtdr4G8Un0WVcGn55nfp72mr2SM8ozDGGFPFLwpjjDFV/KIwxhhTpd9SeOiaAu2ntE9qQY5Ro0aVmJZE1fP5GQsWLCjxySefnNrRDnj88cenY7QG0nqnGVmbihV1UpSHmqn+PXVb6t6aEZK6I219qj/z89jPU6ZMSe0OO+ywEr/wwgvpGPVz6ri6lsHror2wlt22FdTuzHUcHtPx1mT7/MM//MPUjveM2rQW5Jk3b16PfxORi//wnup943imvVs/r91UMBH/W7/nOOXn094ZETFjxowSc82O6TYi8vNG26uuVfHztXDRrrvuWmKOKy1e1rQO2ElW3VoKDz5HXDeYNWtWasd1J2bR5ZpERE7pwSywuo7Dsanjm2sP/E3SdCHsP943XV9tdb3LMwpjjDFV/KIwxhhTpd92Zqt1jNNGZmDVaTanmrTTsThHRMTPfvazEnPqqpLB2LFjS1yrUc3zUIvZyJEjS0z7mrZr19ao005O73neeu20vVJ2Y79GZOmD137ccceldiw2o5ID7wFjtYg23VPtk3Yzpaq9j9NxyjxqReUuWe4IVomK50qp7g/+4A9SO36+ygDccU0LsUpPHNvsF+2T3hbEishjqVZsi+fL3cSs+RyRd7dPnjy5xGrt5TOlUg+lKN67mqTEvu2tjKm/Sfxs3pvvfve7qR2vg5KejiX2+RNPPFHiO+64I7Vjxl2VAiklc1yo9Z33h5Kz9pHtscYYY7qCXxTGGGOq9Jv0pFMguiM4baI7ICJPBymXcFoXkXeA8vM08RrloXvvvTcdO+qoo0pMt486B+gqoDuiE3cKJQfdbUlZhTuINbkak5nRkUVXSUTEqlWrSszpqe5Qp0uJrrOIfL2cdusOZzqLeH4qTagza3OoXMB7wx28TMYXkV1ZU6dOLbHucqcbbM6cOSXW8cu+VXmTLhaVbAjHc223dCfJJlXiY78xVimCY4GfoVIHE0eyr7UOPe+Jfgb7mtesY4T3mMc6ed5qUNphn1OqjMjPB3fsq5uJUhTdUTomWHebhbP0u7hjXT+D/6Ys2GmiUs8ojDHGVPGLwhhjTBW/KIwxxlTptzUKhfo7dTi1BlLzpJ782GOPpXb8DBZVUf2YWS+1yDkttvw8bUfNnbqraqbtWj9rUPNXXZnnw8yRzH4aka2ztGqq7k+rou60ZV/w+rhuE9Fs91SLZG9pKoqkBbBoZ+W1z58/P7Vj3/K8qftGREybNq3EaovkegPPj1p0RHPmAl1/6wa8liYLcEQ+d9q1VetmgR2OP31WuKagujo/n7GuB/Hf/Dy1t/cWngN/n2gDj4hYs2ZNibl7X9fpONanT59eYu40j8j3W9coaJ2lBV3XsbgWxPXaTtdxPKMwxhhTxS8KY4wxVQZMzWxOhZuslBHZmkbrnkpKTejOYk7ZdCc0d9hyR6TaRzkV5tSut1JTbSc3JQFNPsbpPqfjujOb10TbK3diR2QpSu3F7AvKJWoh5r9ru457CyUmno/KErxPc+fOLTFlhIi8M/mkk04q8aJFi1K7v/zLvyzxIYccko7xGlnYRu9brbb7loR9ozImz53yq+68Z39SYtHElpRt1P7N7+azx9+DiDx+dEx3kyb5S2tms4Aai2Wp7Ea5ju1UWmMho0mTJqVjlAb520VJKiJLcpTD9Tel1USKnlEYY4yp4heFMcaYKgPG9dQkQagDh9AdoG4N/pufzZ3EEXmarNNpThX5XZ1O39pFP5dTYTq+VFah44HTU3VrcDcx+0inzJRzdDdt03epdLKl+khhvzQlvovIriX2H+uDR+RrontEr4fOOkoREdltxsR3Orb5b469bu84jmi+H/pdvI+U4RStLbEJ7Qv2p0pvrKHN+6XSzJaUm0hTFgiVVXnvueNfxxzHAftVa3DzGJ2Jeh7sS71vfNZ5rzt9Dj2jMMYYU8UvCmOMMVX8ojDGGFNlwKxRkJottCm7qP4NdU3q77X6w6op6rrHJnRXKj+/27tDCc+9ljWTWjePcT0hIuuVtNfpjlnuxq4Vh6G2qju4m/TeLUmTJTciX3ttvPEz+Ddq2eT11YpyMdb7tqXXJZrg9et94/VznKttffXq1SXmLmYtzsQxyKy6EXlNif2klmz+BnSjiFMT7BfeU60Hz/UArnnquivPm5+tWQya2kXk6+U90N373f5N8ozCGGNMFb8ojDHGVNmq3TrOxhhj/v/CMwpjjDFV/KIwxhhTxS8KY4wxVfyiMMYYU8UvCmOMMVX8ojDGGFOlT3dmX3311QPOi9uqPbjb2U8vv/zyHj/wiiuu6HUf8Zq4k1OvoSljr/732rXzu7pttb7qqqt6/OI///M/77Nx1OoO7lrxny3JX/zFXzTenAsuuGDAPW/9xY9+9KMe+2nWrFnuo/9m9uzZjWPJMwpjjDFVBmSup1ZhXpXa/+3x//CYhyYi59dh3YWInN+FuVQ0z43+u7/hNWnuHsJ8RczT9POf/zy103z5hLmfmJNH82TxWKv/l95XNOX4V3je2o79rHVN2Ee8N3rtW3J21im8Zj5HtRK2rbZTmnIS1fppoNFqmV+Og9qMvfYZfVXjJcIzCmOMMZvBLwpjjDFV/KIwxhhT5dd6jYI6n9ZobsoLz1rJEVkX1fUL5tJnHv1aXeFWNcreUtOBudbCXPma9541i6m5a7t33nmnxB9++GE6xvUZ9rmua/C7mM9f+3JL6c+q5/K+cy1qzz33TO24NsUa46qns1+0LjvZa6+9Gtux31kXekuOo4h6n3Ns83nTdTmuw/A50vUaHtP65OvXry/xsmXLSqzrXRzftVozW2os6f1oGks6RniM/cVaMBERn/3sZ0usv0lNdXa0Zgf/js9YrZ5MDc8ojDHGVPGLwhhjTJUBIz1xGtXqdJJTKkobEXla/9Zbb5X4zTffTO3477333rvxGKdynBpG5Ck5JRwtiaklVNuF8glLoWof8TooZ7z22mup3c4771zi7bbbrsQjR45M7RYtWlRilZ623XbbHs9Dz4myFGNFJcR2abKwqgTCMbZu3boSv/LKK6kdJRZO2ymNREQcfPDBJVabNWWBN954o8RamnannXaKnlAJoxsb+prkLLVT8/7yuiiNReT+pe1a+51j7qWXXkrHtt9++xLXxkuT3Fkbc1sSlYc2sWHDhvRv9h/vtf59zYo/dOjQEtdK/fL3waVQjTHGbHH8ojDGGFNlwEhPhBKNTss4naQExCltRHaXUEp54YUXUruFCxeWeI899kjHli5d2uP30v0SETFq1KgS0yml03N1E/UGSiwq17DP6PKi2ygi4sYbbywxZYAjjjgiteN5q1Nn5syZJaZ0oOdE5wrPvdt91CSp7LLLLunfGzduLPFHH31UYp2mjx07tsSU4FTC5PjTXdvHHHNMia+77roS69jm/eFYpPwTUd9t3yo8R94bPXe6wCilqLzGz6A8QqktIl/zoEGD0rFnn322xLvttluJd99999Ru+fLlJVYXI6HjrxOaMgioU499xrGkULocNmxYifmboe0oQ0VE7LDDDiVmBgV9jihr8ndSx3eTbKZ4RmGMMaaKXxTGGGOq+EVhjDGmyoBZo2jKeKr6LPVBapDPP/98anfssceWmFa0NWvWpHYnn3xyidXOxt3F1Lhpt43IGir/hva1iN7bGtkvtHGqNY7nynUWtdpxHeHoo48u8aRJkxq/V9cQTjvttBJ/+umnJVZd+emnny4x1zLUjtoK1I51xzXHB62Z2vfcbU6NmTbXiLzmQb34kEMOSe3Wrl1b4rlz56ZjXJf45JNPSvzHf/zHqR31dp6fauK6U7kVdIxQt+a94tqA/h3Hi+4m/uCDD3psp3ZqPuczZsxIx6jbsw85hiPybwKtuFx3imjNFlrbvd2UOVf7n78vvL8TJ05M7bjudNZZZ5X43nvvTe24xqM2bN4rbgl48cUXUzs+i7TKKq1moPWMwhhjTBW/KIwxxlTpN+mpNi2kZUttX5MnTy4xp6qvvvpqasfpL6doOo2n7VUlA07zrr322hLrNI/SBXc4K7Up4CZqNrwm66j25d13311i7jrWnecnnHBCidmXan3k/dCpOiWSBx98sMSUsiIiFixYUOJ99tmn8bs0uVlP1PqIfUEZQGXAVatWlZhSGBPTRWQ5ktN0Ta5GSVMTC9L2SSukyqA8D/arZh3opHyv2oYpy7EPKaFFZHsw7ayaZYD9vnjx4hJPmDAhteNz+dBDD6VjlMP4TM2aNSu1oxRKGej+++9P7VopKFaTXpoSIuoOelqlKSmpbMSx/vrrr5dYbfnXXHNNifWZ5bh4++23S6y2XMpwtNQq+vw04RmFMcaYKn5RGGOMqdJv0pNO+ehe4BRU3SpczX/88cdLrFNhuqDoZNGEd3RUaAIz7sDmTseXX345taMkxLi2S7MJ9ovuyiR0V6kUwWk75QKVMIYPH15i7riePn16asdkgrfffns6xs+n1KMuNJ4TP4876CParyFQcz3Rnaafqwn5NvHYY4+lf9OBwns7bty41I7Te73vBx10UIk5FnXXMmUuSqyaXFW3dw4AABxLSURBVLIVCTMiX7NKepQaOc6eeuqp1I7SDqUUfS6nTZtWYkqLKouOGTOmxPvvv386RkmXEpjKI3RmPfPMMyVWebHdOh61miX8fZo6dWpqx+/lvdLz4W/XPffcU2IdL5Q19TmiVE4pi58dkZ1hvA69b5aejDHGdAW/KIwxxlTxi8IYY0yVflujUG2sqdas2hC5I5TtNKMrLYpcv1C7HrXbESNGpGPMzkg7Gy2DEVkL5fmqRqkFjzaHatPUnKmn6toK9Wda6LSQy80331xiauyaiZc7hlXrv+uuu0pMa7DaLKnxcq1EraTtoroyLZFcU9D1HurhXD9RDZdjgNr7kCFDUjtaKXmtEXlNZvXq1SWuZbSlVVbHDXdBt4qua/C7qPPrTnk+p1y/0LU+niP7XdfFfvrTn5ZY9fczzjijxLTAasbnfffdt8S04upY0Ey4m0PHNn83OLb1OWKf3XbbbSXWscR1RY4/Xk9E/g3hGllEftY5RnS9i9fC6+i0MJhnFMYYY6r4RWGMMabKgJGeuAOb01hNwEc75ejRo0usu1xZBIZ2VloVI7L0oTWlCaUtLbiyYsWKEnParZbEVmyNTcVSIrJUwammToWZEJH2Xybm07+78sorS0zrXkTEww8/XGJNhkc5pmaPbSoQpUVbWk1S1gTHDqfcLHYTkeVC7sCnxBiRE09yJ7smoOP30gIakfuFMp7KAJSzKHWo9buTPtKxxGeCY0nlEtqFawVwLrvsshJz53JNorrjjjvSMcpSvD9TpkxJ7Sh3UlpVmaa30H7KZ5fPQ0SWyShV6n175JFHSkzZ6MQTT0ztVq5cWWIdj/ztoVV9v/32S+0oW1PK0oSGrdbT9ozCGGNMFb8ojDHGVBkw9SjoVuEOVa2JS/mE0o7KQXQV1NxRlHMo2UTkqTDdVjXHVs1B0wqUCFRSohxB95a6Yuh6otOCCQIjsozHabbWADn77LNLrI4eSgRMRqiOL07D2X+auK3VGr6bqNVZ4Lmqk4s7pNmXjz76aGpHyYFOrlNOOSW1++EPf1hivXZeI+UrrT9OGYXn3tsdxxH/eyzyu+kI4279iPwsUt4YP358asf7yxryrMUekcewyiCUmXkeek/4zFKWatpt3yl8/vg7pBI127EvuVs9IsvjlJtqtT1OPfXUdIy/a/xelUJrrshO8IzCGGNMFb8ojDHGVPGLwhhjTJUBs0ZBnZ/am9q3aI2jlkddPiKvFRx22GE9/o22U72cFkKugWihEe4+pX6p9jjdab05VH/n+XEXOe2XEVmPpuVy5syZqR2td9SHtdYvLb+6A/TJJ58sMe2emhmU1kXGujO7tzozNXBq6qq9s5gQ9Wfdcc17ePzxx5dYNXpaEHXM8rtpn1SNnmOMayN6PzTDbSewn3g/9PpZU552Vlo4I/IzwWdA9XwW4tF7Qus1n5X58+endrSWsp3q9LWCPa3A54jfo/Xg+TvBtSXNCks7P23XDzzwQGrH9QW1mXPNhzbkWhZYjiVdA2w1W7NnFMYYY6r4RWGMMabKgJGeaPnjlFwTe7EWM2vVqqTEaS3lKp3Gc9p9ww03pGOUlHh+8+bNS+14jrSWqs20FemJ006VrjgV5m5QWmAjIm699dYSs9iMfj+vj8VgDj/88NSOVkqdqlIG4G54taOy0A+/i/bLiPYtxbpLmX3O/tMEfKzhTYlAd4rzOij5cEzpZ2htc9quaVGmDBWRZTh+nspxndhjVQ5jPzEpnZ4T/47jRXdBU/qg3KQWUX6eJvvjuKD1Xe8Jbcrsax07nfRTExxn+pvE54P9os8Rky/y+VUJjr9lKt1RsuLvpBYA45hhP+jzYunJGGNMV/CLwhhjTBW/KIwxxlTptzUK1fmonzOm7h2RbZy0YKpt87nnnisxdVfN7DlnzpzGz6CVj7Yytd1Rp6c9rpVssUothQc1WOqis2bNSu3uvPPOEjNjpRaRoV7OLLCqmdL+pxlPufbAPtJ0IewL6sqanqJVzbSpPTVY3guuZ0XktCS8Bk2rcd9995WYY5FjIyJi/fr1JT7vvPPSsUWLFpWY+jr7PCLbLqlTq0WyZoVsQsci1wo+/PDDEs+dOze1Y/oHroUx5Yt+HtNYsFBTRMQ777xTYn22ademlVTT8zDTNKHuH9H+WFL9nmtc/Cy1EM+YMaPEHNtMtxGR+4X3VM+bn69rQUxBxHuq45H2Z97fTrMze0ZhjDGmil8UxhhjqvSb9KR2vaZdkGoRpSWM0zAtXMRdzLTUqqzCKSCzXkZkSWnq1Kkl5lQuIssa/N5OpCeidlZaBnkO3/3ud1M7SlbsP80yy6nwE088UWItKMPsljrt5g5x2vA+/fTT1I5yHWVHrYneScZdQmmslsmXU3DuzNbz5g5sFuHR3fBN9ZD17yhzaVEurVe9CZWaWh1XNas1pS2OK63fTNslP0/HEiUl9sXs2bNTu1r9eu6WZ1/omKNllM+s7phuV3pS+Hxw/OhYYlYI3lOVqDnOJk+eXGK9n7RGq/xMKYo70WuSEu+vPm+t4hmFMcaYKn5RGGOMqdJv0pO6ZzjNo2RAx01EnpZxZV8dJJwecje2OpvoiNLdu5S2mPxOkwfyfCm/tFqPtlX42ZzCa3EYyiKsFa2yG+UDuqN0ysy621pznN9FmUI/g//mFFwlkd5CRwzHAGVE/TfPhxJjRN4Je+2115aYLqeILAnornRKLP/wD/9QYu4Oj8iOPLqNNJGbumSaoPSiMiblDu7i5TMVkZ1IdDo99NBDqR2lFI6rSy+9NLXjPaEbLCIXbuJ56FiilMJYn7d2HT4qVTU5MVV64ljiZ6iMyWJZtd8d3g/9DLrm+Luj8hXdhDzWiWMuwjMKY4wxm8EvCmOMMVX8ojDGGFOl39YoVCujvkhNjcU5IvJuTu7+1Yyd1IVp3dOdoty9y6yrEdkqyAyWqhlTD6R9t9NdkE1wXYfnQB09IluFaVVUXZ3Wu+nTp5dYdWquH+kaBa2z1NV15z11V1ozO9VMm+C9oF6suj7Ph/eJGnBExD333NPjZ7PITkTuI117YAbfVatWlVivnefIZ0Atkp1kRVX9nZ9Jnb9m1eQz+qUvfSm1mzRpUok5frSgGLMFa2GfCy+8sMS0mbJvI3KWXc3Q3E3Yz7xXWnCK44fPqK6/cX2U65x6DbwHuj7Dz2estlf+m5/X6bqpZxTGGGOq+EVhjDGmyoApXMQpEaeumsiOEhB3bFJe0s/jdFen7ZzW6k5R2uAopahk0G35pImmqabuEqbNkJZLneJyasx2Oo1lARZKDBHNRaYoSUXk6S8tf7Wkfp3Ae0aJS4v/UNrg9aqsQImPNbjVtsh7QzkzIttlKc9pjWeORUoTnRabqUG5ibZXtX5zJzklTe1Pjjk+iyqbsda2ZjigBZXnwYJGEdkCzc/vttRL+HtSK5DEZ5H3OiL/TvC8dRxQSlarNb+b0ruOOY6RpiSK7eAZhTHGmCp+URhjjKkyYKQnQkmkJpesWLGixJxKRzS7D7jbOiJPV3VKSfmE0zd1PXFnZm+T2tVo2oWqNR2Yy58uMT03OsrYX1qDm8fU0cPzqMlznE6zz7stF1DioiSgzjBO/WsOI14TJZpW62BEZEce+0XHbJPLphtSk9LkitHrpzOJ7TQpIBMhsi+0vjyfP82mQKmQY1AddJTo2E/q6OltvzWNTR3bfD7U5UW0tsQmKNtF5OtV6Z0JEfk8q1zcDbmJeEZhjDGmil8UxhhjqvhFYYwxpsqAXKOg3qbFXZh1kVqh2l6pV1KrVFsf/041yaassFvCrtgKTdlAtfYw9XhqztpHvD5+tu5yb2oXkXVSWhp1N+2WzKrbBL9T1wN0nWkTtXvL89Z21O81M3LTOWm7vhpH+l08D13v4m5x3mtdy+D1c7yo3bhp93nt8zXzLXcrN9W17ja1Xf7sM95ftRozKwTHHy3/Efk3SrNn87niGNTxXSva1QmeURhjjKniF4UxxpgqW/XldNcYY8yvH55RGGOMqeIXhTHGmCp+URhjjKniF4UxxpgqflEYY4yp4heFMcaYKn26M3vWrFn24v43s2fP7jE15be//e0+6yNao7nLs2aZru1c7nYm2G9961s9fuA555zTZ33UlOlWM4hyh3Bt53kn9a5r3HzzzY2d7n76H5r66eKLL+6X560bdPt5+8EPftD4gZ5RGGOMqeIXhTHGmCoDMilgq3AqV5uqcrpbm67VPmNL1uPdkrCPNDlYU/+pXMCkbHqMf9fq1Hog9CXPgQna9BpYAIYJ2Wr1kLVwEYv88DM4LiO2bNGrTnE/bZ5WC3HxWakl66wln2RfMNbnsulZ7FT+8ozCGGNMFb8ojDHGVPGLwhhjTJUBv0ZR0++onavVjsdYCOndd99N7aiLajEb/l2rRXCoFWrB876iVR2S7XiuWpSGhWJUV6ZOygI4eu39kaW4phdzvFDz3rhxY2r3yiuvlPjTTz8t8aRJk1K7nXfeucQbNmxIxz7/+c/3+L1akIdjh+fUbauo4n5qD/0e/oZwTUaLNvFZ4e/QG2+8kdqxHwYNGpSO8bdn2223LbEWCnv//fdLzPuhv5Otrhd6RmGMMaaKXxTGGGOqDHjpSWmqdazT2G222abEO+20U+Pfc8qmNW6HDh1aYtbFVRmFtX/7qh40z0GtcYT1s5WFCxeWeN999238G0pKI0aMSMc+/PDDEnNarLWXWeucU2Gtm9xNmup5R+Tz5hjQ+8frvffee0usls2JEyeWWKUSnseQIUNKvMsuu6R2rKmsteJJtyUW91PPNNVLV0mJUDYaM2ZMOka5idId5biIiHnz5pV4/Pjx6RjPg3+nUu8nn3zS49+odKwycxOeURhjjKniF4UxxpgqA0Z6akpKp7LKZz7zmRJ/9NFHjZ/HqdiwYcNKPHjw4MZ26hyg24fSCXehRkS89957JaYDQqfnTbJZb1HnAs+bU/jXX3+98e943pQbInIf3XPPPekYp+GUFbSf99xzzxLT5fH222+ndpwyt4JeO+UL3k916fB7tt9++xKvWbMmteP1TZgwocQchxFZ+mT/K/zejz/+OB3juKfsqeNcx2kruJ/ah7IZJRuVZinXUV5SOZzP0dKlS0usvwu8V3Qv6b8prz///POpHWUpyoK77bZbatfqb5JnFMYYY6r4RWGMMaaKXxTGGGOq9OkaRasFcaifqhWNVlfqmNTHIyL22GOPEp911lklpnUvImucy5YtS8d23333En/hC18o8YsvvpjatWr3bGUXZM3Sx/UafpZa49avX19iapArV65M7b74xS+WmDtrdaco2WeffdK/2UeLFi0qserKBxxwQIl5b9SOqes/7cK+oI6uu+mpM3O88V5GRCxZsqTEXLsZN25casf79sEHH6RjHMO8N2oPpZ4/fPjwEmsf9VZ7j3A/baJWeIvPMs9t7733Tu1eeOGFEtMWznW/iIhf/vKXJeYzoL8nBx54YInVzrpgwYIS0zastnVaiHk/tttuu9TOaxTGGGO6gl8UxhhjqvSp9FSTXrj7l7Y0Sk0REW+++WaJKSmpbETrGG2hnPJFRFxzzTUl1inlO++8U2LaONWGR0thzfJX20G9iVpRFvYfp/B6Ppya0846duzY1I7SHSUfTm8jIk477bQS0yYckfuZx7hDNSJixYoVPV6H2jHbTR6oY4qSCseO3heOg1/84hcl3n///VM7/t0VV1xRYpVEeW/VXrx27doSjx49usdzjYgYNWpUiZnwTfukk8JP7qeeaXqmIvKuZUptlNkisnzDZ6pWcImykSb+42/Ns88+m45RCuTOb0p1EdkGy35W27p3ZhtjjOkKflEYY4yp0m87s3Va2JS4aurUqakdXQV0Q2gSOk4VKb+oTMNpre5u5LSMEos6Pjj9bcrfH9Ga9MR+URcHv5eftXz58tSOcgGdF+vWrWv8Lk5/NQkbd7br9JxyE+/BSy+9lNpRtuBnqOuiFemJ5619Sglkr732KjF3hkdktxvPR8clj3EcLV68OLV76KGHSswdzHqOlE61L+nS4b1i30W0XjPa/dS72trsI7qFKElHZDcTx7O2467qV199tcQqrdFhqb9/vD+77rpridX1xN8E7tJ2PQpjjDFbBL8ojDHGVPGLwhhjTJV+W6NQLZpWMuqBat/iDuLbbrutxKpH0p7JnY8s0BOR9UHqsRG5/i31VN25zGtpqiHdCaon8t9cr1B7HdcYaJvT85k+fXqJaTnU3aDcuXvrrbemYzNnzuzxu9Qeq+sem9D71krhp9o6Bq3BvJ9f/epXUzveT+q5uv704IMPlpj9xYzBEREjR44scS0DLsevWkwJdXi1WbaqK7uf2rMRa39R26fNV3d881z5+6LroewLPg+6lnHccceVmOtHEflZZD/r2tJf/dVflZjrlLrzvpV10wjPKIwxxmwGvyiMMcZUGTCFi2g/ZTKuhx9+OLWjFY3WTJ12PvLIIyXm9PnEE09M7ZgoTwv7UNK5/fbbS7zffvuldrTpUsrSXant1tPWqTNlOO6mVemJ01VOhVnEKCJi2rRpJWbBFZWoaBNkcr+IvOuT7dT2yn/z/vJ+RvzvpGU90VTkSo/xs1577bXUjrtraevV3cK8JkoHl156aWo3e/bsEqutmVKCypuEO3Ipyan82qpc4H5qrZ82oc8bxyblJpXT+Jzzd0hlIyZIfOqpp0pM6SoiJ+vk72JEfo6YjFCtxryn/BstJGXpyRhjTFfwi8IYY0yVASM9cdrIHYw6FWY7Tgcpo0RkdwDlJkosETkn/qmnnpqO0S3F79VEdpyy0inVW3RHapOLY/z48enf3NnJ69O/57T25ptvLnFtR/hbb72VjlF2W7VqVYmZsCwi3yv2kU59a/U4NlGrIUB5jy6dJ554IrVjvn7KBSqFsW85vVe3FuUCdZZQlqGT5sknn4wmKGdoPYZW+ijC/dRqP21CxyJlZI5fdT0dfvjhJeZvl2ZMoLRNp9Mll1yS2nHHtSYgZFJAOqdU1mZf8F7xtyHC0pMxxpgu4ReFMcaYKn5RGGOMqTJg1iioZVJfY03miIiXX365xNxBrLsgWfiEut4DDzyQ2lG71eyxzIBKO2pN16P1s5PMqDX494yZrTMi4sgjjywxdVZdX6AOzKJNuubx4x//uMRa05r1fWlp1CJJtNxyRy4LGkX0fjct11cWLlxYYloqI7KmS7uz1jmmLs/v0rHCdRzNBsrzoEasGjrHFfVs1fK1+EwruJ82jz7XvA6uUbIoUES2nDLmeoUeY0aDY489NrXjjmtmpo7I2XK5hqprFPy9asq4HZF/r2p4RmGMMaaKXxTGGGOqDBjpiVB+0J2EH3/8cYkpddCiFhHxzDPPlJj2sOHDh6d2tI+qFZeSFW14uuOSOzVrxV3alZ60Paf7vHbdlc5ds7XzefTRR0vMQjF33XVXanfQQQeVWOuK07rIgkkqA1DqUHthu/A61H5J6zLvu07heW+5i1WTGTYlz9OdyXPmzGn8Lp4Tdx/fe++9qR2vheNNLdet1jl2P7X386bPGyUbfpYm8aOUSslHnwHa9P/sz/6s8Tz/5m/+psR8LiNyv/O5VwmXGRloV9ZkjlrwrQnPKIwxxlTxi8IYY0wVvyiMMcZU6bc1CtXLm+x1mvF0xowZJWYxdVrFIrIOToueph7g52vGSm6lp41MdXpqt9Rk27V6bg5qulwPUI2T58OiL8xYGZH7gpY/pj+JaC5mH5G1UFrvuPYTkW2X1KLV1tfKOg7b1LJh8ly5zqJ/x/7T8fbcc8+VmPZizepJfVwth1OmTCkxx4Su1bD4DI/p57Wahdj91F62Zm2vWWI3wd+diJzFlalrtI9OOeWUErP4maZN4XOp6YIWLVrU4+erhZjWY6ZN0TUjp/AwxhjTFfyiMMYYU2XA2GM5haT9TW19w4YNKzGnuMw8GZF3RU6ePLnEOj3ljm6VcChFcQpYk5RoidOdp61AuUCnwtzpTZuc7pJlFlfa5nQqzXOl/KAyBftFM+zS7kgbnloVacvjd3FaHNF7uY79R+uk1memjfFnP/tZiZ999tnUjuOFY0B353KsqOTAMcZaxrR6R0RMmDChx+9VuaC3O/z1M9xP/5eanZ1SkWYn4PNG+VV3uTNDM/tcrcYHH3xwiVlYTf+OErNK6uxL/k52mmHXMwpjjDFV/KIwxhhTpd+kJ50WckrEWKUnyhv8DN1xyOkba2uz2EdElmP0M9auXVtiyjEqX3F3I4+1W7M3Ik9/9e8pC3C6q84SujI47dTzpluDfa5Fh3geek5MzMjv1XPifeQu7d7uXtdr4lSazjCtX06pk99JR01EPm/+jbbjONLdrpRFKb1o0khKgfyudt07PeF+2jw69piYkONZCynRWThx4sQS665qFjKiHK6up/nz55dYk50SyusqKVEe473Xa9Td4014RmGMMaaKXxTGGGOq+EVhjDGmyoCxx1IzpQ6umik1bRbD0QyqtLNRE9eMldTv1GLLz2estlf+m5/XDW2Z8Np5fbqOw53VI0eOLPFRRx2V2h1wwAElZkZM/TzeD72mESNGlJhWPrUG8txpie2t1VPXOHh/qduqpZGW4uOPP77Hv4nIa0HUi9n/ihasYX8OGjSoxLQ3RuR7sCXHToT7qRX4m8L+4w7yiJypgRkJVq9endrRZs51CK4RReRr1/7j/eHfcW1Ez5frK7pW1erz5xmFMcaYKn5RGGOMqTJgpCfC6aTKIJSoaBfVncCUSzjl0yRbLMzCGtL63dxNTEtoRJ6+6dS9N+i0sEl2e/fdd1M7Ts2ZtE+TAjbZkNUyt2TJkhJzWhyR7wd30OoucEoYlBO7scuYcGrNWO8Zr4m7hzkeIrJsyYJVKlOyX5YuXZqOUZLjbmS1ffK7OGZb3T3bDu6n/43Kc7TL0/qtzwCTh/LcNMkof9f4GUx0GpElr3HjxqVjlHR5D7SfmyzonVj2IzyjMMYYsxn8ojDGGFNlwEhPTcngdKpEyYUJAhWd9m1C3Tjccc2dmBG5hjalGXU9dVNuIrWaHZzGqlxA6WjhwoUl5g71iOba1eo0Gzt2bIl1Vyq/m9KdSoacavOedjMJYEQ+d95blSW4M5Y7hHV8UE7jfddd/NyFq0kaee2UBLSfKaN0W5JzP20e/SzKOYw1aSZdXpTAzz333NSOz8eyZctKTOkqIj+X2n9sy+9VeY6/Fep06gTPKIwxxlTxi8IYY0wVvyiMMcZUGTBrFIRaoRbkoE5KPZWaZkTeFUn9bvDgwakdbZwvv/xyOkatkFq62kepWao2302asriqZsqdomzHXdoRzXZbrXdNG+3o0aPTsaa1El23oa7c7VriTfC8VXvnbl/2kdoM+e+m7AER+ZpUE9ZsAE3nRLq9RlHD/dQzPFeegz7jfF7YTnee63O6CS24xPUFLabG662t4zTdg06fPc8ojDHGVPGLwhhjTJWt+nKKa4wx5tcPzyiMMcZU8YvCGGNMFb8ojDHGVPGLwhhjTBW/KIwxxlTxi8IYY0wVvyiMMcZU8YvCGGNMFb8ojDHGVPGLwhhjTBW/KIwxxlTxi8IYY0wVvyiMMcZU8YvCGGNMFb8ojDHGVPGLwhhjTBW/KIwxxlTxi8IYY0wVvyiMMcZU8YvCGGNMFb8ojDHGVPGLwhhjTBW/KIwxxlT5PwQhMMeM9H6dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = 5\n",
    "cols = 5\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "indexes = np.random.choice(25, rows*cols)\n",
    "count = 0\n",
    "for i in range(0,rows):\n",
    "    for j in range(0,cols):\n",
    "        ax1 = fig.add_subplot(rows, cols, count+1)\n",
    "        ax1.imshow(theta1[:,1:][indexes[count]].reshape((20,20), order='F'), cmap='gray')\n",
    "        ax1.set_axis_off()\n",
    "        count+=1\n",
    "plt.subplots_adjust(wspace=.1, hspace=.1, left=0, right=1, bottom=0, top=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Trying Different Learning Settings\n",
    "\n",
    "> Neural networks are very powerful models that can form highly complex decision boundaries. Without regularization, it is possible for a neural network to “overfit” a training set so that it obtains close to 100% accuracy on the training set but does not as well on new examples that it has not seen before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 57 s, sys: 994 ms, total: 58 s\n",
      "Wall time: 58.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "lambda_r = 0.1\n",
    "opt_results = opt.minimize(nn_cost_function, nn_params, args=(input_layer_size, hidden_layer_size, num_labels, \n",
    "                                                              mat['X'], mat['y'], lambda_r), \n",
    "                            method='TNC', jac=True, options={'maxiter':100})\n",
    "theta1 = np.reshape(opt_results['x'][:hidden_layer_size * (input_layer_size+1)], newshape=(hidden_layer_size, input_layer_size+1), order='F')\n",
    "theta2 = np.reshape(opt_results['x'][hidden_layer_size * (input_layer_size+1):], newshape=(num_labels, hidden_layer_size+1), order='F')   \n",
    "y_pred = predict_nn(theta1, theta2, mat['X'])\n",
    "accuracy = np.mean(y_pred == mat['y'].T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Train accuracy with lambda=0.1 and maxiter=50: 99.98'"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Train accuracy with lambda={lambda_r} and maxiter=50: {accuracy * 100}'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = 5\n",
    "cols = 5\n",
    "fig = plt.figure(figsize=(5,5))\n",
    "indexes = np.random.choice(25, rows*cols)\n",
    "count = 0\n",
    "for i in range(0,rows):\n",
    "    for j in range(0,cols):\n",
    "        ax1 = fig.add_subplot(rows, cols, count+1)\n",
    "        ax1.imshow(theta1[:,1:][indexes[count]].reshape((20,20), order='F'), cmap='gray')\n",
    "        ax1.set_axis_off()\n",
    "        count+=1\n",
    "plt.subplots_adjust(wspace=.1, hspace=.1, left=0, right=1, bottom=0, top=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}