hongtaoz_hongtao_zhao_ps2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Set 2: Classification\n",
    "\n",
    "To run and solve this assignment, one must have a working IPython Notebook installation. The easiest way to set it up for both Windows and Linux is to install [Anaconda](https://www.continuum.io/downloads). Then save this file to your computer (use \"Raw\" link on gist\\github), run Anaconda and choose this file in Anaconda's file explorer. Use `Python 3` version. Below statements assume that you have already followed these instructions. If you are new to Python or its scientific library, Numpy, there are some nice tutorials [here](https://www.learnpython.org/) and [here](http://www.scipy-lectures.org/).\n",
    "\n",
    "To run code in a cell or to render [Markdown](https://en.wikipedia.org/wiki/Markdown)+[LaTeX](https://en.wikipedia.org/wiki/LaTeX) press `Ctr+Enter` or `[>|]`(like \"play\") button above. To edit any code or text cell [double]click on its content. To change cell type, choose \"Markdown\" or \"Code\" in the drop-down menu above.\n",
    "\n",
    "If a certain output is given for some cells, that means that you are expected to get similar results in order to receive full points (small deviations are fine). For some parts we have already written the code for you. You should read it closely and understand what it does.\n",
    "\n",
    "Total: 100 points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Logistic Regression\n",
    "\n",
    "In this part of the exercise, you will build a logistic regression model to predict whether a student\n",
    "gets admitted into a university.\n",
    "\n",
    "Suppose that you are the administrator of a university department and you want to determine\n",
    "each applicant’s chance of admission based on their results on two exams. You have historical\n",
    "data from previous applicants in *ex2data1.txt* that you can use as a training set for logistic regression. For each\n",
    "training example, you have the applicant’s scores on two exams and the admissions decision.\n",
    "\n",
    "Your task is to build a classification model that estimates an applicant’s probability of admission based on the scores from those two exams. This outline and code framework will guide you through the exercise.\n",
    "\n",
    "**1\\.1 Implementation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tested with:\n",
      "Python 3.6.2 |Anaconda, Inc.| (default, Sep 21 2017, 18:29:43) \n",
      "[GCC 4.2.1 Compatible Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "{'numpy': '1.13.1', 'matplotlib': '2.0.2'}\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "print('Tested with:')\n",
    "print('Python', sys.version)\n",
    "print({x.__name__: x.__version__ for x in [np, matplotlib]})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.1.1 Visualizing the data**\n",
    "\n",
    "Before starting to implement any learning algorithm, it is always good to visualize the data if possible. This first part of the code will load the data and display it on a 2-dimensional plot by calling the function plotData. The axes are the two exam scores, and the positive and negative examples are shown with different markers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "################################################################################\n",
    "# Try to fit your code and comments into 80 charecters because\n",
    "# - it is guaranteed to look as intened on any screen size\n",
    "# - it encourages you to write \"flater\" logic that is easier to reason about\n",
    "# - it encourages you to decompose logic into comprehansible blocks.\n",
    "# \n",
    "# Try to avoid reassinging/mutating variables because when you encounter an \n",
    "# unexplainable bugs (you will) it is easier to have the whole history\n",
    "# of values to reason about.\n",
    "#\n",
    "# Using %debug magic to run pdb might be useful for debugging. \n",
    "# It is just like gdb but for Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2) 30.0588224467 99.8278577969 float64\n",
      "(100, 1) 0.0 1.0 float64\n",
      "(100, 3) 1.0 99.8278577969 float64\n",
      "(100, 1) 0 1 int32\n"
     ]
    }
   ],
   "source": [
    "# it is good to isolate logical parts to avoid variables leaking into the\n",
    "# global scope and messing up your logic later in weird ways\n",
    "\n",
    "def read_classification_csv_data(fn, add_ones=False):\n",
    "    # read comma separated data\n",
    "    data = np.loadtxt(fn, delimiter=',')\n",
    "    X_, y_ = data[:, :-1], data[:, -1, None]  # a fast way to keep last dim\n",
    "\n",
    "    # printing statistics of data before working with it might have saved\n",
    "    # hundreds hours of of my time, do not repeat my errors :)\n",
    "    print(X_.shape, X_.min(), X_.max(), X_.dtype)\n",
    "    print(y_.shape, y_.min(), y_.max(), y_.dtype)\n",
    "    # aha, y is float! this is not what we expected\n",
    "    # what might go wrong with further y == 0 checks?\n",
    "    # A: floating point equality comparison, that's what!\n",
    "\n",
    "    # insert the column of 1's into the \"X\" matrix (for bias)\n",
    "    X = np.insert(X_, X_.shape[1], 1, axis=1) if add_ones else X_\n",
    "    y = y_.astype(np.int32)\n",
    "    return X, y\n",
    "    \n",
    "X_data, y_data = read_classification_csv_data('/Users/brutto/Downloads/data/ex2data1.txt', add_ones=True)\n",
    "print(X_data.shape, X_data.min(), X_data.max(), X_data.dtype)\n",
    "print(y_data.shape, y_data.min(), y_data.max(), y_data.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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E9BQAkB50sSfPsMWZmV0n6QFJ10rabGaXDvjzN8IODNFheop0o4sBqCxxem1T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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a481908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# how does the *X[y.ravel()==1, :2].T trick work?\n",
    "# https://docs.python.org/3/tutorial/controlflow.html#unpacking-argument-lists\n",
    "\n",
    "def plot_data(X, y, labels, markers, xlabel, ylabel, figsize=(10, 6), ax=None):\n",
    "    if figsize is not None:\n",
    "        plt.figure(figsize=figsize)\n",
    "\n",
    "    ax = ax or plt.gca()\n",
    "    for label_id, (label, marker) in enumerate(zip(labels, markers)):        \n",
    "        ax.plot(*X_data[y_data.ravel()==label_id, :2].T, marker, label=label)\n",
    "    ax.set_xlabel(xlabel)\n",
    "    ax.set_ylabel(ylabel)\n",
    "    plt.legend()\n",
    "    ax.grid(True)\n",
    "    \n",
    "student_plotting_spec = {\n",
    "    'X': X_data,\n",
    "    'y': y_data, \n",
    "    'xlabel': 'Exam 1 score', \n",
    "    'ylabel': 'Exam 2 score',\n",
    "    'labels': ['Not admitted', 'Admitted'], \n",
    "    'markers': ['yo', 'k+'], \n",
    "    'figsize': (10, 6)\n",
    "}\n",
    "    \n",
    "plot_data(**student_plotting_spec)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.1.2 [5pts] Sigmoid function** \n",
    "\n",
    "Before you start with the actual cost function, recall that the logistic regression hypothesis is defined as:\n",
    "\n",
    "$h_\\theta(x) = g(\\theta^Tx)$\n",
    "\n",
    "where function g is the sigmoid function. The sigmoid function is defined as:\n",
    "\n",
    "$g(z) = \\dfrac{1}{1+e^{-z}}$\n",
    "\n",
    "Your first step is to implement/find a sigmoid function so it can be called by the rest of your program. Your code should also work with vectors and matrices. For a matrix, your function should perform the sigmoid function on every element. \n",
    "\n",
    "When you are finished, (a) plot the sigmoid function, and (b) test the function with a scalar, a vector, and a matrix. For scalar large positive values of x, the sigmoid should be close to 1, while for scalar large negative values, the sigmoid should be close to 0. Evaluating sigmoid(0) should give you exactly 0.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SMdpzl4w61tDEt59bz69e3c64IX15/B8vZNq4wWHHEsl5Ku6SMYu3HODuJ1ax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\nSA5ScRcRyUEq7iIiOUjFXUQkB/1/Y5gDPGtQKl4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e49ae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50,) (49,)\n"
     ]
    },
    {
     "data": {
      "image/png": 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gER+Hd77ldBSVgLToq7iWe2onNanTcKWmOx0lYibbZyG1HH7b4SQqEWnRV3Gr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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15140a3978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check out scipy.special for great variaty of vectorized functions\n",
    "# remember that sigmoid is the inverse of logit function\n",
    "# maybe worth checking out scipy.special.logit first\n",
    "from scipy.special import expit\n",
    "sigmoid = expit\n",
    "\n",
    "def check_that_sigmoid_f(f):\n",
    "    # don't use np.arange with float step because it works as\n",
    "    # val_{i+1} = val_i + step while val_i < end\n",
    "    # what might do wrong with float precision?\n",
    "    x_test = np.linspace(-10, 10, 50)\n",
    "    sigm_test = f(x_test)\n",
    "    plt.plot(x_test, sigm_test)\n",
    "    plt.title(\"Sigmoid function\")\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "    \n",
    "    # why should analytical_diff almost== finite_diff for sigmoid?\n",
    "    analytical_diff = sigm_test*(1-sigm_test)\n",
    "    finite_step = x_test[1]-x_test[0]\n",
    "    finite_diff = np.diff(sigm_test) / finite_step\n",
    "    print(x_test.shape, finite_diff.shape)\n",
    "    plt.plot(x_test[:-1]+finite_step/2, finite_diff)\n",
    "    plt.plot(x_test, analytical_diff)\n",
    "    plt.title(\"Numerical (finite difference) derivative of 1d sigmoid\")\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "check_that_sigmoid_f(sigmoid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.1.3 [15pts] Cost function and gradient**\n",
    "\n",
    "Now you will implement the cost function and gradient for logistic regression. Complete the code\n",
    "in the functions *hyposesis_function* and *binary_logistic_loss* below to return the value of the hypothesis function and the cost, respectively. Recall that the cost function in logistic regression is\n",
    "\n",
    "$j(\\theta) \\ = \\ \\frac{1}{m} \\ \\sum_{i=1}^{m} \\ [ \\ -y^{(i)} log(h_\\theta(x^{(i)})) \\ - \\ (1 - y^{(i)})log(1-h_\\theta(x^{(i)})) \\ ]$\n",
    "\n",
    "and the gradient of the cost is a vector of the same length as $\\theta$ where the $j^{th}$ element (for $j = 0, 1,...,n$) is defined as follows:\n",
    "\n",
    "$\\frac{\\partial J(\\theta)}{\\partial \\theta_{j}} \\ = \\ \\frac{1}{m} \\ \\sum_{i=1}^{m} \\ (h_\\theta(x^{(i)})-y^{(i)}) x_j^{(i)}$\n",
    "\n",
    "where $m$ is the number of points and $n$ is the number of features. Note that while this gradient looks identical to the linear regression gradient, the formula is\n",
    "actually different because linear and logistic regression have different definitions of $h_\\theta(x)$.\n",
    "\n",
    "What should be the value of the loss for $\\theta = \\bar 0$ regardless of input? Why? Make sure your code also outputs this value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# we are trying to fit a function that would return a \n",
    "# \"probability of \"\n",
    "\n",
    "# hyposesis_function describes parametric family of functions that we are\n",
    "# going to pick our \"best fitting function\" from. It is parameterized by\n",
    "# real-valued vector theta, i.e. we are going to pick\n",
    "#    h_best = argmin_{h \\in H} logistic_loss_h(x, y, h)\n",
    "# but because there exist a bijection between theta's and h's it is \n",
    "# eqvivalent to choosing\n",
    "#    theta_best = argmin_{theta \\in H} logistic_loss_theta(x, y, theta)\n",
    "\n",
    "def hyposesis_function(x, theta):\n",
    "    n = x.shape[0]\n",
    "    theta = mp.reshape(theta, n, 1)\n",
    "    return sigmoid(x.dot(theta))\n",
    "    #raise NotImplementedError('Implement it yourself.')\n",
    "\n",
    "# negative log likelihood of observing sequence of integer\n",
    "# y's given probabilities y_pred's of each Bernoulli trial\n",
    "# recommentation: convert both variables to float's \n",
    "# or weird sign stuff might happen like -1*y != -y for uint8\n",
    "# use np.mean and broadcasting\n",
    "def binary_logistic_loss(y, y_pred):\n",
    "    y = y.astype(np.float64)\n",
    "    m = np.size(y)\n",
    "    y_pred = y_pred.astype(np.float64)\n",
    "    assert y_pred.shape == y.shape\n",
    "    Y1 = np.log(y_pred)\n",
    "    y_Pred = 1 +(-1 * y_pred)\n",
    "    y_Pred = y_Pred.astype(np.float64)\n",
    "    Y2 = np.log(y_Pred)\n",
    "    p1 = -1 * np.multiply(y,Y1)\n",
    "    yy = 1 + (-1 * y)\n",
    "    yy = yy.astype(np.float64)\n",
    "    p2 = -1 * np.multiply(1 + (-1 * y), Y2)\n",
    "    res = np.mean(p1 + p2)\n",
    "    return res\n",
    "    #raise NotImplementedError('Implement it yourself.')\n",
    "    \n",
    "\n",
    "def logistic_loss_theta_grad(x, y, h, theta):\n",
    "    y_pred = h(x, theta)\n",
    "    point_wise_grads = (y_pred - y)*x\n",
    "    grad = np.mean(point_wise_grads, axis=0)[:, None]\n",
    "    assert grad.shape == theta.shape\n",
    "    return grad\n",
    "    \n",
    "\n",
    "def logistic_loss_theta(x, y, h, theta):\n",
    "    return binary_logistic_loss(y, h(x, theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.69314718056\n",
      "[[-12.00921659]\n",
      " [-11.26284221]\n",
      " [ -0.1       ]]\n"
     ]
    }
   ],
   "source": [
    "# Check that with theta as zeros, cost is about 0.693:\n",
    "theta_init = np.zeros((X_data.shape[1], 1))\n",
    "print(logistic_loss_theta(X_data, y_data, hyposesis_function, theta_init))\n",
    "print(logistic_loss_theta_grad(X_data, y_data, hyposesis_function, theta_init))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.1.4 Learning parameters using *fmin***\n",
    "\n",
    "In the previous assignment, you found the optimal parameters of a linear regression model by\n",
    "implementing gradient descent. You wrote a cost function and calculated its gradient, then took\n",
    "a gradient descent step accordingly. This time, instead of taking gradient descent steps, you will\n",
    "use a scipy.optimize built-in function called *fmin*.\n",
    "\n",
    "The final $\\theta$ value will then be used to plot the\n",
    "decision boundary on the training data, as seen in the figure below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import climin\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def optimize(theta_init, loss, loss_grad, max_iter=10000, print_every=1000, optimizer_fn=None, show=False):\n",
    "    theta = theta_init.copy() \n",
    "    opt_args = (theta, loss_grad)\n",
    "    \n",
    "    if optimizer_fn is None:\n",
    "        optimizer_fn = partial(climin.GradientDescent, step_rate=1e-3, momentum=0.999)\n",
    "\n",
    "    optimizer = optimizer_fn(*opt_args)\n",
    "    \n",
    "    loss_curve = []\n",
    "    for opt_info in optimizer:\n",
    "        n_iter = opt_info['n_iter']\n",
    "        f_value = loss(theta)\n",
    "        loss_curve.append(f_value)\n",
    "\n",
    "        if print_every != 0 and n_iter % print_every == 0:\n",
    "            print(n_iter, f_value)\n",
    "\n",
    "        if n_iter == max_iter:\n",
    "            break\n",
    "    \n",
    "    if show:\n",
    "        plt.plot(loss_curve)\n",
    "        plt.show()\n",
    "    \n",
    "    return theta, f_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000 0.232354925345\n",
      "2000 0.207074363137\n",
      "3000 0.208926453519\n",
      "4000 0.209690773334\n",
      "5000 0.20887886802\n",
      "6000 0.207077523145\n",
      "7000 0.205709848254\n",
      "8000 0.204759862717\n",
      "9000 0.204154010627\n",
      "10000 0.20381418595\n"
     ]
    },
    {
     "data": {
      "image/png": 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VSJLUO7o+WEiSpNYxWEiSpKYxWEiSpKbpmmBx3HFFVyBJkromWKRUdAWSJKlrgsUZZxRd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\nLCRJUtMYLCRJUtMYLCRJUtP8F7fbnIi7Dfz7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d84597278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.20381418595\n"
     ]
    }
   ],
   "source": [
    "theta_init = np.zeros((3, 1))\n",
    "loss = partial(logistic_loss_theta, X_data, y_data, hyposesis_function)\n",
    "loss_grad = partial(logistic_loss_theta_grad, X_data, y_data, hyposesis_function)\n",
    "theta, best_cost = optimize(theta_init, loss, loss_grad, show=True)\n",
    "print(best_cost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zr6+a/vd//xcPPfQQVq1ahYcffhjTpk0DADRr1gxr1qyBl5cXnnzySTz00EPm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LErb9DUvVBEREREUlZQ4BptzJzpOh1evOj/mNa69vKtrW7cmTODK3eUm6kr7+0p6RIRERGRURs/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d47f47cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the decision boundary: two points, draw a line between\n",
    "# Decision boundary occurs when h = 0, or when\n",
    "# theta_0*x1 + theta_1*x2 + theta_2 = 0\n",
    "# y=mx+b is replaced by x2 = (-1/theta1)(theta2 + theta0*x1)\n",
    "\n",
    "line_xs = np.array([np.min(X_data[:,0]), np.max(X_data[:,0])])\n",
    "line_ys = (-1./theta[1])*(theta[2] + theta[0]*line_xs)\n",
    "plot_data(**student_plotting_spec)\n",
    "plt.plot(line_xs, line_ys, 'b-', lw=10, alpha=0.2, label='Decision Boundary')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.1.5 [15pts] Evaluating logistic regression**\n",
    "\n",
    "After learning the parameters, you can use the model to predict whether a particular student will\n",
    "be admitted. \n",
    "\n",
    "(a) [5 pts] Show that for a student with an Exam 1 score of 45 and an Exam 2 score of 85, you should\n",
    "expect to see an admission probability of 0.776.\n",
    "\n",
    "Another way to evaluate the quality of the parameters we have found is to see how well the\n",
    "learned model predicts on our training set. \n",
    "\n",
    "(b) [10 pts] In this part, your task is to complete the code in\n",
    "*makePrediction*. The predict function will produce “1” or “0” predictions given a dataset and a learned\n",
    "parameter vector $\\theta$. After you have completed the code, the script below will proceed to report the\n",
    "training accuracy of your classifier by computing the percentage of examples it got correct. You\n",
    "should also see a Training Accuracy of 89.0. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 3)\n",
      "[[ 0.78755263]]\n"
     ]
    }
   ],
   "source": [
    "# For a student with an Exam 1 score of 45 and an Exam 2 score of 85, \n",
    "# you should expect to see an admission probability of 0.776.\n",
    "check_data = np.array([[45., 85., 1]])\n",
    "print(check_data.shape)\n",
    "print(hyposesis_function(check_data, theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9\n"
     ]
    }
   ],
   "source": [
    "# use hyposesis function and broadcast compare operator\n",
    "def predict(x, theta):\n",
    "    h = hyposesis_function(x, theta)\n",
    "    m = numpy.size(h)\n",
    "    for i in range(m):\n",
    "        if h[i] > 0.5:\n",
    "            h[i] = 1\n",
    "        else:\n",
    "            h[i] = 0            \n",
    "    return h\n",
    "\n",
    "def accuracy(x, y, theta):\n",
    "    p = predict(x, theta)\n",
    "    n = numpy.size(y)\n",
    "    cnt = 0\n",
    "    for i in range(n):\n",
    "        if p[i]==y[i]:\n",
    "            cnt = cnt + 1\n",
    "    res = cnt / 100\n",
    "    return res\n",
    "\n",
    "print(accuracy(X_data, y_data, theta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Regularized logistic regression\n",
    "\n",
    "In this part of the exercise, you will implement regularized logistic regression to predict whether microchips from a fabrication plant pass quality assurance (QA). During QA, each microchip goes through various tests to ensure it is functioning correctly. Suppose you are the product manager of the factory and you have the test results for some microchips on two different tests. From these two tests, you would like to determine whether the microchips should be accepted or rejected. To help you make the decision, you have a dataset of test results on past microchips in *ex2data2.txt*, from which you can build a logistic regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.1 Visualizing the data**\n",
    "\n",
    "Similar to the previous parts of this exercise, plotData is used to generate the figure below,\n",
    "where the axes are the two test scores, and the positive (y = 1, accepted) and negative (y = 0,\n",
    "rejected) examples are shown with different markers.\n",
    "\n",
    "The figure below shows that our dataset cannot be separated into positive and negative examples by a\n",
    "straight line. Therefore, a straightforward application of logistic regression will not perform well on this dataset since logistic regression will only be able to find a linear decision boundary.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(118, 2) -0.83007 1.1089 float64\n",
      "(118, 1) 0.0 1.0 float64\n",
      "(118, 2) -0.952841559322 1.01612109153 float64\n",
      "(118, 1) 0 1 int32\n"
     ]
    }
   ],
   "source": [
    "X_data_, y_data = read_classification_csv_data('ex2data2.txt')\n",
    "X_data = X_data_ - X_data_.mean(axis=0)[None, :]\n",
    "print(X_data.shape, X_data.min(), X_data.max(), X_data.dtype)\n",
    "print(y_data.shape, y_data.min(), y_data.max(), y_data.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YEu5OFDwzkplZC6/3MNauPQKv9zAyM2tRWDgv5qIlnhz357acWwFzTla2dOlSZGVlmR1G\nRCxYSDcigvT004h2lUMpIC3tdF+TaGlpqYHRmU+LMyPx5rg/t+XcCphzSlZ7ezvuvfdedHR0aL5v\npVRCl6aNwIKFdKOUQnd3KqINWhEBurtT+/7nWLdunXHBWUAyZ0aC4s1xf27LuRUw55SsV155Bffe\ney8OHz5sdiiGYsFCusrLK8KBA5HfZgcOpGDhQk/fz25axj7ZMyOh4slxf27KuVUw55SsRBv07Y4F\nC+mqoqIajY3ZaGlJ6TsLIAK0tKSgsTEbq1d7zQ3QJMmeGQnFHJPZfD6fbfbf0dGB7373u/jiF7+I\nESNGYMyYMbj55pvxxhtvDHhsZ2cnVqxYgaysLJx55pmYOHEivvGNb+D999/ve0x3dzfWrVuH6dOn\nY/jw4TjvvPNwww034NChQ32PERH8+Mc/xsyZMzF8+HCMHz8et99+Oz788MOw402ePBkejwe7d+/G\nZZddhuHDh2PGjBl46qmn+h6zfft23HzzzQCAhQsXIiUlBcOGDcNvf/vbvsc888wzWLBgAc466yyM\nGjUKhYWFeOWVVwa8vrq6ur6YLrnkEtTV1SWeWAOwYCFdZWRkoKFhPzo7y1BVNRnr109AVdVkdHaW\nuX64bTJnRkIxx2Q2OxUsBw4cwB/+8AcUFxfj/vvvx3e+8x3s2bMHV155Zdjihh9//DHmz5+P2tpa\nXHPNNdiyZQu+853v4NVXX8Xf/vY3AEBPTw8KCgrwb//2b8jJycEPf/hD/Ou//itOnDiBl19+uW9f\n3/72t/H//t//wxVXXIEtW7agtLQUv/jFL3DNNdfg008/7XucUgqvvfYabr31VixevBg1NTVITU3F\nTTfdhD179gAAFixYgPLycgDAmjVr8Oijj+KRRx5BdnY2AOCRRx5BYWEhMjIysGnTJqxduxbt7e24\n4oorwnpedu3ahRtvvBFnnHEGampqcN1116GkpAR//OMfNcu15kSEt343ALMBSGtrq5C2enp6ot73\n0EMPGRhJdI899pghxzlx4oQsWDBDNm5Mkb17Ifv2QfbuhWzcmCILFsyQEydOJLTfwXLcn1Vy7iZ2\nyHlra6vE8xlYVFSkazxa7v/kyZMDtj3//POilJJHH320b9vatWslJSVFnn766aj7+ulPfypKKdm8\neXPUx/zud78TpZQ8/vjjYdt37dolSinx+Xx92yZPniwpKSlSV1fXt+3EiRNy3nnnyZw5c/q27dix\nQ1JSUqSpqSlsnx999JGcffbZcvvtt4dtP3r0qGRmZsqyZcv6ts2aNUsmTJggfr+/b9tzzz0nSinJ\nysqK+npEhn5/BO8HMFs0/G7mGRYy1GCXONra2gyMJDq9/1oM0uvMSDzXtq2Sczdhzs2Vnp7e9+9P\nPvkE77//PqZMmYLMzMyw382TTz6JSy+9FB5P9DOdTz75JMaOHYuysrKoj9mxYwcyMzORn5+P48eP\n990uu+wynHXWWdi3b1/Y48877zx87Wtf6/s5IyMDS5YswQsvvICjR48O+tp2796Nzs5O3HrrrWHH\nUkrhy1/+ct+x3nnnHbz00ktYunQpzjrrrL7n5+fn46KLLhr0GGbiTLdkGbW1tWaHYLiMjAxUV28G\nsNmURjo35txsTsi5z+cLK+x37twZ9sVeXFyM4uJiS+7/5MmTuO+++/Dwww/jyJEjfY3tSil0dnb2\nPe4vf/kLbrzxxkH39Ze//AXTp09HSkr0v/1ff/11fPjhh/j85z8/4D6l1IAiZNq0aQMed+GFFwIA\nDh8+HHE/occSEVx55ZURjzV69GgA6OvXiXSs6dOn44UXXoh6DDOxYCGyCDd2/ZM99S8YPB4P6uuH\nHoZvhf2XlZVh+/btWLFiBb7yla9g9OjRUErhlltuQU9P5GkGktHT04Nx48bhscceizjqb+zYsZoe\nSymFRx99FOPGjRtw/xln2Psr397RE2lA778Wicg6fvWrX2Hp0qXYtGlT37bu7u4BI3amTp0a1jgb\nydSpU9HS0oJPP/0Uw4YNi/qYPXv24PLLLw+7HBXNn//85wHbXn31VQCBUURA9D9upk6dChHB2LFj\ncdVVV0U9xvnnnw8gcEYm2rGsiD0s5HrFxcWor6/vuxUVFYX9zGKFyDmGDRs24EzKli1bwkbrAMAN\nN9yAl156CU8//XTUfd1www147733sHXr1qiPufnmm/HJJ59g/fr1A+779NNPwy5DAcBbb70VNoz5\nxIkTeOSRR3DZZZf1XQ4aOXIkRGRAkXX11Vdj1KhRuO+++/DJJ58MOF5wWYjx48dj1qxZ2L59e9gS\nILt37444/NkqeIaFLEPr08o0NL1zbkZfjtU58X2ud1Gv5f4LCwvxyCOPYNSoUbjooouwf/9+7Nmz\nB2PGjAl73MqVK7Fjxw7cdNNNKCkpwZw5c3D8+HHs3LkTDz74IC6++GIsWbIEP//5z3HnnXfi+eef\nxxVXXIGPPvoIe/bswfLly1FUVIQFCxZg2bJlqKmpwYsvvohFixYhNTUVr732Gnbs2IEtW7bg+uuv\n7zvuhRdeiG9+85s4cOAAxo0bh23btuHo0aPYvn1732NmzZqFYcOGYePGjfjwww+Rnp6O/Px8jBkz\nBg888ACWLFmC2bNn49Zbb8XYsWPR0dGBxsZGzJ8/H1u2bAEAbNiwAYWFhcjNzUVpaSmOHz+OrVu3\nYubMmfjoo480y7emtBxy5JQbOKzZFM8++6zZIYiI/kM0rUSPnJ84cUIqKu6Qyy+fLFdeOUEuv3yy\nVFTckfAwbaexyvt8MPEOa7aTzs5Oue222+Tzn/+8jBo1ShYvXiyvvfaaZGVlSWlpadhjP/jgAykv\nL5eJEyfKmWeeKZMmTZLS0lJ5//33+x5z8uRJqaqqkqlTp0p6erqcd955csstt8ihQ4fC9vXQQw9J\nTk6OjBw5UkaPHi2XXnqpVFRUyDvvvNP3mMmTJ0tRUZHs3r1bLr30Uhk+fLhcdNFF8uSTTw54Hdu2\nbZNp06ZJamrqgCHOTU1Ncu2118rZZ58tI0aMkAsuuEBKS0ulra0tbB9PPfWUzJgxQ4YPHy4zZ86U\nuro6Wbp0qUyZMmXQHJo1rFlJhCYgt1NKzQbQ2traymm0Xcjn8/EyUIKCK1AXFLQjJyewqKNIYCK8\nxsZsTmRnE21tbZgzZw74GWisrKwsXHzxxZY/AzfU+yN4P4A5IqLZOH72sJBt6VVsu61Y0TKPWqxA\nTUQUCQsWshW/34/KynLk5mYhP38icnOzUFlZHtY4RkPTK49arEBNRBQJCxayjKEW3gpebsjMrIXX\nexhr1x6B13sYmZm1KCycx6IlRqF5vOYa7fIoot0K1E5m9QXmyDxKKTapD4IFC+kqni+noabE5+UG\nbYTmce/ewDYt8qjlCtROZtTSD2Q/f/3rXwcdRu12LFhIc4lebnjiiScGvZ+XG7QRmsd77gm/L9k8\narUCtZMN9T4nosg4DwtpKnSUiNcbOkqkFoWFexMeJRLP5Qa3/wU/GL3zWFFRjcLCvQCijRLyJvcC\niMi1eIaFNKXXZRtebtCG3nnUawVqIiIWLKQpPS/b8HKDNvTOY3AF6ubmQ9iz5000Nx9CdfVmFisa\ncXvTMrkXCxbSTLKjREpKSgbdf0VFNRobs9HSktJ3hkAEaGkJXG5YvZqXG2IRmseamsA2vfLIM14D\nDfU+j4TD+YnYw0IaCr3cEOl7aqjLDYsWLRp0/8HLDTU1a1BVVY+0tNM4dSoVeXkeNDR4+Rd8jELz\neOjQY1i/Pp15NNBQ7/P+9OoLi0V7e7su+yV7M+t9wan5I+DU/ImrrCxHZmYt5s4deFmopSUFnZ1l\nqK7erMmx2GCrDebR2oz8fyqoo6MD2dnZ6Orq0nS/5BwjRoxAe3s7Jk2aNOA+vabm5xkW0pSRo0T4\nJasN5tHampp2wuuN3hdWVVUPQNuCZdKkSWhvb8exY8c03S85x5gxYyIWK3piwUKa4mUbIu2YOZx/\n0qRJhn8hEQ2GBQtpLjhKBNgc1wdpc3Mz5s+fr29wFIY5N148OU+2L4wC+D53Bo4SIl3F80G6adMm\nHSOhSJhz48Wbcw7nTx7f587AptsI2HRrjq6uLowYMcLsMFyFOTdevDkPHSUUuS+ME/INhe9zY7Hp\nlhyPHyjGY86NF2/O2ReWPL7PnYEFCxGRxSXaF0bkJOxhISKyERYr5FYsWMgyVq5caXYIrsOcG485\nNx5z7gwsWMgyOOeD8Zhz4zHnxmPOnYGjhCLgKCEiIqLE6DVKiGdYiMi1+AcbkX2wYCEiV/H7/ais\nLEdubhby8yciNzcLlZXl8Pv9ZodGRINgwUKWcfDgQbNDcB235Tw4CVtmZi283sNYu/YIvN7DyMys\nRWHhPEOKFrfl3AqYc2dgwUKWsWrVKrNDsAWfz6fZvtyW8w0b7kZBQTvmzu3pW5tHKWDu3B4UFLSj\npmaN7jG4LedWwJw7AwsWsoytW7eaHYItaFmwuC3nTU07kZPTE/G+nJweNDXV6x6D23JuBcy5M7Bg\nIcvg0EPjuSnnIoL09NMRVz0GAmda0tJO696I66acWwVz7gwsWIh0pOXZEEqOUgrd3amIVo+IAN3d\nqZxJlsiiuJYQkY58Ph+Ki4uT3kdo4bNz5054PJ6+n4uLi5M+hlvk5RXhwIFazJ078LLQgQMpWLjQ\nE+FZRGQFPMNClrFx40azQ7Ck4uJi1NfX992KiorCfk6mWHFbzisqqtHYmI2WlpS+My0iQEtLChob\ns7F6tVf3GNyWcytgzp2BZ1jIMrq6uswOwXXclvOMjAw0NOxHTc0aVFXVIy3tNE6dSkVengcNDV5k\nZGToHoPbcm4FzLkzcGr+CDg1PyUq0uWboqKivp+1uHzj8XhQX6//aJYgEdGtr0PPfdvh+EROpNfU\n/DzDQq6lRX9Jf/0LEj2KCyP6Vfx+PzZsuBtNTTuRnn4a3d2pyMsrQkVFddJnIfTcd7xYrBDZBwsW\nci09ChYj6B1zcDbYgoJ2eL2BCdZEgAMHalFYuBcNDfsTLiz03DcRORubbskyjh07ZnYIrhMp53rO\nBmuFmWbNxve58ZhzZ2DBQpZRWlpqdgias/oZnEg513M2WCvMNGs2J77PrY45dwZeEiLLWLduna77\nN2M+E6sXLP1zHs9ssPH2f+i5b6uIJXa93+c0EHPuDCxYyDL0HpFlREOs3fTPeehssJG+d5OZDVbP\nfZsp3iZijjw0HnPuDLwkRERhArPBRv5oSHY2WD33bYZgE3FmZi283sNYu/YIvN7DyMysRWHhPPj9\nfrNDJHIMFixEFEbP2WCtMNOslthETGQcFixkGdu2bTP0eFbvLzFCpJwHZ4Pt7CxDVdVkrF8/AVVV\nk9HZWZb0sGM9922GRJqIjX6fE3PuFOxhIctoa2vDbbfdZtjxWLBEz3lGRgaqqzcD2Kx5E6ye+zZS\nok3ERr/PiTl3Cp5hIcuora01OwTXiSXnehYUdi1WgPAm4kiiNRHzfW485twZWLAQESXIiCZirvdG\nFMBLQkRECaqoqEZh4V4A7cjJCV1qINBE3NCQWBOxldZbIrIKFixERAkKNhHX1KxBVVU90tJO49Sp\nVOTledDQ4E2ouOB6S0SR8ZIQWUborLNkDOY8ecEm4ubmQ9iz5000Nx9CdfXmqEXFUDnnUGnt8X3u\nDCxYyDLKysrMDsF1mHNtxdJEPFTOud6S9vg+dwYWLJQULRsCFy1aZNixKGConJP2Bst5PEOlKXZ8\nnzsDCxaKm9/vR2VlOXJzs5CfPxG5uVmorCzXZRpyI49FZLZEh0oTuQGbbikuRjYEsvmQ3CgwVLoW\nc+cOvCxkx/WWiLTCMywUFz0bAuvq6gw7lt58Pp/ZIcTkzjvvNDsE1+n/Pu/PaestWcFQOSd7YMFC\ncdGzIbD/l7ydmw/tUrA88cQTZofgOkO9N5y23pIV2OX/RxqcLQsWpdRypdQhpdTflVJ/UErlDPLY\nPKVUT7/bp0qpzxsZs1H0bMbTuyEw9MvT6s2HTvkAnDNnjtkhaMJOv49YisR4h0rT4FiYO4PtChal\n1C0AfgDgHgCXAXgJwLNKqTGDPE0AXABgfO/tXBE5qnesRjGqMdXIhkCrNx/q+QVppy9fq3Byzthg\nSxRgx6YrWAqIAAAgAElEQVTbFQAeFJGfA4BS6nYABQBKAWwa5HnvicgJA+IzlNGNqUY2BNqp+dDn\n84V9ae7cuTNssqri4uKYV4f2+Xy6rSStZZxEREayVcGilEoFMAfAfcFtIiJKqecAzBvsqQBeVEqd\nCeBlAOtE5Pe6BmuQ0MbUoGBjKhBoTK2u3qzZ8fRaO8XsYyWr/xe9x+NBfb31emzsEicRUX+2KlgA\njAEwDMC7/ba/C2B6lOe8DWAZgD8CSAfwLQC/UUrNFZEX9QrUKE1NO+H1Rm9MraqqB6BdwaLH2ilB\nJSUl+NnPfmbIseLl1DMTL75oz/8F7Pz76P8+J/0x585gt4IlbiLyGoDXQjb9QSk1FYFLS98wJypt\nxNOYquV18GBDILBZ031Hmo1Sr2PFS88zE2Z++Y4dO1aX/erNqDNFelyec8qsq2b+/xgvp+Tc7ezW\ndHsMwKcAxvXbPg7AO3HspwXAtKEetHjxYng8nrDbvHnzBozp37VrV8TFtZYvX45t27aFbWtra4PH\n48GxY8fCtt9zzz3YuHFj2LaOjg54PB4cPHgwbPv999+PlStXhjWmnjwJ3H038Kc/ffY4EeBvf+tG\naWnpgNhuueUWTV7H8ePHk34dQcXFxejq6oLH40Fzc3PYY30+n66vQ4vfR6jrr78+6usoKSkJ21Zc\nXIzhw4ejtLQU9fX1KCoqQn19fd/6J/2/MLV8HXfdddegr2Ow30f/1wFY9/eR6OsILSS1eh0dHR2G\nv45QybyOYIP/xImZmDYtM6zB38qvY/r06ZZ6XyX6Oqz2/0fwMcHvxvHjx8Pj8WDFihUDnqMFZbc1\nKZRSfwDwvIj8S+/PCkAHgC0i8r0Y97ELwAkRuTHK/bMBtLa2tmL27NkaRa6PyspyZGZGbkxtaUlB\nZ2eZpj0sFKBn7wf7SuKnV874u/hMaIN/5J4yzhFDAW1tbcEpE+aISJtW+7XbGRYA+CGAbymlliil\nvgjg3wGMAPAwACilNiiltgcfrJT6F6WURyk1VSk1Qyn1YwBXAthqQuya46yY5rBqf4Rb8fehPzvP\nPE3OYLuCRUR+CeAuAOsBvADgEgBXi8h7vQ8ZD2BiyFPSEJi35X8A/AbAxQDyReQ3BoWsKyfNitn/\ndKSV6fkFaeSXr51yPhitchY8vR28BfuJgjct5nuxa87tPPO0XXNO4Wx3ScgIdrok1J+dGuH6c9Lp\ndz3nUtGSk3KuBz3yY8eciwjy8ydi7dojUR+zfv0E7NnzpiU/f+yYczvjJSGKiRU/LGL1+OOPmx2C\nZuwy86qTcm4XeuVczz8+rT7z9FD4PncGFixkGSNGjDA7BNdhzo2nZc6NWpYDCM48Hfkrw2ozT/fH\n97kzsGAhw9nl7AORlS/rBUftZGbWwus9jLVrj8DrPYzMzFoUFs7TvGhhgz+ZjT0sEdi5h8UOnHg9\nOdLkb0VFRX0/W3nmVbInM6Y08Pv9qKlZg6am8JmnV682duZpsja9elgcP9Mt2cfKlSvxve/FNJWO\n5dh1jR4759yutMq50ctyANaZeTpefJ87Ay8JkWVMmjTJ7BBcx645t/OZYS1yHs+yHHqxS7EC2Pd9\nTuF4hoV0F+taOXfccYcZ4bmanXLu9/uxYcPdaGraifT00+juTkVeXhEqKqptdTlCi5yHjtqJVDdY\nfdSO0ez0PqfoWLCQ7ux6uSQZ7FfRVui08F5v6LTwtSgs3Gu7SRK1EBi1E7mHxeqjdogSwUtCRDpg\nwaItTgs/EEftkNuwYCHL6L+qKOnPLjm387Tw/WmVcycty6E3u7zPaXAsWMhw0c4+rFq1yuBIyA45\nt0KDqZZiyXmsryU4aqe5+RD27HkTzc2HUF29mcVKP3Z4n9PQWLDQAHpP7BatYNm61RELaNuKHXJu\n92nh+4uW82RnrbXL6zeDHd7nNDQWLDSAWTPRcuih8eyScztPC99fpJwbPWut29jlfU6DY8FCRJbn\n9AZTNhUTDY0FCxFZ3lANpg0NDWaHmBQnNRUT6YUFC8Hn88Hj8fTdghO7BW9GXSLauHGjIcehz9gp\n54M1mNppQc3+OXdaU7EV2el9TtFx4jiyzMRuXV1dhh/T7ZLNuc/nM2XOGTs3mPbPOWet1R8/W5yB\nZ1jIMu69916zQ3CdZHNupzMbVhEp505qKrYifrY4A8+wEJHtxLo+lV1UVFSjsHAvgHbk5IQuPRBo\nKm5osHdTMZEWWLDQAHb6oCd3ssplTK0Em4pratagqqoeaWmncepUKvLyPGho8HIiOCKwYKEIzCpY\njh07hjFjxphybLeKN+dOO7Nhhmg5DzYVA5shIuxZ0RA/W5yBPSxkGaWlpWaHYAlG9oXEm/Pi4mLU\n19f33YqKisJ+ZrEytFhyzmJFW/xscQYWLGQZ69atMzsESzCyYHFKzu1UKDkl53bCnDsDCxabc9Lc\nDLNnzzY7BN1ZbVSNU3Jup4LFKTm3E+bcGViw2FCyi6SReaxWsCQrUqHgtNdIRNbAplubCS6SVlDQ\nDq83dPhjLQoL96KhYT9HFNiMnRtZoxUsVo2XiOyLZ1hsxsmLpG3bts3sEExhZiOrW3NuJubceMy5\nM7BgsRknL5LW1tZmdgias8o6TdE4MedWx5wbjzl3Bl4SspF4Fkmz47DI2tpas0PQnNUnONMi58lc\n0nLj5SMnvs+tjjl3BhYsNsJF0tzBbl/gyRRlbixYiCgxvCRkM1wkzfn4BU5ENFDcBYtSapVSaniE\n7WcqpVZpExZFU1FRjcbGbLS0pCA4BYsI0NISWCRt9WoukmZlLEaIiBKTyBmWDQAijZsd2Xsf6Si4\nSFpnZxmqqiZj/foJqKqajM7OMtsPaQ7te3AqqxUseuR8sNdo9SZkI1j5fe6kiShDWTnnFLtEelgU\ngEjv6mwAHyQXDsXCqYuklZWVxf0c9kAkJ5GcD2Ww34fVm5CNoEfOk+H3+7Fhw91oatqJ9PTT6O5O\nRV5eESoqqm39B1Aoq+WcEhNzwaKUehuBQkUA/EkpFTq2dhiAcwA8rGl0NCS9ixUjC6JFixbF/RwW\nLMlJJOeUHCvl3C0TUVop55S4eM6wrEPg7MpPAPwAwImQ+04BOCwi+7QLjczihr+4iCh8Isqg4ESU\nQGAiysDZXCLzxVywiMiDAKCUOgRgr4ic1i0qMo1b/uIia3Db2TGrnRFsatoJrzf6RJRVVfUAWLCQ\nNcTUdKuUSgveAOwLbPpsW7/7ycbMnPq/rq5uyMewaVNbseRcT1b68jaCz+czPedB8UxEaXdWyTkl\nJ9ZRQicB/D3GG9mYmVP/x1JsmLnujhOxwDOeVXIeOhFlJE6aiNIqOafkxHpJ6FpdoyBLMHvq/yee\neELzfdLgmHPjWSnngYkoa8N6WIKcNBGllXJOiYupYBGRZ/UOhMzn1qn/rdZXQM6RzDpLRqioqEZh\n4V4A7cjJCe1ZC0xE2dDAiSjJOuKeh0UpNXew+0WkJfFwyGxa/sVlRCGgxf5ZsJBerD7vTHAiypqa\nNaiqqkda2mmcOpWKvDwPGhq8bLAnS0lk4rg/IDAXS+if2aFXQYclFRGZSsu/uOxSsBC5mVMnoiTn\nSWRq/nMBnNf733MBTAJwHYAXwV4X2zNz6v+SkhLd9k2RMefGs3LOnVqsWDnnFLu4z7CIyLsRNv9N\nKfUxgBoAu5KOikxl1l9cRs1GafW+AiNxBlBjueV9ZTV8nzuD0mqMvVJqOoA2ERmpyQ5NpJSaDaC1\ntbUVs2fPNjsc24hUCBQVFfX9bNVCwGp9BUREdtbW1oY5c+YAwBwRadNqv4k03V7YfxMCl4YqAfyP\nFkGRPVm9wZCI2GRO9pVID8tBAO39bnsBjAHwTe1CIyIirXESNbKrRAqWbAAXhdymAzhHRGaLyP9q\nGRy5S3NzsynHdfNfm2bl3M2Yc+Mx584Qd8EiIq/2u72OwNT9RGHiLQQ2bdqkUySDc3PBYlbO3Yw5\nNx5z7gxxN90qpVYAeFNEdvT+/HMA/wzgDQBFTjjLwqZbc3R1dWHEiBFmh+EqzLnxjM65XZvhtcT3\nubEs03QLoAzANwBAKXUVgK8B+EcANwL4PjgXCyWIHyjGY86NZ3TO2QzP97lTJFKwnIfA2RQAKALw\nSxGpV0q9CmC/ZpERERER9Uqk6fZDBIoWALgGwHO9/xYAqVoERURERBQqkYKlHsAvlFINAMYDeKZ3\n+6UA/qpVYOQ+K1euNDsE12HOjWd2zp3erxKJ2TknbSRSsJQDeBjAEQBXi8iJ3u2TATyoTVjkRpMm\nTTI7BNdhzo1nds7dWLCYnXPShmZT8zsJRwkRERElRq9RQomcYYFS6ial1HNKqb8qpSb1bluulFqs\nVWBElBjOZEpEThR3waKU+iYCl372I9DDEhxpdBLA/9UuNCJKBAsWInKiRM6wrADwLRGpAvBpyPYW\nAJdoEhW50sGDB80OwXWYc+Mx58Zjzp0hkYJlCoA/Rth+EsBZyYVDbrZq1SqzQ3Ad5tx4zLnxmHNn\nSGTiuDcAXIzPJo8L+ioCKzkTJWTr1q1mh2BLkaZe93g8fT8PNvU6c2485tx4zLkzJFKwbAawVSk1\nrPfnS5VS/whgLQLT9hMlhEMPE5PM1OvMufGYc+Mx584Qd8EiIg8opU4B2ApgJIBfATgGoFJEHtE4\nPiIiIqKEzrBARLYB2KaUOgeBvpU3hRO6EBFRAkQESimzwyCLS2geliAReV9EOkRElFKpSileEqKE\nbdy40ewQHCGemUyZc+Mx5wF+vx+VleXIzc1Cfv5E5OZmobKyHH6/X/NjMefOENcZFqVUJoAvATgF\n4He9hcowAN8EsAZABgKXioji1tXVZXYIjhBPwcKcG485DxQrhYXzUFDQDq+3B0oBIsCBA7UoLNyL\nhob9yMjI0Ox4zLkzxDw1v1LqKwAaAJyDwMrMvwdQCuApAMMB3A9gm4hoXx4bjFPzUyx8Pp8r12Uh\nSlZlZTkyM2sxd27PgPtaWlLQ2VmG6urNJkRGWrDC1PzVAH4DIAdALYBcBAqYGgDTROTHTihWiGLF\nGWWJEtPUtBM5OQOLFQDIyelBU1Nso9zIXeK5JHQpgDwR+V+lVDuA5QAqRORJfUIjIiKnERGkp59G\ntB5bpYC0tNNsxKUB4jnDcg6A9wBARLoAdAH4Hz2CInc6duyY2SG4DnNuPLfnXCmF7u5UROtGEAG6\nu1M1LVbcnnOniHeU0FSl1IVKqQt7fz4/+HO/7URxKy0tNTuEQfl8Png8nr5bcEbZ4M2Ol4isnnMn\nYs6BvLwiHDgQ+evnwIEULFzoiXhfophzZ4in6bYHgWbbvk29/5WQn0VEhsHm3NZ0a5Xm0ba2Nlvl\nO54ZZa3Kbjl3AuY8fJRQTk7oKKEUNDZmaz5KiDk3ll5Nt/H0sGRrdVCyFqsULPxAMR5zbjzmHMjI\nyEBDw37U1KxBVVU90tJO49SpVOTledDQ4NW0WAGYc6eIuWARkVf1DISIiNwjIyOjd+jyZjbYUkyS\nmumWyM2scFaKyAlYrFAsWLAYzApLLlm1eXTbtm2mHDdRTihY7JZzJ2DOjcecOwMLFgMYuWZGLIqL\ni1FfX993KyoqCvvZrC/itrbEe7PsOELHCpLJOSWGOTcec+4MMY8SchMtRwkZ3Q2fCCeMdnHCayAi\ncgIrTM1PCdiw4W4UFLRj7tyevpkdlQLmzu1BQUE7amrWmBsgERGRDcRVsCilspVSdymlSntXbg69\nL0Mp9RNtw7M/O6yZ4YReDCIicraYhzUrpa4E8GsARwCMBHCfUuoGEfnv3oeMALAMwHc1j9KmtFwz\nQ89hf3YsWHw+X1jfSrBxOKi4uNiWr4uIiCKLZ+K49QC2ishKpdQwAHcDeEYpdZ2I7NUnPHsLXTMj\nUq0x1JoZfr8fGzbcjaamnUhPP43u7lTk5RWhoqLa9L4XPcTTh9K/IGEPS2KYN+Mx58Zjzp0hnoLl\nEgBLAUBEPgWwXin1JoCnlVI3AHhJ+/DsL7BmRi3mzh14WWiwNTNCm3W93tBm3VoUFu61RLOu1srK\nyswOwXWYc+Mx58Zjzp0hnh6WUwBGh24QkZ8BWA7gSQAFGsblGBUV1WhszEZLS0rf6qQiQEtLYJTQ\n6tXeiM9zY7PuokWLzA7BdZhz4zkl53YaYeqUnLtdPAXLSwDy+m8UkZ8DKAPwoFZBOUlwzYzOzjJU\nVU3G+vUTUFU1GZ2dZYOeJbFDs66VsF+FSH9Wm1OK3CWeS0IPAlgY6Q4Rebi3D2OZBjE5TrxrZmjZ\nrOsWLFiI9OXGy9RkLTGfYRGR/xKR5YPc/7CIzNMmLOeKpcAIbdaNZKhmXbuqq6szOwTXYc6N1z/n\ndpml2c6Xqfk+dwZOHGdRgWbdyL+ewZp17cwuH9xOwpwbr3/O7fI7sPNlarvkmAYXzyUhMlBFRTUK\nC/cCiDalf+RmXTt74oknzA7BdZhz49kx53a/TG3HnNNALFgsKtisW1OzBlVV9UhLO41Tp1KRl+dB\nQ4OX14qJyDDJzilFpAUWLBYWb7MuEVmfXWdpTnROKSKtxF2wKKVWAbhfRP7eb/uZAMpFZJNWwdFn\nWKwQOYNdZ2l242VqspZEmm43AIh0PWJk731ECSkpKTE7BNdhzo1n15wnOqeUFdg15xQukUtCCkCk\nAbfZAD5ILhxyM85GaTzm3Hh2zrldL1PbOef0mXhWa34bgUJFAPxJKRV6IXMYgHMAPKxpdOQqVrxu\n73TMufH659yuvwO7FCuAfXNM4eI5w7IOgbMrPwHwAwAnQu47BeCwiOzTLjQiIufjlylRbGIuWETk\nQQBQSh0CsEdEPtEtKiIiIqIQiTTdvgXgguAPSqlrlVKPK6XWKqU4TJoS1tzcbHYIrsOcG485Nx5z\n7gyJFCwPAZgJAEqp8wE8CSANQAmAGu1CI7fZtCkwIp7TaBsnmHMyDnNuPObcGRIpWL4I4IXef98M\n4L9F5HoAS3p/JkrI448/DoAFi5GCOSfjMOfGY86dIZGCJfQ5XwXQ2PvvNwCMTToisrVkio0RI0Zo\nGAnFgjk3HnNuPObcGRIpWNoArFJK3QTgSgC/7t1+PoCjWgVG9sSzI0REpIdEmmRXAHgCwP8B8AMR\nebV3+w0A9msVGLmHXddWISIi48R9hkVE2kTkAhEZLiIVIXetRaDxliguxcXFqK+vx/Tp01FfX4+i\noiLU19f33Vis6GflypVmh+A6zLnxmHNnSGgYslLqLADXAZgKYIuIfABgEoD3APx9sOdqQSm1HMBd\nAMYDeAnAHSJyYJDHL0RgsrsZADoAVIvIdr3jdAMtz45MmjRJ8/hocMy58Zhz4zHnzqBEIi0LNMgT\nlLoIwB4ApwGcC2C6iPxVKVUDYJyI6HqWRSl1C4DtAL4NoAWBS1Q3AbhQRI5FePxkAC8jMEPvNgQa\nhX8MYLGI7I5yjNkAWltbWzF79mwdXoVzabHyrF1WryUiooHa2towZ84cAJgjIm1a7TeRptsfA/gl\nAk22J0O2NwBYqEFMQ1kB4EER+bmIHARwO4AuAKVRHv8dAH8VkVUi8qqI1ALY0bsfsiBeAiIiov4S\nKVjmArhfBp6a+RsCl2h0o5RKBTAHgTM8AIDeOJ4DMC/K077Se3+oZwd5PJmMBQsREfWXSMFyGsDI\nCNunAng/uXCGNAaBlaHf7bf9XUQvlsZHefwopVS6tuFRMsXGwYMHNYxEf04Ywm23nDsBc2485twZ\nEilYGgHcrZQa1vuzKKXOBbABwFOaRUa2lEzBsmrVKg0j0Z8TCha75dwJmHPjMefOkEjBcieAcQDe\nBjAcwC4AfwXwKYCKQZ6nhWO9xxnXb/s4AO9Eec47UR5/QkS6BzvY4sWL4fF4wm7z5s1DXV1d2ON2\n7doVNjImaPny5di2bVvYtra2Nng8Hhw7Ft4ffM8992Djxo1h2zo6OuDxeAb8dXD//fcPGKbX1dUF\nj8czYJEvn8+HkpKBfdC33HKL5V7H1q1bHfE6APv8PrZu3eqI1xHK6q9jxowZjngddvp9LFu2zBGv\nw4q/D5/P1/fdOH78eHg8HqxYoU+LaNyjhPqeqNRXAVwC4CwEZr/9tYj0aBhbtOP+AcDzIvIvvT8r\nBIYqbxGR70V4fA2Aa0Xk0pBtjwHIFJHFUY7BUUI0JI5mIiIaSK9RQjHPw6KU2gvgehH5EABE5DkM\nbGY1wg8BPKyUasVnw5pHAHi4N84NAM4TkW/0Pv7fASxXSm0E8FMA+QBuBBCxWCGKhjPykpl8Ph/f\nX+Rq8UwctxBAmk5xxExEfqmUGgNgPQKXdl4EcLWIvNf7kPEAJoY8/rBSqgDAjwCUIzCa6bbegoso\nZv0LEp5hISOxYCG3S6SHxXQi8hMRmdy7PMA8EfljyH0lInJVv8f/VkTm9D7+AhF5xPioaSj9r8GS\n/phz4zHnxmPOnSHeqfkvUkoNOteKiPxPEvGQi3V1dZkdgusw58Zjzo3HnDtDzE23SqkeAAJARbg7\nuF1EZFiE+22FTbcUC56iJz1F6pkqKirq+5k9U2RVpjfd9voyAgscErkevyxIT+yZIgoXb8HSISJH\ndYmEiIiIKApbNt2SM/WfDIn0x5wbjzk3HnPuDPEULE0ATukVCFFpabQFt0kvzLnxEs05L0Emju9z\nZ4j5kpCIXKlnIETr1q0zOwTXYc6Nl2jOWbAkju9zZ+AlIbIMjsgyHnNuPObceMy5M7BgISIiIstj\nwUJERK6R6IK/ZL6kChbVS6tgyN36L6VO+mPOjcecG6+2thaVleXIzc1Cfv5E5OZmobKyHH6/3+zQ\nKA4JFSxKqduUUi8DOAngpFLqZaXUN7UNjdymrU2zCREpRsy58ZhzY/n9flRXVyEzsxZe72GsXXsE\nXu9hZGbWorBwHosWG4l5av6+Jyi1HsCdAO4HsL938zwAZQB+JCJrNY3QBJyan4jIGSory5GZWYu5\nc3sG3NfSkoLOzjJUV282ITLn0mtq/kTOsHwHwLdEpEJE6ntvFQC+DeC7WgVGRESUbM9JU9NO5OQM\nLFYAICenB01NXO7ALhIpWFIB/DHC9lbEP9U/ERFRGL/fr0nPiYggPf00onVaKgWkpZ1mI65NJFJg\nPILAWZY7+23/NoBfJB0RERG5lt/vR2HhPBQUtMPr7YFSgAhw4EAtCgv3oqFhPzIyMmLal1IK3d2p\nEEHEokUE6O5OBceO2EOio4Ru6220faj39icA3wLQo5T6YfCmYZzkAh6Px+wQXIc5Nx5zPrgNG+5G\nQUE75s7t6SsylALmzu1BQUE7amrWxLW/vLwiLF8e+b4DB1KwcCF/H3aRSMEyE0AbgPcATO29Hevd\nNhPAZb23WRrFSC5RVlZmdgiuw5wbjzkfnNY9JxUV1Rg27Hy0tKQgeOVHJNBw29iYjdWrvcmGTAaJ\n+5IQ1xQivSxatMjsEFyHOTcecx5dPD0nsV7GycjIwO9//yfU1KxBVVU90tJO49SpVOTledDQ4I35\n8hKZj02yRERkCXr1nGRkZPQOXd4cV7FD1hJTwaKUehLAUhE50fvvqETkek0iIyIi18nLK8KBA5Hn\nTdGi54TFin3F2sPSCUBC/j3YjSghdXV1ZofgOsy58ZjzwVVUVKOxMVvTnhPm3BliKlhEpERE/CH/\njnrTN1xyMp/PZ3YIrsOcG485H1xGRgYaGvajs7MMVVWTsX79BFRVTUZnZ1lcQ5pDMefOEPfU/G5g\n56n5eX2WiJyEn2n2Y5mp+ZVS45RSjyil3lJKfaKU+jT0plVgFDutZoUkIrIaFisUlMgooYcBTALw\nbwDexme9LWQCLWeFJCIisqpECpb5AK4QkRe1DobiFzorZFBwVkggMCukk1Yi9fl8KC4uNjsMIiIy\nWCIz3b4JgOfoLMJJK5GWlAzds61V8xyb8AJiyTlpizk3HnPuDIkULP8KoEYpNVnbUCheTluJ1MgZ\nQFmwBHDWVeMx58Zjzp0h1onjPkB4r8pIAH9RSnUBOB36WBE5R7vwaDBOW4mUl3qMx5wbjzk3HnPu\nDLH2sPyrrlFQwvSeFdJsPp8v7GzIzp07w1a7LS4u5ocRkYNwGDNFw3lYIrDTPCyho4RyckJHCQVm\nhXTaKCGPx4P6+vj7ciIVPkVFRX0/s/ChWLDpWx9+vx8bNtyNpqadSE8/je7uVOTlFaGiotpRn19u\nodc8LHGPElJKLQbwqYg822/7IgDDROQZrYKjoQVnhdRrJVIjP6Cbm5sxf/58XfbdvyBJtPBxGj1z\n7kRa/P/AnIczYmoG5twZEmm6rRlkX9HuIx0FVyJtbj6EPXveRHPzIVRXb9bkLxMjm1M3bdpk2LEo\ngDk3HnMeLnRqhuCVoODUDAUFgakZksWcO0MiBcsFAF6NsP0ggGnJhUPJsvO138cff3zIx/B0vLZi\nyTlpizkPZ8TUDMy5MyQycVwngCkADvfbPg3Ax8kGRO41YsSIIR+jVcHCwicglpy7mR5N38z5Z+KZ\nmiGZP8aYc2dIpGB5GsCPlVL/KCJ/AQCl1DQAPwDApgCbc8uoHCe8BtIfe5/05bSpGUhfiRQsqwD8\nfwAOKqX+1rvtCwB+B+AurQIjc/ADemgcKUKkHadPzUDaibuHRUQ6AVwOoADATxA4s5IvIleJyIca\nx0cusnLlSrNDiImTZsm1S86dhDkPV1FRjcbGbLS0pCA4y4YI0NISmJph9Wpv0sdgzp0hkTMskMDk\nLbt6b0SamDRpktkhuA5zHh8tzqwx5+H0npoBYM6dIqGJ45RSeQhc/snu3fQKgO+JyO80jM00dpo4\nTm+8/DEQL5ORWdwwC6wbXqPTWWniuK8D+BmAJwFs6d2cC2CPUmqpiDymVXBkPhYr7mlEJmty2yyw\nLFYomrjPsCil2gH8h4j8qN/2OwF8S0SyIz/TPniGhQbDMyxkFLctvUHOoNcZlkQmjpsCYGeE7fUA\nspILh9zs4MGDZofgOsy58eLJuRGzwLoB3+fOkEjB8iaA/Ajbv9p7H1FCVq1aZXYIrsOcGy+enBsx\nC8AZqrYAACAASURBVKwb8H3uDImMEvoBgC1KqVkAft+7LRfAUgD/olFc5EJbt241O4SYOKlfxS45\nd5JYc27ULLBuwPe5M8RdsIjIA0qpdwD8XwA3925uB3CLiDytZXDkLnYZeuikgsUuOXeSWHPOWWC1\nw/e5M8R1SUgpNUwptQDAPhGZLyKf673NZ7FCdpTIsH4iowRmgY38Mc1ZYMlt4ipYRORTBCaLO1uf\ncMhsbvgC9/v9qKwsR25uFvLzJyI3NwuVleXw+/1mh0YUxohZYInsIpGm25cRGClEDmGVL/CNGzfq\nfozgMNHMzFp4vYexdu0ReL2HkZlZi8LCea4rWozIOYWLJ+fBWWA7O8tQVTUZ69dPQFXVZHR2lnFI\ncxz4PneGRJpu1wD4vlKqCkArgI9D7xSRE1oERsYInefB6w2d56EWhYV7Df1Q7Orq0v0YocNEg4LD\nRIHAMNHq6s26x2EVRuScwsWb84yMjN735GY22CaI73NnSGTiuNAxdqFPVggsMzRMi8DM5KaJ4yor\ny5GZGXml1JaWFHR2ljnqCzw3Nwte7+GoTYxVVZPR3HzI+MCIiBzCMlPzA7hSq4NTcrT4a6upaSe8\n3ujzPFRV1QNwRsHCYaJExuH/R6S1RIY1N+kRCMVGy3VF3PYFzmGiRPpy27pHZKxEFj8sAfCRiPxX\nv+03ARghItu1Co7Cad1vYrUv8GPHjmHMmDG6HiMwTDTyJTA3DhM1IucUzqk5t1I/XH9OzbnbJDJK\nqALAuxG2HwVQmVw4NBg91hWx0jwPpaWluh+Dw0TDGZFzCufUnFt53SOn5txtEilYJgHoiLD9jd77\nSCd6rCtipS/wdevW6X4MDhMNZ0TOKZxTc27ldY+cmnO3SaTp9iiASwAc7rf9UgDHkw2IItOr3yT4\nBV5TswZVVfVISzuNU6dSkZfnQUOD19AvcKNGZHGY6GecPgrOipyYc6v3wzkx526USMHiQ2DxQz+A\n3/Zuy0NgKMnjWgVG4fTsN3HzF7ibXiuRXqzWD0fOlMgloSoAzwPYA+DvvbddAPaCPSy6MqLfhB8o\nRJQIK/XDkTPFXbCIyCkRuQXAFwH8M4DrAUwVkVIROaV1gPQZK/Wb6GHbtm1mh+A6zLnxnJpzK38+\nOTXnbpPIGRYAgIi8JiL/JSINIvKGlkFRZE5vGG1r02xCRIoRc248p+bcyp9PTs2528Q0Nb9S6ocA\nqkTk495/RyUid2oVnFnsMjW/2/pNiMg++PnkXmZPzX8ZgNSQf0cT38JElBR+GBCRVfHzibQWU8Ei\nIldG+jdRMvgXGBERxSrhHhaiRPj9flRWliM3Nwv5+RORm5uFyspy+P1+s0MjIiILi3keFqXUT2N5\nnIhwDmSKaKi1RkaOnIRf//rXZofpKh6PB/X15s1A6kZa5Nzn86G4uFijiJyP73NniOcMy1IAVwLI\nBHD2IDeiiIZaa2T06DRzA3ShsrIys0NwHS1y7vP5NIjEPfg+d4Z4Zrp9AEAxgCwAPwPwqIi8r0tU\n5EhNTTvh9UZfa6S+/iWDI6JFixaZHYLrMOfGY86dIeYzLCKyHMC5ADYBKALwplLql0qpqxU7J2kI\n8aw1QkRE1F9cawmJSDcCawn5lFLnI3CZ6CcAzlBKzRCRj7QPkZyAa40QJc7n84VdBtq5cyc8ns+m\nui8uLmZPCzleMqOEehCYd0UBGKZNOORkQ601cu65MwyOiOrq6gCwJ8JIwZzHo7i4GPX19X23oqKi\nsJ9ZrAwukZyT9cRVsCil0pVSxUqp3QBeA3AxgDIAk3h2hYYy1FojIunmBuhCwUKFBYtxmGvjMefO\nEM+w5p8AuBXAmwB+CqBYRI7pFRg5T3CtkZqaNaiqqkda2mmcOpWKvDwPGhq8tl8LyY6eeOIJs0Nw\nHebceMy5M8TTw3I7gA4AfwWQByAvUr+BiFyvTWjkRBkZGaiu3gxgM2e6JUoQLwGRG8VTsPwcXCuI\nNMRixTxs4rQ3/m7IjWIuWERkqY5xEJGB+hcknAmUiKyOawmRZZSUlJgdgmXp1TTInCcnkd+LVXLu\npkZUq+ScksOChSzDqNko7fhBrVfMnAE0OYn8XqySczv+f5Aoq+ScksOChSzDqOvybvqgHkow5+yJ\nMA5zbTzm3BlYsBARP9CJyPLimpqfiIzBUTzWZOffi1Vi53QGlCjFxeYGUkrNBtDa2tqK2bNnmx2O\nZqz+QdHc3Iz58+drvt9IH9RFRUV9P1v5SyZIr1E8euXcLRL5vVgl50aODPP7/diw4W40Ne1Eevpp\ndHenIi+vCBUV1YZMGGmVnLtFW1sb5syZAwBzRKRNq/3yDIvDmf1BEY9Nmzbp8qGixRBen89n+aIm\nEXrlnKJzW879fj8KC+ehoKAdXm8PlAosyXHgQC0KC/eioWG/7p9Fbsu5U7GHxcGCHxSZmbXweg9j\n7doj8HoPIzOzFoWF8+D3+80OMczjjz9udghRObVR18o5dyq35XzDhrtRUNCOuXN7+lZqVwqYO7cH\nBQXtqKlZo3sMbsu5U7FgcTArfFDEY8SIEWaHYFl6nd1hzpOTyO/FKjk36oxhU9NO5OT0RLwvJ6cH\nTU36X5aySs4pOSxYHMwKHxRWZMdLO3aM2Q3s/HsxqsE2Pf00orXOKQWkpZ0GeykpFuxhcah4Piis\n3Iirh1g+qK0yooIGcmo/kRMppdDdnQoRRPwsEgG6u1Nd9xlEieEZFocK/aCIxIofFCtXrjQ7hD7F\nxcWor6/vuxUVFYX97JQvTCvlPFZ27yeyY86TkZdXhAMHIn/VHDiQgoULPRHv05Lbcu5ULFgczAof\nFPGYNGmS2SG4DnNuPLflvKKiGo2N2WhpSen7A0oEaGlJQWNjNlav9uoeg9ty7lQsWBzMCh8U8bjj\njjvMDsF1mHPjJZtzu51hysjIQEPDfnR2lqGqajLWr5+AqqrJ6OwsM2RIM8D3uVOwh8XBgh8UNTVr\nUFVVj7S00zh1KhV5eR40NHgtNw+LlTnlEpAdsZ8onB17eDIyMlBdvRnAZlf2zZE2ONNtBJzplsi6\njJyh1Yrc/vrJ+vSa6ZaXhGwmmQLT6sXKwYMHY3oci2ztxJpz0g5zbjzm3BlYsNiA3+9HZWU5cnOz\nkJ8/Ebm5WaisLLfcTLXJWrVqVdT73JIDow2Wc9JHvDn3+XzweDx9t+AlseDNbj0tZuD73Bl4SSgC\nK10SCl2HIycndB2OQOOsUU1rRujo6IjYze+mHBgtWs6tzI49HKGSzTkvCcXPju9zO+MlIZey2/T6\nyYj2geKmHBjNjh/idi5WAHvm3O6Yc2dgwWJxbp9e3+fzOSoHPH1PRJQYFiwWxnU4Al/wTsoBCxZK\nlt3PMBEligWLhdlxev1kbNy4MeJ2N+XAaNFyTvpJNucsWOLH97kzsGCxOLtNr5+Mrq6uiNvdlAOj\nRcs56Yc5Nx5z7gwcJRQBRwmZJ9Ksptdeey2ef74Z48b5cf31wFe/ap8cRHo9RUVFfT+7bZZWInI+\nvUYJsWCJwEoFCxAoWmpq1qCpKXx6/dWrnT+9fnAIp1NywCGpROR0ehUsXEvIBpyyDkcysTslB0RE\nlBj2sNiM3b6o45mh9tixYzHt0245sLJYc07aYc6Nx5w7AwsW0k2w/yYzsxZe72GsXXsEXu9hZGbW\norBw3oCipbS0dMA+nNbfYbXXEynnpC/m3HjMuTPYqmBRSp2tlPqFUqpTKfWBUuohpdTIIZ7zM6VU\nT7/br42K2c3inaF23bp1A/ZhtS/4ZFnt9UTKOemLOTcec+4MtipYADwGIBtAPoACAAsAPBjD854B\nMA7A+N6btb41HCreGWqt0ODsNsy58Zhz4zHnzmCbplul1BcBXI1A1/ELvdvuANColLpLRN4Z5Ond\nIvKeEXFSQDyz9LInhYiIhmKnMyzzAHwQLFZ6PQdAAHx5iOcuVEq9q5Q6qJT6iVLqHN2iJADum6WX\niIj0ZaeCZTyAo6EbRORTAO/33hfNMwCWALgKwCoAeQB+rfhNqbt4Z6jdtm2bEWFRCObceMy58Zhz\nZzC9YFFKbYjQFBt6+1QpdWGi+xeRX4pIg4j8r4jUAygEMBfAwqGeu3jxYng8nrDbvHnzUFdXF/a4\nXbt2weMZOD388uXLB/yP0tbWBo/HM2CY3T333DNgvYuOjg54PB4cPHgwbPv999+PlStXhm3r6uqC\nx+NBc3Nz2Hafz4eSkpIBsd1yyy26v46Kimo0Nmbj2WcVKiuBjo7AmZWWlsAMtZmZXwh7HW1tbZZ8\nHUF2/31Eeh1tbZ/N6WTn1xHK6q/joYcecsTrsNPv49lnn3XE67Di78Pn8/V9N44fPx4ejwcrVqwY\n8BwtmD7TrVLqcwA+N8TD/grg/wD4voj0PVYpNQzASQA3isjTcRzzKIC7ReQ/o9xvqZlu7cwpM9QS\nEVFsHDvTrYgcB3B8qMcppfYDyFRKXRbSx5IPQAF4PtbjKaW+gECB9HYC4VKcOEMtERFpwfRLQrES\nkYMAngXwn0qpHKVULoD7AfhCRwj1NtZ+rfffI5VSm5RSX1ZKna+UygdQB+C13n2RgVisEBFRomxT\nsPT6JwAHERgd1ADgtwCW9XvMBQBG9/77UwCXAHgawKsA/hPAAQALROS0EQETERFR8mxVsIjIhyLy\ndREZLSJni8i3RKSr32OGicjPe/99UkSuEZHx8v+3d//RcZ31ncffXxPbqalApQ1JN+SHadjiPYUE\nuzJ1nUUupmZBsk/ItqerUpLGLaVptc5mqUOkWGkwErZT2uAS0aXgOKdLEN4uSyLLpKG1U4GpiVQ7\nEBpsiMEOLhCCIShDjBUTPfvHc0cejWekGWnm3ufe+bzO0TmemXtH3/n60cx3nvv8cO5859wrnXM3\nak2WMJUaeCb1pZzHTzmPn3KeDakqWCTbOjs7kw6h4Sjn8VPO46ecZ0Pis4RCpFlCUmsacCyNQm1d\n6jVLSD0sInWSy+Xo7t7AypWLWb36ElauXEx394ZzdqkWSTu1dYlD4tOaRbIol8vR3r6CtrbD9Pb6\n3aqdg9HRftrb9zE0dEDr0EgmqK1LXNTDIsEoXgEyzbZsuY22tsMsXz4xuQGkGSxfPkFb22G2bt2U\nbICRLOU8LbKW8zS09azlvFGpYJFgDAwMJB1CzQwP76alZaLkYy0tEwwPD8YcUWlZynlaZC3naWjr\nWct5o1LBIsHYtWtX0iHUhHOOhQvPUG7coRksWHCGEAa8ZyXnaZKlnKelrWcp541MBYtIjZkZ4+Pz\nKfce7RyMj8/XTApJPbV1iZMKFpE6aG1dy+ho6T+v0dF5rFqlhawkG9TWJS4qWETqoKurjz17ljAy\nMm/y26dzMDIyjz17lnDrrb2Tx+r6uqRZNW1dZC5UsEgwbrjhhqRDqJmmpiaGhg4wNtZJT8/lbN58\nMT09lzM21nnONM8kC5Ys5Twtspbzatp6UrKW80aldVgkGGvWrCn7WBpXz2xqaqKvbzuwPdH4BwYG\n6OjoKPnYdDmX+shizkNp6+VkMeeNSD0sEoziD9UsrZ6Z5Bv4dD045QqZODXaJbEQcl5PoRUrkP2c\nNwr1sEhZSX5TyvLqmQMDA1M+pHfv3j1lN9mOjo6GeoOdrgcoRCH2IIg0AhUsMkUul2PLltsYHt7N\nwoVnGB+fT2vrWrq6+mItEApXz8zLr54JfvVM3wWdPsUFybp16xgcTH5xLSkvlL8LkUamgkUmJd2r\nsX//fq6++mrAr57Z21t+9cyenkEgnQVLvVXTg1OYcymt1n8Xynn8lPNsUMEik5Lu1bjzzju5+uqr\nq1o9U13z56qmByef8zil7ZJYrf8uksh5o1POs0EFi0xKulfjk5/8JDB19cxS9UjWVs9M8sM5n/M4\npe2SWK3/LpLIeaNTzrNBs4QECGNPkEWLFk3+u5FWz0yyYCnMuZyrHn8Xynn8lPNsUA+LAOH1anR1\n9dHevg84TEtL4bgBv3rm0JBWz6xUSJdX0ia0vwuRRqYeFpkUUq9GGlbPnK24d64NvWAJPb6Q/i5E\nGpkKFpmU9J4gGzdunHI7v3rm/v3H2Lv3BPv3H6Ovb3sqi5VQF8ErznkSQi9Yav13EULOG41yng26\nJCST8r0aW7duoqdnkAULzvD88/NpbV3H0FBv3QuFSy+9tOxjae5yT3q6+HSmy7l4tf67UM7jp5xn\ng8XdPZ0GZrYUOHjw4EGWLl2adDiJ0bTh2uju3kBzc/+UabF5IyPzGBvrTO0ieI1Ifxci0zt06BDL\nli0DWOacO1Sr59UlISlLb8q1MTy8m5aW8tNih4fDndIr59LfhUgyVLCI1FEI08VFRLJABYsE48iR\nI0mHUHOF02JLSXpabBZzHjrlPH7KeTaoYJFg3HLLLUmHUBchT4vNas5DppzHTznPBs0SkmDcfffd\nSYdQFyEvgpfVnIdMOY+fcp4NKlgkGFmdepj0dPHpZDXnIVPO46ecZ4MKFpEY5BfBg+2aFisiMgsa\nwyISMxUrIiLVU8Eiwdi2bVvSITQc5Tx+ynn8lPNsUMEiwTh16lTSITQc5Tx+ynn8lPNs0NL8JWhp\nfhERkdnR0vwiIiLSsFSwiMisDAwMJB2CiDQQFSwSjJMnTyYdQsOZS85VsMxOltp5WoYUZCnnjUwF\niwRj/fr1SYfQcJTz+isu7NKe81wuR3f3BlauXMzq1ZewcuViurs3kMvlkg6trLTnXDwVLBKMO+64\nI+kQGo5yXn/FBUuac57L5WhvX0Fzcz+9vce5/fZv09t7nObmftrbVwRbtKQ553KWVrqVYGhGVvyq\nyfnAwMCUD9/du3ezbt3ZjRs7Ojro6OioaXxZlOZ2vmXLbbS1HWb58onJ+8yIbh9m69ZN0YrOYUlz\nzuUsFSwiUpHigmTdunUMDg4mGFEyBgYGgizM4ohreHg3vb0TJR9raZmgp2cQCK9gkWxQwSIiUoWZ\nCoOkeqLqXbA451i48AzldpYwgwULzmivLKkbjWGRYOzYsSPpEBqOcl57HR0dDA4OTv6sXbt2yu20\nrrpqZoyPz6fcxCDnYHx8fpDFitp5NqhgkWAcOlSzBRGlQnPJeYiXRdIgze28tXUto6OlPzZGR+ex\natW6ko8lLc05l7O0NH8JWppfRPJKXeJZu3bt5O2ZLvHUa6zPXOOqRv4yT36WUFvbYVpaJjDzPSuj\no/PYs2cJQ0MHaGpqqsnvlPSq19L8GsMiIjKNuQ42rldPVL0HQedyObZsuY3h4d0sXHiG8fH5tLau\nZWDgs/T3b6OnZ5AFC87w/PPzaW1dx9BQr4oVqSsVLCIidZTGS2eFPSm9vYU9Kf10dOxjaOgAfX3b\nNcBWYqUxLCLScLStwPQK11vJ1yP59Vba2vx6K/4+FSsSHxUsEozCqZ8Sj0bN+VwKlrn2mNQr57Xs\nyRke3k1LS/n1VoaH07X+TqO286xRwSLB6OzsTDqEVKjlQPla5TzEwfv1immuhUG92nktB9hWut5K\nWui9JRtUsEgw1qxZk3QIwarXhnNzyXmIm+CFGFOx0Nt5mtdbKSf0nEtlNOhWJHDTDYBsb9+XyFTS\ntMW0fPmnWbz4NZx3nn/L0z5I0/PrrfRP2TMoL+T1ViTbtA5LCVqHRULS3b2B5ubSHx4jI/MYG+uM\nfcO5tMfUqPsgVUrrrchc1GsdFl0SkmDcf//9SYcQpHoOgJxtzkMclBlSTNN9EUxDO29qamJo6ABj\nY5309FzO5s0X09NzOWNjnaksVtKQc5mZChYJhqaanqveAyBnk/MQB2WGEFOl42fS0s6bmpro69vO\n/v3H2Lv3BPv3H6Ovb3vqihVIT85leipYJBi7du1KOoTg1HsA5GxyPtuY6vmhUW1MtR6vkr+E0tzc\nT2/vcW6//dv09h6nubmf9vYVU4qWNLbzNA2wLSWNOZdzqWARCVyIG87NJqZ6f8utJqZaFyyVLrQm\nIrOngkUkcF1dfezZs4SRkXmTPQjO+YGke/Ys4dZbexVTwjGFNH5GJKs0rVkkcPkBkFu3bgpmwznF\ndFY142fSfmlFJEkqWCQYN9xwAzt37kw6jCDlB0BCbTecm0vOZ4ppYGBgymWgONY+qVeeplM4fqbU\nryseP6N2Hj/lPBtUsEgwtBplZWr5IVyrnJeKqbggiXvtkzh7M6pZaE3tPH7KeTaoYJFgaKXR+Cnn\ntdHV1Ud7+z6g3EJrZ8fPKOfxU86zQQWLiMgchTimRyRrVLCIVEADJucu699ykxg/I9JINK1ZgrF/\n//6kQ5giDTv/zlWcOc96wVJoumIltHbeCJTzbFDBIsG48847kw5hUjUrl6ZZSDlvFMp5/JTzbNBu\nzSVot+ZknDp1ikWLFiUdBhDmbsT1EFLOG4VyHj/lPF7arVkyL6Q3lEZZuTSknDcK5Tx+ynk2qGAR\nKRLCzr8iIjKVChaRIvXeIVlERKqngkWCsXHjxqRDmBTiDsn1EFLOG4VyHj/lPBu0DosE49JLL006\nhEnVrFyaZiHlvFEo5/FTzrNBs4RK0CwhAT+1eevWTQwPT1259NZbtXKpiEg59ZolpB4WkTK0cqmI\nSDg0hkWkAipWRESSpYJFgnHkyJGkQ2g4ynn8lPP4KefZoIJFgnHLLbckHULDUc7jp5zHTznPBhUs\nEoy777476RAajnIeP+U8fsp5NqhgkWBo6mH8lPP4KefxU86zQQWLiIiIBE8Fi4iIiARPBYsEY9u2\nbUmH0HCU8/gp5/FTzrNBBYsE49SpU0mH0HCU8/gp5/FTzrNBS/OXoKX5RUREZqdeS/Orh0VERESC\np4JFREREgqeCRYJx8uTJpENoOMp5/JTz+Cnn2aCCRYKxfv36pENoOMp5/KbLucYU1ofaeTaoYJFg\n3HHHHUmH0HCU8/gV5zyXy9HdvYGVKxezevUlrFy5mO7uDeRyuWQCzCC182zQLKESNEtIROKQy+Vo\nb19BW9thWlomMAPnYHR0Hnv2LGFo6ABNTU1JhylSFc0SEpHY6ItMPLZsuY22tsMsX+6LFQAzWL58\ngra2w2zduinZAEUCooJFRABdmkjC8PBuWlomSj7W0jLB8PBgzBGJhEsFiwRjx44dSYfQcPI5z1+a\naG7up7f3OLff/m16e4/T3NxPe/sKFS01lM+5c46FC89M9qwUM4MFC86ot6sG9N6SDSpYJBiHDtXs\nUqdUKJ9zXZqITz7nZsb4+HzK1SPOwfj4fKxcRSMV03tLNqhgkWD09/cnHULDyec8LZcmstDbUNjO\nW1vXMjpa+m14dHQeq1atiyusTNN7Szacl3QAIpKsai5NJPFtP5fLsWXLbQwP72bhwjOMj8+ntXUt\nXV19qZ9B09XVR3v7PqDcLKHepEMUCYYKFpEGV3hpolQ9kuSlicJpv729hR/o/bS370v9tN+mpiaG\nhg6wdesmenoGWbDgDM8/P5/W1nUMDfWm+rWJ1JoKFhGJLk30s3z5uZeFkrw0UTi2Ji8/tgb82Jq+\nvu2JxFYrTU1N0WvYnlgvlkgaaAyLBGPdOl2vj1s+511dfezZs4SRkXmTg0Cdg5ERf2ni1luTuTSR\nlrE11ZiunatYqQ+9t2SDelgkGJ2dnUmH0HDyOQ/x0kToY2tmS+08fsp5NqhgkWCsWbMm6RAaTmHO\nQ7s0EfLYmrlQO4+fcp4NuiQkIucIpQjQtF8RyVMPi4gES9N+RSRPPSwSjPvvvz/pEBpO6DnPj60Z\nG+ukp+dyNm++mJ6eyxkb60ztlObQc55Fynk2WJpWjjSzbqANuAoYd869rMLzNgN/CDQDXwBudM4d\nneb4pcDBgwcPsnTp0rkHLhVZsWIFBw4cSDqMhpK2nIcwtmau0pbzLFDO43Xo0CGWLVsGsMw5V7N9\nEdLWwzIf+D/A31R6gpm9B+gE/ghYDjwHPGRmC+oSoczaBRdckHQIDSdtOU97sQLpy3kWKOfZkKox\nLM659wKY2fVVnHYT8D7n3FB07nXA94Br8MWPiIiIBC5tPSxVMbPFwEXA3vx9zrlngUeAFUnFJSIi\nItXJdMGCL1Ycvkel0Peix0RERCQFEr8kZGZbgPdMc4gDljjnvh5TSADnAxw+fDjGXykjIyMcOlSz\n8VlSAeU8fsp5/JTzeBV8dp5fy+dNfJaQmf088PMzHPZN59xPC865HrhrpllC0SWhbwBXOeceK7j/\nn4FHnXM3lznvd4H7KnsFIiIiUsLbnXOfqNWTJd7D4pz7AfCDOj33MTN7ClgNPAZgZi8BXg/0T3Pq\nQ8DbgePA6XrEJiIiklHnA5fjP0trJvGCpRpmdgnwMuAy4EVmdmX00FHn3HPRMUeA9zjnHoge+yCw\nycyO4guQ9wH/DjxAGVERVbOqUEREpMH8S62fMFUFC7AZuK7gdv6i5G8An4v+/SrgpfkDnHN3mtki\n4CP4heM+D7zFOfd8/cMVERGRWkh8DIuIiIjITLI+rVlEREQyQAWLiIiIBE8FS8TMus3sC2b2nJn9\nsIrzNpvZd8zslJn9o5ldUc84s8TMfs7M7jOzMTN7xsw+ZmYvnuGcnWY2UfTzmbhiThsz+1MzO2Zm\nPzGzL5pZywzHrzKzg2Z22sy+XuU2GEJ1OTez1hLt+QUze3mcMaeZmf1nMxs0s29H+VtXwTlq53NQ\nbc5r1c5VsJyljRXj9wlgCX7aeRvwBvzg6Jk8CFyIX634IqCjXgGmmZn9DvCXwJ8DrwO+jG+fv1Dm\n+MuBIfxWFlcC24GPmdlvxhFvFlSb84jDTxbIt+dfdM49Xe9YM+TFwJeAP8Hnclpq5zVRVc4jc27n\nGnRbpNJF6aJjvwP8hXPuruj2S/DL/l/vnNPGitMws1cDX8VvP/5odN+bgT3AK5xzT5U5byfwUufc\ntbEFm1Jm9kXgEefcTdFtA04Af+2cu7PE8dvwM+heW3DfAD7fb40p7FSbRc5bgX3Az0X7nMkcmNkE\ncI1zbnCaY9TOa6jCnNeknauHZZa0seKcrQCeyRcrkX/CV+Gvn+HcVWb2PTM7YmYfNrMZi8tG14Bj\nXgAACfdJREFUY2bzgWVMbZ8On+Ny7fPXoscLPTTN8VJgljkHMOBL0aXlz5rZr9c30oandp6MObdz\nFSyzp40V5+YiYEp3oHPuBeCHTJ+/B/Fr8bwRuAVoBT4TfZOVs34BeBHVtc+Lyhz/EjNbWNvwMmk2\nOf8u8C7gvwLX4ntj/tnMrqpXkKJ2noCatPO0LRxXlUA3Vsy0SnM+2+cvutT2uJl9Bb9f1Crg4dk+\nr0gSoveewvefL5rZLwE3AxoIKplQq3ae6YIF+ACwc4ZjvjnL534K38V1IVOr9QuBR0ue0RgqzflT\nwJQR4mb2IvzWCyXHr5QS7Rd1ErgCFSyFTgIv4NtjoQspn9+nyhz/rHNuvLbhZdJscl7KCLCyVkHJ\nOdTOw1B1O890wRLoxoqZVmnOzewA0GxmrysYx7IaXwQ+UunvM7NX4Hf7/u4sws0s59wZMzuIz+kg\nTA4AXQ38dZnTDgBvKbpvTXS/zGCWOS/lKtSe60ntPAxVt/NMFyzVsJg2VhTPOXfEzB4CPmpmNwIL\ngA8BA4UzhApzHq3R8ufAp/Dfkq4AtuG7Gmu6K2hG/BVwb/QhOoLvfl0E3AuTl+/+g3Mu3yX7v4A/\njWZR3IP/oP0tQDMnKldVzs3sJuAY8Dh+h9t34vdG0xTbCkXvC1fgv+wAvDJ6//6hc+6E2nntVZvz\nmrVz55x+/NTunfju3OKfNxQc8wJwXdF5dwDfAU7hPzSvSPq1pOUHvxnlx4Ex4Bngo8CiomMmcx41\n9H/AFyun8ZeW/ga4IOnXEuoPfp2E48BP8N8gf7XgsZ3AvqLj3wAcjI5/AnhH0q8hbT/V5BzYGOX5\nOeD7+BlGb4g75jT/4AfeT5R4776nVM6j+9TOY8x5rdq51mERERGR4Glas4iIiARPBYuIiIgETwWL\niIiIBE8Fi4iIiARPBYuIiIgETwWLiIiIBE8Fi4iIiARPBYuIiIgETwWLSEqY2cNm9lcJx3C9mT0z\nwzE7zez/xRWTlGZmbzazCTNbkHQsIrWggkUkIWZ2b/SB8uESj/VHj91TcPfbgJ74IixrpuWxNwC/\nP9snjwqziWl+9s32uQt+x7vMbMaN18zsEjMbMLOvm9kLZvb+Cs755aJ4T5rZXjP7tbnGPQuT/1eV\nvmaRUKlgEUmOA74F/DczW5i/M/p3B/DklIOd+5GLNuKcDTN70WzPrYZzLuece3YOT/E24KLoZzk+\nT28suO/aOQfpN22rZF+S8/F7hb0X+GoVz++Alfh4W/F7ZQ2ZWXOVcdZSpa9ZJEgqWESS9Shwgqkf\nwtfii5VHCw8sviRkZgvMbJuZfcvMTke9ADdEj7VG3+7/i5n9q5mdxn+AYmY3mtlRMxs3s8Nm9ntF\nv+elZvYRM3vKzH5iZo+Z2VuLjlljZl81s5yZPWhmFxY8NuWSUBT3h6KfH5nZ981sc7mERIXZ0865\np/EbpRl+F9ino58fRc/7sqiX6vvR837WzP5Twe9dambDUYxjZvaImb3GzN4MfBi4MMrRC2Z2S5lY\nnnDOvds5dx/w43Ixl/GDKN7HgS343eB/tSiPN5rZkSjPj5vZHxY8tjD6f/hu9Pg3zOzm6LF8L85/\nLDg+/3qWFwdSzWsWCdV5SQcg0uAcfov79cBAdN96/G6nvzHDuf8beD3QCTwGXApcWHTMFuDP8Dtb\nP2NmbwM+iL9ssxdYC+w0sxPOuWEzM/yO2C8Gfjc675eLnvPFwLuBt0fx3wd8AHjHNLFeB+wAWvAf\n2h81syedcztmeI3T+TTwPeBN+F1g/zuw18xe5Zz7MbALeBj4g+j41wE/jV73e6LX8Bp8QZSbQxzT\nMrNFwPX4XD1fcP8fRHF0Al/hbF7GnHN/j9/hdjVwDb6X5zJ8j01eqd6Scj0o+4jxNYvUgwoWkeTd\nB2w1s0vwvZ6/DvwO0xQs0Tfr3wZWO+ceju4+XuLQHufc3oLz3o3fAv4j0V13RWMr/gwYBn4T/8H5\naufcN8o873nAu5xzx6PnvJuZx9accM79z+jfT5jZa4Gb8UVM1czsTcAS4I3OuRei+/4H/nLSNcDH\ngVcA/+icOxqddrTg/GeBCefc92fz+ysJETjo6z8WRbe/AHy+4Jg7gE7n3FB0+0kzuwp4F/D3wCXA\nEefcI9HjJyr8vedwzp2J4TWL1JUuCYkkzDl3EhgCbsAPVt3jnPvhDKddie8t+Nx0Tw0cLLpvCfAv\nRfd9Ibo//7z/XlCslHIqX6xEvgu8fIZ4v1h0+wDwqqhHZzZei7/E8qPokk8OeBb4ReCXomM+CNxn\nZg+Z2UYzu2yWv2u2rsH36vw28ASw3jnnwF/OAi4GPp6PP3oN7wZeGZ2/A1gZXba7y8zeGHP8IkFR\nD4tIGHYCd+OLjD+p4PifVPi81Q7SreR5zxTddpT5Zl9HPwscA9aU+N3PADjnuszsXuCtQBuw2cyu\ndc49GEN8Dt+rdBQ4Gl0W+rSZXRn1CP1sdNx1wJeLzv1pFP9IVGS9BX/Z69Nm9oBz7jpgAv+6C1/7\n/Pq9HJHkqYdFJAz/ACzAf4n4bAXHfwX/99ta5e85TDT4tsBKzs6AeQx4hZldUeXzzuT1RbdXAE/k\nexxmUOqYQ/hLPqedc98s+plcJ8Y59zXn3F3OuTcBD+LHkoAfSxLLrKnIfcDPAPlBtSeAk8ArS8T/\nrYL4n3XO7XLOvRM/RujtZnY+fjAy+B6lvNcx/SyguF+zSE2ph0UkAM65CTN7dfTvGT/EnXNPmtnf\nAfeY2U34b+mXAS+PBmxC6V6PvwB2mdmXgH8C1uHHfayOnvdzZvZ54FPReJejwKvxYx8qKaTKudTM\nPgD8LbAMP9D05grPLfU6PgN8CXjAzLqAb+ALmHb8+JVvAZuBT+FnXF2G/0DfGZ1/HHiZmV2NL+Ke\nc86dLvnLza6MYlgEvDy6fdo597VKY3bOOTP7ELDJzO6JxpS8F3i/mZ3C/1+cj5/Gfb5zrt/MNkZx\nfjl6vt8CnoziPB39H3abX1vlYvyYmOlU/JpFQqQeFpFAOOd+HM1uKXtI0e0/Bv4v0I//APpb/Idq\nueNxzj0A3IQfK/FvwDuB33fOFQ4GvRYYBT4BPA5sY+7fzP8O38MwAnwIuMs597EKzy31Oibwl4NG\nouc+jJ81dSG+9+EMfkbNx4Gv4Xs4PgW8Pzr/YeBe4H7gafysqXOYXxPnUfxYoF/BjzM6hJ+hVFXM\n+DEpTfhBtTjn+vGF2x/he7b24WdmHYuOfw7YFP3uA8AF+Fldee+Inu8QsBXomjagCl+zSKissh5Z\nEZHZMbOHgUcLZgmJiFRNPSwiIiISPBUsIlJv6sYVkTnTJSEREREJnnpYREREJHgqWERERCR4KlhE\nREQkeCpYREREJHgqWERERCR4KlhEREQkeCpYREREJHgqWERERCR4KlhEREQkeP8feVLPpGmI0wAA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d47ed02e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chip_plotting_spec = {\n",
    "    'X': X_data,\n",
    "    'y': y_data, \n",
    "    'xlabel': 'Microchip Test 1 Result', \n",
    "    'ylabel': 'Microchip Test 2 Result',\n",
    "    'labels': ['rejected', 'accepted'], \n",
    "    'markers': ['yo', 'k+'],\n",
    "    'figsize': (6, 6)\n",
    "}\n",
    "\n",
    "plot_data(**chip_plotting_spec)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.2 Nonlinear feature mapping**\n",
    "\n",
    "One way to fit the data better is to create more features from each data point. In *mapFeature* below, we will map the features into all polynomial terms of $x_1$ and $x_2$ up to the\n",
    "sixth power as follows:\n",
    "\n",
    "\\begin{equation}\n",
    "mapFeature(x) \\ = \\\n",
    "\\begin{bmatrix}\n",
    "    1 \\\\\n",
    "    x_1 \\\\\n",
    "    x_2 \\\\\n",
    "    x_1^2 \\\\\n",
    "    x_1x_2 \\\\\n",
    "    x_2^2 \\\\\n",
    "    x_1^3 \\\\\n",
    "    \\vdots \\\\\n",
    "    x_1x_2^5 \\\\\n",
    "    x_2^6 \\\\\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "As a result of this mapping, our vector of two features (the scores\n",
    "on two QA tests) has been transformed into a 28-dimensional\n",
    "vector. A logistic regression classifier trained on this\n",
    "higher-dimension feature vector will have a more complex\n",
    "decision boundary and will appear nonlinear when drawn in our\n",
    "2-dimensional plot.\n",
    "While the feature mapping allows us to build a more expressive\n",
    "classifier, it is also more susceptible to overfitting. In the next parts\n",
    "of the exercise, you will implement regularized logistic regression\n",
    "to fit the data and also see for yourself how regularization can help combat the overfitting problem.\n",
    "\n",
    "Either finite dimentional (or even infinite-dimentional, as you would see in the SVM leacture and the corresponding home assingment) feature mappings are usually denoted by $\\Phi$ and therefore our hyposesis is now that the Bernoulli probability of chip matfunctioning might be described as\n",
    "\n",
    "$$ p_i = \\sigma(\\Phi(x_i)^T \\theta)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  0  1  0  2  1  0  2  3  1  4  2  1  3  0  5  3  0  2  4  1  0  6  2\n",
      "   5  4  3  1  4  0  1  2  6  7  3  5  2  3  4  6  8  5  7  0  1  4  7  3\n",
      "   6  9  8  0  2  1  5  9  3  5  7  8  4 10  6  1  0  2  0  9  1  4  5  2\n",
      "  10  7  8  6 11  3  7  0  1  9 12  4  6  2  8 11 10  3  5  6 13  1  5  7\n",
      "   9  8  4 12  2 10  0 11  3  0 12 11 14 10  9  7  6  8 13  4  2  3  1  5\n",
      "   5  4  9  0 15 14  7  1 10  8  3  2 11  6 12 13  8  3 11  2 14  9 12 13\n",
      "  10 16  4  0  6  5  1 15  7 12  5  2 13 11  6 15  3 10  7  0  1 16 14  8\n",
      "   4  9 17  5 12  2  4  8 14 13 16 11  9  6 15  0  1 10  3 18  7 17 15 13\n",
      "  14 17 19 18 16  2 12  3  1  4  5  0  7  8  6  9 10 11 11 18  3  1 17 10\n",
      "   4 16 13  5  0 19 15 12  6  9  7 14  2  8 20]\n",
      " [ 0  1  0  2  0  1  3  1  0  2  0  2  3  1  4  0  2  5  3  1  4  6  0  4\n",
      "   1  2  3  5  3  7  6  5  1  0  4  2  6  5  4  2  0  3  1  8  7  5  2  6\n",
      "   3  0  1  9  7  8  4  1  7  5  3  2  6  0  4  9 10  8 11  2 10  7  6  9\n",
      "   1  4  3  5  0  8  5 12 11  3  0  8  6 10  4  1  2  9  7  7  0 12  8  6\n",
      "   4  5  9  1 11  3 13  2 10 14  2  3  0  4  5  7  8  6  1 10 12 11 13  9\n",
      "  10 11  6 15  0  1  8 14  5  7 12 13  4  9  3  2  8 13  5 14  2  7  4  3\n",
      "   6  0 12 16 10 11 15  1  9  5 12 15  4  6 11  2 14  7 10 17 16  1  3  9\n",
      "  13  8  0 13  6 16 14 10  4  5  2  7  9 12  3 18 17  8 15  0 11  1  4  6\n",
      "   5  2  0  1  3 17  7 16 18 15 14 19 12 11 13 10  9  8  9  2 17 19  3 10\n",
      "  16  4  7 15 20  1  5  8 14 11 13  6 18 12  0]]\n",
      "total power per monomial [ 0  1  1  2  2  2  3  3  3  3  4  4  4  4  4  5  5  5  5  5  5  6  6  6  6\n",
      "  6  6  6  7  7  7  7  7  7  7  7  8  8  8  8  8  8  8  8  8  9  9  9  9  9\n",
      "  9  9  9  9  9 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11\n",
      " 11 11 11 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13\n",
      " 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15\n",
      " 15 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 16 16 16 16\n",
      " 16 16 16 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 18 18 18 18\n",
      " 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19\n",
      " 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20\n",
      " 20 20 20 20 20 20]\n",
      "(118, 231)\n"
     ]
    }
   ],
   "source": [
    "from itertools import combinations_with_replacement\n",
    "\n",
    "def polynomial_feature_map(X_data, degree=20, show_me_ur_powers=False):\n",
    "    assert len(X_data.shape) == 2\n",
    "    group_size = X_data.shape[1]\n",
    "    assert group_size == 2\n",
    "    # hm.. how to get all ordered pairs (c, d) of non-negative ints \n",
    "    # such that their sum is c + d <= dergee? \n",
    "    # it is eqvivalent to getting all groups of integers (a, b) such that\n",
    "    # 0 <= a <= b <= degree and definintg c = a, d = b - a\n",
    "    # their sum is below degree, both are >= 0 \n",
    "    # then feature_i = (x_0 ^ c) * (x_1 ^ d)\n",
    "    comb_iterator = combinations_with_replacement(range(degree+1), group_size)\n",
    "    not_quite_powers = np.array(list(comb_iterator))\n",
    "    powers_bad_order = not_quite_powers.copy()\n",
    "    powers_bad_order[:, 1] -= not_quite_powers[:, 0]\n",
    "    # let's reoder them so that lower power monomials come first\n",
    "    rising_power_idx = np.argsort(powers_bad_order.sum(axis=1))\n",
    "    powers = powers_bad_order[rising_power_idx]\n",
    "    if show_me_ur_powers is True:\n",
    "        print(powers.T)\n",
    "        print('total power per monomial', powers.sum(axis=1))\n",
    "    X_with_powers = np.power(X_data[:, :, None], powers.T[None])\n",
    "    # tu tu power rangers (with replacement)\n",
    "    X_poly = np.prod(X_with_powers, axis=1)\n",
    "    return X_poly\n",
    "\n",
    "X_pf = polynomial_feature_map(X_data, show_me_ur_powers=True)\n",
    "print(X_pf.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.3 Cost function and gradient**\n",
    "\n",
    "Now you will implement code to compute the cost function and gradient for regularized logistic\n",
    "regression. Recall that the regularized cost function in logistic regression is:\n",
    "\n",
    "$j(\\theta) \\ = \\ [ \\ \\frac{1}{m} \\ \\sum_{i=1}^{m} \\ [ \\ -y^{(i)} log(h_\\theta(x^{(i)})) \\ - \\ (1 - y^{(i)})log(1-h_\\theta(x^{(i)})) \\ ] \\ ] \\ + \\frac{\\lambda}{2m} \\sum_{j=2}^{n} \\theta_j^2 $\n",
    "\n",
    "Note that you should not regularize the parameter $\\theta_0$ (Why not? Think about why that would be a bad idea).\n",
    "\n",
    "The gradient of the cost function is a vector where the j element is defined as follows (you should understand how to obtain this expression):\n",
    "\n",
    "$\\frac{\\partial J(\\theta)}{\\partial \\theta_{0}} \\ = \\ \\frac{1}{m} \\ \\sum_{i=1}^{m} \\ (h_\\theta(x^{(i)})-y^{(i)}) x_j^{(i)} \\quad \\quad \\quad \\quad \\quad \\quad$ for $\\quad j=0$\n",
    "\n",
    "$\\frac{\\partial J(\\theta)}{\\partial \\theta_{j}} \\ = \\ (\\frac{1}{m} \\ \\sum_{i=1}^{m} \\ (h_\\theta(x^{(i)})-y^{(i)}) x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j \\quad \\quad \\quad$ for $\\quad j \\ge 1$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.3.1 [10pts] Implementing regularized logistic regression**\n",
    "\n",
    "Re-implement computeCost with regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Cost function, default lambda (regularization) 0\n",
    "def logistic_loss_theta_w_reg(x, y, h, theta, lambda_=0.0): \n",
    "    y_pred = h(x, theta)\n",
    "    y = y.astype(np.float64)\n",
    "    y_len = np.size(y)\n",
    "    y_pred = y_pred.astype(np.float64)\n",
    "    assert y_pred.shape == y.shape\n",
    "    Y1 = np.log(y_pred)\n",
    "    y_Pred = 1 + (-1 * y_pred)\n",
    "    y_Pred = y_Pred.astype(np.float64)\n",
    "    Y2 = np.log(y_Pred)\n",
    "    p1 = -1 * np.multiply(y,Y1)\n",
    "    yy = 1 + (-1 * y)\n",
    "    yy = yy.astype(np.float64)\n",
    "    p2 = -1 * np.multiply(1 + (-1 * y), Y2)\n",
    "    res = np.mean(p1 + p2)\n",
    "    Theta = theta\n",
    "    Theta[0] = 0\n",
    "    Theta = np.multiply(Theta, Theta)\n",
    "    re = lambda_*sum(Theta)/(2*y_len)\n",
    "    res = res + re\n",
    "    return res\n",
    "\n",
    "def logistic_loss_theta_w_reg_grad(x, y, h, theta, lambda_=0.0): \n",
    "    y_pred = h(x, theta)\n",
    "    y_len = np.size(y)\n",
    "    points = (y_pred - y) * x\n",
    "    grad = np.mean(points, axis = 0)[:, None]\n",
    "    Theta = theta * lambda_ / y_len\n",
    "    Theta[0] = 0\n",
    "    grad = grad + Theta\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once you are done, you will call your cost function using the initial value of\n",
    "θ (initialized to all zeros). You should see that the cost is about 0.693. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    {
     "data": {
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MG1d0q0bWhg2wciU8+SSsW5f3tbRAaytsuy1ssUWx7ZMk1S/DxzDZfvt8t9tj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\n1ZThQ5Ik1dT/B6gDCVc5DwyFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2d47f8f438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best loss 0.311343379418\n",
      "best acc 0.847457627119\n"
     ]
    }
   ],
   "source": [
    "theta_init = np.zeros((X_pf.shape[1], 1))\n",
    "print(logistic_loss_theta_w_reg(X_pf, y_data, hyposesis_function, theta_init))\n",
    "print(logistic_loss_theta_w_reg_grad(X_pf, y_data, hyposesis_function, theta_init))\n",
    "\n",
    "loss = partial(logistic_loss_theta_w_reg, X_pf, y_data, hyposesis_function)\n",
    "loss_grad = partial(logistic_loss_theta_w_reg_grad, X_pf, y_data, hyposesis_function)\n",
    "theta, best_cost = optimize(theta_init, loss, loss_grad, max_iter=10000, print_every=0, show=True)\n",
    "print('best loss', best_cost)\n",
    "print('best acc', accuracy(X_pf, y_data, theta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.3.2 [15pts] Learning parameters using *minimize***\n",
    "\n",
    "You will use *optimize.minimize* to learn the optimal parameters $\\theta$. If you\n",
    "have completed the cost and gradient for regularized logistic regression correctly, you should be able to learn the parameters\n",
    "$\\theta$ using *minimize*. Implement the function *optimizeRegularizedTheta* below.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.4 Plotting the decision boundary**\n",
    "\n",
    "To help you visualize the model learned by this classifier, we have provided the function\n",
    "*plotBoundary* which plots the (non-linear) decision boundary that separates the\n",
    "positive and negative examples. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_boundary(theta, ax=None):\n",
    "    \"\"\"\n",
    "    Function to plot the decision boundary for arbitrary theta, X, y, lambda value\n",
    "    Inside of this function is feature mapping, and the minimization routine.\n",
    "    It works by making a grid of x1 (\"xvals\") and x2 (\"yvals\") points,\n",
    "    And for each, computing whether the hypothesis classifies that point as\n",
    "    True or False. Then, a contour is drawn with a built-in pyplot function.\n",
    "    \"\"\"\n",
    "    ax = ax or plt.gca()\n",
    "    x_range = np.linspace(-1,1.5,50)\n",
    "    y_range = np.linspace(-1,1.5,50)\n",
    "    xx, yy = np.meshgrid(x_range, y_range)\n",
    "    X_fake = np.stack([xx, yy]).reshape(2, -1).T\n",
    "    X_fake_fm = polynomial_feature_map(X_fake)\n",
    "    y_pred_fake = hyposesis_function(X_fake_fm, theta)\n",
    "    return ax.contour( x_range, y_range, y_pred_fake.reshape(50, 50).T, [0.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2.4.1 [10pts] Plot Decision Boundaries**\n",
    "\n",
    "(a) [2 pts] Use *plotBoundary* to obtain four subplots of the decision boundary for the following values of the regularization parameter: $\\lambda \\ = \\ 0, 1, 5, 10$\n",
    "\n",
    "(b) [2 pts] Comment on which plots are overfitting and which plots are underfitting.\n",
    "\n",
    "(c) [2 pts] Which is the model with the highest bias? The highest variance?\n",
    "\n",
    "(d) [2 pts] What is another way to detect overfitting? \n",
    "\n",
    "(e) [2 pts] Considering that later components of theta correspond to higher powers of monomials, plot values of theta and commend on effects of regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# (a) Build a figure showing contours for various values of regularization parameter, lambda\n",
    "\n",
    "np.random.seed(2)\n",
    "train_idx_mask = np.random.rand(X_pf.shape[0]) < 0.3\n",
    "X_pf_train, y_train = X_pf[train_idx_mask], y_data[train_idx_mask]\n",
    "X_pf_test, y_test = X_pf[~train_idx_mask], y_data[~train_idx_mask]\n",
    "print([x.shape for x in (X_pf_train, y_train, X_pf_test, y_test)])\n",
    "\n",
    "def silent_optimize_w_lambda(lambda_):\n",
    "    theta_init = np.zeros((X_pf.shape[1], 1))\n",
    "    data = (X_pf_train, y_train, hyposesis_function)\n",
    "    loss = partial(logistic_loss_theta_w_reg, *data, lambda_=lambda_)\n",
    "    loss_grad = partial(logistic_loss_theta_w_reg_grad, *data, lambda_=lambda_)\n",
    "    optimizer_fn = partial(climin.GradientDescent, step_rate=1e-4, momentum=0.999)\n",
    "    theta, final_loss = optimize(\n",
    "        theta_init, loss, loss_grad, optimizer_fn=optimizer_fn, \n",
    "        max_iter=1000, print_every=0, show=False\n",
    "    )\n",
    "    return theta, final_loss\n",
    "\n",
    "thetas = []\n",
    "plt.figure(figsize=(12,10))\n",
    "\n",
    "# wow, I mutates an object used in the scope of another function (plot_data)\n",
    "# don't do that! it is really hard to debug later\n",
    "chip_plotting_spec['figsize'] = None\n",
    "\n",
    "# you might find following lines useful:\n",
    "#\n",
    "#    cnt_fmt = {0.5: 'Lambda = %d' % lambda_}\n",
    "#    ax.clabel(cnt, inline=1, fontsize=15, fmt=cnt_fmt)\n",
    "# \n",
    "# red dots indicate training samples\n",
    "\n",
    "for id_, lambda_ in enumerate([0, 1, 5, 10]):\n",
    "    ax = plt.subplot(2, 2, id_+1)\n",
    "    plot_boundary(theta, ax=None)\n",
    "    \n",
    "plt.show()\n",
    "\n",
    "# (e) [2 pts] Considering that later components of theta correspond to higher powers\n",
    "# of monomials, plot values of theta and commend on effects of regularization\n",
    "ax = None\n",
    "for th_id, theta in enumerate(thetas):\n",
    "    ax = plt.subplot(2, 2, th_id+1, sharey=ax)\n",
    "    plt.plot(th_id, thetas)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Written part\n",
    "\n",
    "These problems are extremely important preparation for the exam. Submit solutions to each problem by filling the markdown cells below.\n",
    "\n",
    "**3.1 [10pts]** Maximum likelihood for Logistic Regression\n",
    "\n",
    "Showing all steps, derive the LR cost function using maximum likelihood. Assume that\n",
    "the probability of y given x is described by:\n",
    "\n",
    "$P(\\ y=1 \\; \\vert \\; x \\ ; \\ \\theta \\ ) = h_{\\theta}(x)$ \n",
    "\n",
    "$P(\\ y=0 \\; \\vert \\; x \\ ; \\ \\theta \\ ) = 1 - h_{\\theta}(x)$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3.2 [10pts]** Logistic Regression Classification with Label Noise\n",
    "\n",
    "Suppose you are building a logistic regression classifier for images of dogs, represented by a feature vector x, into one of two categories $y \\in \\{0,1\\}$, where 0 is “terrier” and 1 is “husky.” You decide to use the logistic regression model $p(y = 1 \\ \\vert \\ x) = h_{\\theta}(x)=\\theta^Tx.$ You collected an image dataset **D**$\\ = \\{x^{(i)},t^{(i)}\\}$, however, you were very tired and made\n",
    "some mistakes in assigning labels $t^{(i)}.$ You estimate that you were correct in about $\\tau$ fraction of all cases.\n",
    "\n",
    "(a) Write down the equation for the posterior probability $p(t = 1 \\ \\vert \\ x)$ of the label being 1 for some point x, in terms of the probability of the true class, $p(y = 1 \\ \\vert \\ x).$\n",
    "\n",
    "(b) Derive the modified cost function in terms of $\\ \\theta, x^{(i)},t^{(i)}$ and $\\tau$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3.3 [10pts] Cross-entropy loss for multiclass classification**\n",
    "\n",
    "This problem asks you to derive the cross-entropy loss for a multiclass classification problem using maximum likelihood.\n",
    "Consider the multiclass classification problem in which each input is assigned to one of $K$ mutually exclusive classes. The binary target variables $y_k$ ∈ {0, 1} have a \"one-hot\" coding scheme, where the value is 1 for the indicated class and 0 for all others. Assume that we can interpret the network outputs as $h_k(x,\\theta) = p(y_k = 1|x)$, or the probability of the kth class.\n",
    "\n",
    "Show that the maximum likelihood estimate of the parameters $\\theta$ can be obtained by minimizing the multiclass *cross-entropy* loss function \n",
    "<p>\n",
    "$L(\\theta)= - \\frac{1}{N}\\sum_{i=1}^{N} \\sum_{k=1}^{K} y_{ik} \\log(h_k(x_i,\\theta))$\n",
    "</p>\n",
    "<p>\n",
    "where $N$ is the number of examples $\\{x_i,y_i\\}$. </p>"
   ]
  }
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