{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "<div align='left' style=\"width:400px;height:120px;overflow:hidden;\">\n",
    "<a href='http://www.uff.br'>\n",
    "<img align='left' style='display: block;height: 92%' src='imgs/UFF.png' alt='UFF logo' title='UFF logo'/>\n",
    "</a>\n",
    "<a href='http://www.ic.uff.br'>\n",
    "<img align='left' style='display: block;height: 100%' src='imgs/logo-ic.png' alt='IC logo' title='IC logo'/>\n",
    "</a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Machine Learning\n",
    "# 3. Linear Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Luis Martí](http://lmarti.com)\n",
    "#### [Instituto de Computação](http://www.ic.uff)\n",
    "#### [Universidade Federal Fluminense](http://www.uff.br)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### About the notebook/slides\n",
    "\n",
    "* The slides are _programmed_ as a [Jupyter](http://jupyter.org)/[IPython](https://ipython.org/) notebook.\n",
    "* **Feel free to try them and experiment on your own by launching the notebooks.**\n",
    "\n",
    "* You can run the notebook online: [![Binder](http://mybinder.org/badge.svg)](http://mybinder.org/repo/lmarti/machine-learning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "If you are using [nbviewer](http://nbviewer.jupyter.org) you can change to slides mode by clicking on the icon:\n",
    "\n",
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-3\"><span/></div>\n",
    "      <div class=\"col-md-6\">\n",
    "      <div class='well well-sm'>\n",
    "              <img src='imgs/view-as-slides.png'/>\n",
    "      </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-3\" align='center'><span/></div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import random, math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.rc('text', usetex=True); plt.rc('font', family='serif')\n",
    "plt.rcParams['text.latex.preamble'] ='\\\\usepackage{libertine}\\n\\\\usepackage[utf8]{inputenc}'\n",
    "\n",
    "# numpy - pretty matrix \n",
    "np.set_printoptions(precision=3, threshold=1000, edgeitems=5, linewidth=80, suppress=True)\n",
    "\n",
    "import seaborn\n",
    "seaborn.set(style='whitegrid'); seaborn.set_context('talk')\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Fixed seed to make the results replicable - remove in real life!\n",
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Classification$\\renewcommand{\\vec}[1]{\\boldsymbol{#1}}$\n",
    "\n",
    "* Given an input vector $\\vec{x}$ determine $p\\left(\\left. C_k\\right|\\vec{x}\\right)$ where $k\\in \\{1\\ldots K\\}$ and $C_k$ is a discrete class label.\n",
    "* Available da\n",
    "* We will discuss **linear models** for classification.\n",
    "\n",
    "**Note:** the algorithms described here can also be applied to transformed input, $\\phi(\\vec{x})$, to determine $p\\left(C_k\\right|\\left.\\phi(\\vec{x})\\right)$, where $\\phi$ may be a nonlinear tranformation of the input space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our **first model assumption** is that our target output can be modeled as\n",
    "\n",
    "$$y(\\phi(\\vec{x})) = f(\\vec{w}^\\intercal\\phi(\\vec{x}))$$\n",
    "\n",
    "where $y$ will be a vector of probabilities with $K$ elements. \n",
    "\n",
    "* Elements of $y$ are $y_k = p\\left(C_k\\right|\\left.\\phi\\left(\\vec{x}\\right)\\right)$ i.e. the probability that the correct class label is $C_k$ given the input vector $\\vec{x}$. \n",
    "* Often we will have simply that $\\vec{w}^\\intercal\\phi(\\vec{x}) = \\vec{w}^\\intercal\\vec{x}+w_0$ in which case we will simply omit $\\phi$ from the notation.\n",
    "* The function $f$ is known as the **activation function** and its inverse is known as the **link function**. \n",
    "* Note that $f$ will often be nonlinear."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "It should be noted that nearly all of the material presented fails to be a fully Bayesian treatment of the classification problem. Primarily this is because a Bayesian approach to the classification problem is mathematically intractable. However, Bayes' Theorem will appear often in the discussion, which can lead to confusion. Where appropriate, I will try to clarify the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The target variable, $y$, does **not provide a decision** for a class assignment for a given input $\\vec{x}$. \n",
    "\n",
    "* In real world cases where it is necessary to make a decision as to which class $\\vec{x}$ should be assigned;\n",
    "* one must apply an additional modeling step based on [*decision theory*](https://en.wikipedia.org/wiki/Decision_theory).\n",
    "\n",
    "There are a variety of decision models, all of which leverage the class posterior probability models, $p\\left(C_k\\right|\\left.\\vec{x}\\right)$, such as\n",
    "\n",
    "* Minimizing the misclassification rate - this effectively corresponds to chosing the class with the highest probability for a given $\\vec{x}$.\n",
    "* Minimizing the expected loss - minimizes the expected value of a given loss function, $\\ell(\\cdot)$, under the class posterior probability distribution.\n",
    "* Reject option."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear models\n",
    "\n",
    "The models discusses today are called *linear* because, \n",
    "* when the decision criteria is that of minimizing the misclassification rate, \n",
    "* they divide the input space into $K$ regions, \n",
    "* where the boundaries between regions are linear functions of the input vector $\\vec{x}$. \n",
    "* The decision boundaries will correspond to where $\\vec{w}^\\intercal\\vec{x}=\\text{constant}$, and thus represent a linear function of $\\vec{x}$. \n",
    "* In the case of transformed input, $\\phi(\\vec{x})$, the decision boundaries will correspond to where \n",
    "$\\vec{w}^\\intercal\\phi(\\vec{x})=\\text{constant}$, and thus represent a linear function of $\\phi(\\vec{x})$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-4\"><span/></div>\n",
    "      <div class=\"col-md-4\">\n",
    "          <div class='well'>\n",
    "              <img class='img-thumbnail' src='https://upload.wikimedia.org/wikipedia/commons/2/20/Svm_separating_hyperplanes.png'/>\n",
    "          </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-4\" align='center'><span/></div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Probabilistic generative models\n",
    "\n",
    "Our first step is to form a model of the class posterior probabilities for the *inference stage*:\n",
    "* This can be done by modeling the *class-conditional densities*, $p\\left(\\vec{x}\\right|\\left.C_k\\right)$, and the class priors, $p(C_k)$, and then applying [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) to obtain the posterior model, or\n",
    "* can be done directly, as in *probabilistic discriminative modeling*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Remembering Bayes' theorem\n",
    "\n",
    "Bayes' theorem describes the probability of an event, based on conditions that might be related to the event.\n",
    "\n",
    "$$ P\\left(A\\right|\\left.B\\right) = \\frac{P\\left(B\\right|\\left.A\\right) \\, P(A)}{P(B)},$$\n",
    "where $A$ and $B$ are events.\n",
    "\n",
    "* $P(A)$ and $P(B)$ are the probabilities of $A$ and $B$ without regard to each other.\n",
    "* $P\\left(A\\right|\\left.B\\right)$, a *conditional probability*, is the probability of observing event $A$ given that $B$ is true.\n",
    "* $P\\left(B\\right|\\left.A\\right)$ is the probability of observing event $B$ given that $A$ is true."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "* We will see that our class posterior probability model will depend only on the input $\\vec{x}$ \n",
    "    * (or a fixed transformation using basis functions $\\phi$) \n",
    "* and the class labels, $C_k$. In this case, for $K$ classes, our activation function will take the form of the *softmax function*\n",
    "$$\n",
    "f_k = p\\left(C_k\\right|\\left.\\vec{x}\\right) = \n",
    "\\frac{p\\left(\\vec{x}\\right|\\left.C_k\\right)p\\left(C_k\\right)}{p(\\vec{x})} =\n",
    "\\frac{\\exp(a_k)}{\\sum_j \\exp(a_j)},$$\n",
    "where $$a_j = \\ln\\left(p\\left(\\vec{x}\\right|\\left.C_k\\right)p(C_k)\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the **case of $K=2$**, the activation function will reduce to the *logistic sigmoid* function\n",
    "\n",
    "$$f = p(C_1|\\vec{x}) = \\frac{1}{1+\\exp(-a)} = \\sigma(a)$$\n",
    "\n",
    "where \n",
    "\n",
    "$$a = \\ln \\frac {p(\\vec{x}|C_1)p(C_1)} {p(\\vec{x}|C_2)p(C_2)}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
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   "source": [
    "* Note this is not the only possible form for the class posterior models. For example, one might also add a noise term to account for misclassification. \n",
    "* This particular form for the activation function is a consequence of the model we choose for $p(\\vec{x}|C_k)$ in sections below. \n",
    "* Showing the outcome may be a bit of \"putting the cart before the horse\" but it will simplify the notation as we proceed.\n",
    "* Although we have applied Bayes' Theorem, this is **not** a Bayesian model. \n",
    "    * Nowhere have we modeled the parameter posterior probability $p(\\vec{w}|\\vec{t})$. \n",
    "* Indeed, we will see shortly that we will use a *maximum likelihood* approach to determine $\\vec{w}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "These models are **known as generative models** because they can be used to generate synthetic input\n",
    "data by applying [inverse transform sampling](http://en.wikipedia.org/wiki/Inverse_transform_sampling) to the marginal distribution for $\\vec{x}$ defined as\n",
    "\n",
    "$$p(\\vec{x}) = \\sum_k p(\\vec{x}|C_k)p(C_k)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Model assumptions\n",
    "\n",
    "To move forward, it is necessary to start making **model assumptions**. \n",
    "Here we will *assume* that:\n",
    "* we have continuous inputs, i.e. $x\\in \\mathbb{R}^n$ (see Bishop p.202 or Andrew Ng's Lecture 5 pdf for discrete input using Naïve Bayes & Laplace), and\n",
    "* that the *class-conditional densities*, $p(\\vec{x}|C_k)$ are modeled by a Gaussian distribution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Transformation under the Gaussian assumption\n",
    "\n",
    "Under the Gaussian assumption, the class-conditional density  for class $C_k$ is\n",
    "\n",
    "$$p(\\vec{x}|C_k) = \\frac{1}{\\left(2 \\pi \\right)^{n/2}} \\frac{1}{\\left|\\vec{\\Sigma}\\right|^{1/2}} \\exp \\left( -\\frac{1}{2} \\left(\\vec{x} - \\vec{\\mu}_k\\right)^\\intercal \\vec{\\Sigma}^{-1} \\left(\\vec{x} - \\vec{\\mu}_k\\right) \\right)$$\n",
    "\n",
    "* where $n$ is the dimension of the input vector $\\vec{x}$, \n",
    "* $\\vec{\\Sigma}$ is the *covariance matrix*, \n",
    "* $\\vec{\\mu}$ is the mean vector and \n",
    "* where we have *assumed* that all classes share the same covariance matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "A [logistic function](https://en.wikipedia.org/wiki/Logistic_function) or logistic curve is a common \"S\" shape (sigmoid curve), with equation:\n",
    "\n",
    "$$\\sigma(x)={\\frac {L}{1+\\mathrm {e} ^{-k(x-x_{0})}}}$$\n",
    "where\n",
    "\n",
    "* e: the natural logarithm base (also known as Euler's number),\n",
    "* $x_0$: the x-value of the sigmoid's midpoint,\n",
    "* $L$: the curve's maximum value, and\n",
    "* *k*:the steepness of the curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   "source": [
    "In the case of **two classes**, this result is substituted into the logistic sigmoid function and reduces to\n",
    "\n",
    "$$p(C_1|\\vec{x}) = \\sigma \\left( \\vec{w}^\\intercal \\vec{x} + w_0 \\right)$$\n",
    "\n",
    "were we have defined: \n",
    "\n",
    "$$\\vec{w} = \\mathbf{\\Sigma}^{-1} \\left( \\mathbf{\\mu}_1 - \\mathbf{\\mu}_2 \\right),$$\n",
    "\n",
    "$$w_0 = -\\frac{1}{2} \\vec{\\mu}_1^\\intercal \\vec{\\Sigma}^{-1} \\vec{\\mu}_1 + \\frac{1}{2} \\vec{\\mu}_2^\\intercal \\vec{\\Sigma}^{-1} \\vec{\\mu}_2 + \\ln \\frac{p(C_1)} {p(C_2)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What about the $p(C_k)$?\n",
    "\n",
    "* The class prior probabilities, $p(C_k)$, effectively act as a bias term. \n",
    "* Note that we have yet to specify a model for these distributions. \n",
    "\n",
    "If we are to use the result above, we will need to make **another model assumption**. \n",
    "* We will *assume* that the *class priors* are modeled by a [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution) with $p(C_1)=\\gamma$ and $p(C_2)=1-\\gamma$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   },
   "source": [
    "These results can be extended to the case of $K>2$ classes for which we obtain\n",
    "\n",
    "$$a_k(\\vec{x}) = \\left[\\vec{\\Sigma}^{-1} \\vec{\\mu}_k \\right]^\\intercal \\vec{x} - \\frac{1}{2} \\vec{\\mu}_k^\\intercal \\vec{\\Sigma}^{-1} \\vec{\\mu}_k + \\ln p(C_k)$$\n",
    "\n",
    "which is used in the first activation function provided at the begining of this section. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What about the posterior class densities\n",
    "\n",
    "We have not formulated a complete model for the posterior class densities, in that we have not yet solved for the model parameters, $\\vec{\\mu}$ and $\\vec{\\Sigma}$. \n",
    "\n",
    "We do that now using a **maximum likelihood** approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Likelihood function\n",
    "\n",
    "* A **function of the parameters** of a statistical model **given** some data.\n",
    "\n",
    "The likelihood of a set of parameter values, $\\theta$, given outcomes $x$, is the probability of those observed outcomes given those parameter values,\n",
    "\n",
    "$$\\mathcal{l}(\\theta |x)=P(x|\\theta)=\\mult_$$\n",
    "* Frequently, the natural logarithm of the likelihood function, called the **log-likelihood**, is more convenient to work with."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "## Maximum Likelihood Solution\n",
    "\n",
    "Considering the case of two classes, $C_1$ and $C_2$, with \n",
    "* Bernoulli prior distributions, $p(C_1)=\\gamma$ and $p(C_2)=1-\\gamma$, and\n",
    "* Gaussian *class-conditional density* distributions $p(\\vec{x}|C_k)$, \n",
    "* assume we have a training data set, $\\vec{X}$, with $m$ elements of the form $\\left\\{\\vec{x}_i, t_i\\right\\}$ where $t_i=0$ indicates that $\\vec{x_i}$ is in class $C_1$ and $t_i=1$ indicates that $\\vec{x}_n$ is in class $C_2$.\n",
    "\n",
    "The likelihood function is then given by\n",
    "$$p\\left(\\vec{t}, \\vec{X} \\mid \\gamma, \\vec{\\mu}_1, \\mu_2, \\vec{\\Sigma}\\right) = \\prod_{i=1}^m \\left[\\gamma \\mathcal{N} \\left(\\vec{x}_i \\mid \\mu_1, \\vec{\\Sigma}\\right)\\right]^{t_i} \\left[\\left(1-\\gamma\\right) ND\\left(\\vec{x}_i \\mid \\mu_2, \\vec{\\Sigma}\\right)\\right]^{1-t_i}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
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   },
   "source": [
    "Taking the derivate of this expression with respect to the various model parameters, $\\gamma$, $\\mu_1$, $\\mu_2$, and $\\vec{\\Sigma}$, and setting it equal to zero, we obtain\n",
    "\n",
    "$$\\gamma = \\frac{N_1}{N_1+N_2}$$\n",
    "\n",
    "where $N_1$ is the number of training inputs in class $C_1$ and $N_2$ is the number in class $C_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### similarly...\n",
    "\n",
    "$$\\mu_1 = \\frac{1}{N_1} \\sum_{i=1}^m t_i \\vec{x}_i,$$\n",
    "$$\\mu_2 = \\frac{1}{N_2} \\sum_{i=1}^m (1-t_i) \\vec{x}_i, \\text{ and}$$\n",
    "\n",
    "$$\\vec{\\Sigma} = \\frac{1}{m}\\left[ \\sum_{i\\in C_1} (\\vec{x}_i-\\mu_1)(\\vec{x}_i-\\mu_1)^T + \\sum_{i\\in C_2} (\\vec{x}_i-\\mu_2)(\\vec{x}_i-\\mu_2)^T \\right].$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "## Example\n",
    "\n",
    "* We will choose some *truth* values for our parameters and use our generative model to generate synthetic data. \n",
    "* We can then use that data as input to the maximum likelihood solution to see the estimates of the truth parameters. \n",
    "* Let's use 1-D input for simplicity. \n",
    "* We will be using a basic form of inverse transform sampling.\n",
    "* Specifically, we wish for our training input data,  $\\vec{x}$, to be dervied from a distribution modeled by the marginal distribution $p(\\vec{x})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* To obtain this, we first formulate the cumulative distribution function, \n",
    "$CDF(\\vec{X}) = \\int_{-\\infty}^{\\vec{X}} p(\\vec{x})d\\vec{x}$. Note that the range of the CDF is $[0,1]$. \n",
    "* To obtain appropriately distributed $\\vec{x}$ values, we choose some value from a uniform distribution on $[0,1]$, say $y$, and find the value $\\vec{X}$ such that $CDF(\\vec{X})=y$. \n",
    "* This value of $\\vec{X}$ is our input $\\vec{x}$.\n",
    "* This approach requires us to find the inverse of the CDF, which we will do numerically.\n",
    "* Once we have obtained a value for $\\vec{x}$ we need to assign it to a particular class. \n",
    "\n",
    "We will *assume* that the correct class is that for which the posterior probability $p(\\left.C_k\\right|\\vec{x})$ is greatest, **unless** the difference between the two posterior probabilities is less than some minimum value in which case we will chose randomly - this will add some \"noise\" to our input training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "Select truth data values, these will NOT be known to the training algorithm, they are only used in generating the sample data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_mu1 =-2.0\n",
    "true_mu2 = 2.0\n",
    "true_sigma = 2.0\n",
    "true_gamma = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import scipy.integrate as sci_intgr\n",
    "import scipy.optimize as sci_opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Defining probability functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def p_xCk(x, mu, sigma):\n",
    "    'Class conditional probability p(x|Ck)'\n",
    "    denom = math.sqrt(2.0 * math.pi * sigma)\n",
    "    arg = -0.5 * (x - mu) * (x - mu) / sigma\n",
    "    return math.exp(arg) / denom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def p_x(x, mu1, mu2, sigma, gamma):\n",
    "    'Marginal probability p(x)'\n",
    "    return gamma * p_xCk(x, mu1, sigma) + (1.0 - gamma) * p_xCk(x, mu2, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def p_Ckx(x, mu1, mu2, sigma, gamma):\n",
    "    'Posterior class probability vector (p(C_1|x), p(C_2|x))'\n",
    "    a = math.log(p_xCk(x, mu1, sigma)*gamma/(p_xCk(x,mu2,sigma)*(1-gamma)))\n",
    "    pc1 = 1.0/(1.0 + math.exp(-a))\n",
    "    return (pc1, 1.0 - pc1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def cdf(x, mu1, mu2, sigma, gamma):\n",
    "    'Cumulative distribution function P(x<X)'\n",
    "    return sci_intgr.quad(func=p_x, a=-np.inf, b=x, args=(mu1, mu2, sigma, gamma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def inv_cdf(y, mu1, mu2, sigma, gamma):\n",
    "    'Inverse of the CDF'\n",
    "    f = lambda x: cdf(x,mu1,mu2,sigma,gamma)[0] - y\n",
    "    return sci_opt.newton(f, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Class conditional probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "domain = np.linspace(-5, 5, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "px_class1 = [p_xCk(x, true_mu1, true_sigma) for x in domain]\n",
    "px_class2 = [p_xCk(x, true_mu2, true_sigma) for x in domain]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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EqgnAIeP24W43DVKSUSZwRBSxts4+fP0HgUWXNq4oxu99Ora9CValRbPwlT07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wG+m4z46XwnATwtpXzBxzHl7mP8un3SqOqae/DR0XolFhNtwdc+z0+NiW5X0XwWZ1rVdvlJMYl4\nbPEXdcpIf2JOOratnK3ERsfs+Pk7F3TKiMiYFs2cj/Ic9QOPnpE+vHnxfZ0yIqJACqsCzl1IdQO4\nz8dddgB4yTMohChyD9tWCrUpnu81+FixE0Jsc//nLh/nCysOhxP/vvsMPGZ24+FNJchI4XUbRONG\nbaP4xSntiMivLv4yEqMTdMjIOL7+hVLEx6q7/Q+dbcbpy206ZURkTE+UPaIZ7v2u3ItrPc0+jiCi\nUBVWBZzbkwAeE0IoRZT72rRueC+engfwA/f3aZ3PXfStFEJ420L5PFzDvX2tzoWVPcevKtevAEB6\ncgwe2VyiU0ZExvS7Sx+hfaBDiRWnz8HmonU6ZWQcaUmx+OP752viL719Dja7Q4eMiIwpPzkH93lc\n82Z3OvCzyl/D6XT6OIqIQlHYFXBSyt0AngOwTwhRLoRIdRdbuwBs9dFN8jW4irHXPG+YyvmklDsB\n/NC9qrdNCPGUEKISruKt2G//swbW3TeCX7x7URN/8qHFiIsJt945RFPXNtCBty99pIl/s/wrmk/T\nI9UD6wsxOztJiV273o93D0bETnSiCXt88YNIiVFfK1XtV7C//qhOGRFRIITluwP3CtdWACsAPAWg\nU0pZfIcB27ullGnuYm3a53MfsxPAi3BdJ9cJV1fKndP5/wolr7x7Af1DY0qsXMzA+iW5OmVEZEz/\ndWo3xuzqa2Vz4TqUZBTok5ABWS1mPP3wYk381Q8lOnvZpIFoXGJ0Ar5etkMT/+WZN9E30q9DRkQU\nCGG7FOJeGdNc7xbM87kblfgth1Bx7soNfFxxTYlFWc145pElQZ/5RmRkp1rO43iTOjYgPioOX13y\nZZ0yMq4lJVnYsDQXB8/cup5naMSGn//+Av7qieU6ZkZkLBvmrMQndYdxvk3ejPWN9ONXZ9/GMyuf\n0DEzIvKXsFyBI/2M2Rz49zfOaOKPb5uHnMzIbsZAdLvBsSG8VPGqJv74ogeREpusQ0bG940HFyEm\n2qLE9p9qxPGLrTplRGQ8JpMJ31r+FVjN6mf0H9cewqX2iY7BJSIjYwFHfvXWp1fQ2KZu08jLSmTj\nEiIPvzrzFjoG1SY/s1PysL3kHp0yMr6stDg8vm2eJv5vr5/RbNkmimS5ydn48vztmvjLla/C5jFr\nkohCDws48puWGwN4bY/UxL/96BJEWS1ejiCKTOevS+ypOaDETCYTnln5BCxmvlbu5KFNJSjIUVco\nO3uH8QpnwxEpHi69HzMTs5TYtZ5mvCv36pQREfkLCzjyC7vDiX/69UmM2tS23vcuz8fSuVk+jiKK\nPMO2Ebx44r818QfFNjYumYAoqxl/+fgymM3q9bQfHbuKU5Kz4YjGRVuj8c3yr2jivz3/LmfDEYU4\nFnDkF7/bfwVV9Z1KLCEuCt94cKFOGREZ02/O/R7XB24osZzEGXhs4Rd1yij0lMxKxaNetmX/6+un\nMTRi0yEjImMqy1mAtbPUJj82hw3/evQXsNn5WiEKVSzgaNrqW3rxy/cvaeLf+tIipCXF6pARkTHJ\nGzV4//InSswEE7696muItkbrlFVo+sp9AvkzEpVYW9cQ/usP2vmTRJHsz8ofQ1K02kSsrvsa3rj4\nvk4ZEdF0sYCjaRmzOfBPr56Eza5unVy9MBtbV87SKSsi4xm1j+Gnx38JJ5xK/P6STZifxSY/kxUd\nZcFfPr4MnpNJ3j1Uhwu1HfokRWRAqbHJeHLFVzXxt6o+wJWO+uAnRETTxgKOpuW1PRK1zT1KLDkh\nGt/ZWcaZb0S3efXs22juu67EsuLTOfNtGuYXpONLG4s18X/69UkMsCsl0U1rZpVjw5xVSszhdODf\njv0nRm2jOmVFRFPFAo6mTF7txOsfV2vi39m5FKlJMTpkRGRMlc3n8N7ljzXxp1c+gdgobjOejic+\nPx85Ger2sOudg/j33WfgdDp9HEUUeb5R/hjS41KVWFNfK1499zudMiKiqWIBR1MyPGrDP/36JBwO\n9Q3S5uX5WLs4V6esiIync7Ab/37sPzXxLUXrsSS7VIeMwktstBXffbxMs5Xys9NN2Hu8QZ+kiAwo\nMToBz6z8mib+3uWPcf66dgQQERkXCziakpfeOoem9gEllpkSi6ceXqJTRkTG43A48C/HXkHfqPpa\nyU2aiT8t26FTVuFncXEmdmyZq4m/+PY5XLvep0NGRMZUlrMA24vv0cT/9dgv0DPcq0NGRDQVLOBo\n0vYev4o9Xj7Z/ovHlyExLkqHjIiM6a2qD3Ch7bISs5qt+D/XfpNbJ/3sq/fPh5iTpsRGRu144ZcV\nGB2z65QVkfE8UfaIZsB351A3fnL0FTgcDh9HEZGRsICjSalr7sFP3ziriX9xfSGWiRk6ZERkTJfa\na/D6hT9o4l9b+ggK0tih1d+sFjP++okVSIi1KvH6ll78/J0LOmVFZDyx1hh8Z/WfwGxS3wKeu34J\nuy9q/84iIuNhAUcTNjA0huf+8wRGbeondCWzUvGNL3FgN9G4/tEB/OToz+Fwqq+VFblL8Lm59+qT\nVASYmR6P7zxWpon/4VAdjpxr0SEjImMSmcX4o8XaDrhvXHgfp1v4gQeR0bGAowlxOp34yW9PoeWG\nei1PYlwUnv36SkRZLTplRmQsDocDPznyc9wY7FTi6XGp+Paqr3G8RoBtWJqH+9fM0cT/+Tcn0djG\n6+GIxj04fxtW5KrXrTvhxL8cfUXz9xcRGQsLOJqQ3x+oxeGz2k+w/8dXyzEzPV6HjIiM6Vdn38Lp\n1otKzGQy4S/W/BmSYhJ1yiqyfOvLizBrZpISGxi24f/++TH0cz4cEQDAbDLjz1d/HTMSMpR43+gA\n/unwz2Cz23TKjIjuhgUc3VVtUw9e8XINyc6tc7FqQbYOGREZ0/66o3hH7tXEH13wABbMmKdDRpEp\nNtqKH3xtBaKt6j9xTe0D+PEvK2B3cD4cEeAaLfC9dU8hyqxeO1rdUYfXzr+jU1ZEdDcs4OiuPjha\nr3nDs6g4A398/3ydMiIynss3avFixa808eW5i7Fj4QM6ZBTZCnKS8ZdfWaaJn5Rt+MW7vMaHaFxR\n+mz86bLHNPG9tQe5CkdkUCzg6K5iotTr29KSYvCDJ1bAYuGvDxHgGtb9/xx6ETaH+mYnPzkH313z\nZ5pubxQc9yzLx86t2vlwb++vwb4THPJNNG5b8QZsnLNKiVlNFpjN/LuLyIj4yqS7+sL6QuTPcF27\nMyMtDv/zG6uRlswZVkQAMGobxY8P/ge6PYbgJkTH4wcbv434qDidMiMAeOJzpV63ev/r62dw6Sob\nNRABrut0n1zxVazKc3VxjTJb8cTSR/jhE5FBWe9+F4p02RkJ+Ofv3YvuvhEkJ0QjNoa/NkQAYHfY\n8ZNjr6Cm66oSN5vM+N66J5HtMSyXgs9sNuH7f1yOv/6XA2hovdWF0mZ34B9+fhzPf2cDcrPYXIYo\n1hqD769/CjcGOxFrjWHTJSID40crNCHRURbMSI9n8Ubk5nQ68VLFqzjeeFpz258u24nFM3mNqFHE\nx0bh776xGknxUUq8u38Ef/fiYXT0DOmUGZGxmEwmZCVksHgjMjgWcEREk+R0OvHfZ97EJ3WHNbdt\nK9qA+0s26ZAV3Ul2RgKe/ZOVMJvVOXxtXUP4uxePoHdgVKfMiIiIJocFHBHRJP3u0kdexwWUZS/A\nN8of57Bug1pSkoXv7lyqiV+73of//bMjGBphxz0iIjI+FnBERJOwt+YAXj37tiYuMorwvfVPwWrh\nNmMj27ZqDr7x4EJN/HJDN/7hlWMYs9l1yIqIiGjiWMAREU3Qwasn8HLFrzXx2Sl52HXPnyPWGqND\nVjRZD99b4nW8wJnqG/jxf1dizObQISsiIqKJYQFHRDQBH9cexr8cfQVOqEPtZyZk4m83fReJ0Qk6\nZUZT8bXPl+Jzaws08SPnWvCjXxzHyBhX4oiIyJhYwBER3cV7lz/Gf5z4paZ4S4tNwf+89y+QFpei\nU2Y0VSaTCc88sgQbluZqbquouo6//9lRXhNHRESGxAKOiMgHp9OJNy++j1+cel1zW2J0Av5203cx\nk7PeQpbFbML3vroc5fNnaG47e+UG/u7Fw+gfZHdKIiIyFhZwREReOJ1OvHr2bfzm3O81t6XEJuN/\nbf4fmJ2ap0Nm5E9RVjP+9k9XYfXCbM1t8moX/vanh9HdN6JDZkRERN6xgCMi8mBz2PFSxav43aWP\nNLdlxKfh77d8n8VbGImOsuDZP1mJe5Zpn9Pa5h48+28H0HyjX4fMiIiItFjAERHdpm+kH/+w/yfY\nV3tQc1t2Yhb+fsv3kZOk3XJHoc1qMeN7X12O7avnaG5rah/AX/3zZzh7pV2HzIiIiFQs4IiI3Bp7\nWvA3e57HhbbLmttmpeTif2/5PrISMnTIjILBYjbhOzuX4sv3FGtu6xscw//14hG8f6Q+6HkRERHd\njhNniYgAnGo5j//3yP+HobFhzW3F6XPwN/d8B0kxiTpkRsFkMpnwzS8tRHysFb/+SCq32R1O/Pvu\nM2ho7f3/27v34LjO+ozjz9mLLmtJliXHli+yiZTk9SUOGV/IhRBIYiVMIHQCdmhgCmWonWlLh9KW\nOJlOp9NOB3A6dDpDoblMO9BpSoMdkkLJFGxIMLlAEjmxg+O8xJadWL7bsu7SSrt7+sc5q0jWrizL\n2stZfT8zmrN6z8U/+1iXZ9/3vK/+6BNXKxzmPVAAQP4R4ADMaCk3pR+/tVP/9cbTcl133P4bG9fo\njz/wOZVHygpQHQrBcRx95o5laqifpW/94HUlkmMX9v7f5w+p/WSv/vKza1RbzeLtAID84u1DADPW\nuYEufe2X/6LH9z6VMbzdc/Vd+vINXyS8zVC3rm3U1//kg6qtGh/SXn/7tP7sm89qtz1VgMoAADMZ\nAQ7AjLT72G/11Z/+g/ae3D9uX1k4qr+4cZM2rLxTjuMUoDoUi2Xvq9M3//xmXb6wZty+zp64/vbR\nl/RvP/qthhOpDGcDADD9CHAAZpTh5LC++9o2feNX31Z3fPzU8HWVtfr7W/9K1zeuLkB1KEbz5sS0\n9Usf0g2rFmTc//QvD+qr39qlo6dZagAAkHsEOAAzxlunD+qBn31dz/zuFxn3X9uwQt+4/UE11S3J\nc2UodpXlET3wuXX6wsdXKBwa3yt7sL1LX/6n5/TUcweUTNIbBwDIHSYxAVDyeof69PiepzOu7SZJ\n4VBYn73mbt151S0KObyvhcxCIUefvOVKrbpirv7xP1t1/EzfmP3xoaT+/cf79GzrEf3phvfLLK0r\nUKUAgFLGbyoASpbrunr+nZf1lWf+Lmt4W1g9X19bv0UfN7cR3jApVzbO0T9/5cO6dW1jxv2HjnXr\nq9/6lR7+4V71DQznuToAQKmjBw5ASTpw9rAe3/tUxkW50269/Eb94ep7VBFhKnhcnFhFVF+5d7VW\nm3n6zpN71D+YGLPfdaWfvHBIL+49ps/csUwtH1jCunEAgGlBgANQUo71nNR/7/2Rft2+O+sx86su\n06Y19+qahuV5rAyl6MOrF+vq5no99j+/1Qt7jo3bf64nrm9v36Onf3lAf3DnCt24agEzmwIALgkB\nDkBJ6Bjo1PZ9z+gXbS8o5WaeRCIcCuv3lt2uTy7/qMpY2w3TpH52pR743Dq98uYJPfzDvTp1bmDc\nMUdP9+kb33tFVy2p1ec/tkKrmucS5AAAU0KAAxBoR7tP6Mdv7dCud15WIpXIetyyuc3avPazWjw7\n81TwwKVat6JBq5rn6vs/s3p610GlUuMXh//du5366399UWbpHH3qliv0gZULMs5qCQBANgQ4AIHj\nuq7smYP60Vs79OqxvRMeO29WvX5/1Sd045K1TFKCnKsoj+gLd63Uresa9R8/2a+X3zyR8Tj7zjl9\n7buvaOHcWbr7I1fo1rWNKouG81wtACCICHAAAmNgeFAvvPuqftH2gg50HJ7w2JryKn1qxZ1qaf6Q\nImG+1SG/ljbU6G++eJ32tZ3V937ypvYf7sh43LEzffr29j16/P/e0m3rGtVy3S4IqbMAABLZSURB\nVFItuqwqz9UCAIKE32oAFDXXdfW7s236edsLeunIbsUT8QmPL4+U6y6zXneZ9aqMVuSpSiCzlU31\n2vqlm/TyvhP63jP7deRkT8bjOnvjevLZA3ry2QNa2VSv269bohuvWaiKMn5MAwDG4icDgKLjuq7e\n6WzXr9t366Uju3W859QFz5ldXq2PXvkR3X7FzaoupwcDxcNxHF139QKtXdGgl/cd15PPHpB951zW\n4/e1ndW+trN6+Idv6LqrG/TBaxZqtZnHEEsAgCQCHIAikXJTOjZ4Soe6juo7bd/Xyd7TkzpvQdU8\n3bVsvW5+3/UqC0dzXCUwdeGQoxtWLdT1Vy/Qm4c69NRzB/SbfZmfkZOkgXhCz7W267nWdlWWh7Vu\nRYNuvGahYm4yj1UDAIpNSQY4Y0ytpAclNUnqkFQnaYe19tF8XW+6awBKUUd/p14/8ab2nnhTrx3b\np4Hk4KTOc+To2gUrdFvTTVq78BqFQkxOguBwHEcrm+q1sqleR0726JkXD+m51nb1DgxnPWcgntSu\n145q12tHFXKkxXPLtHxJtSJV59S8qFYhZrIEgBmj5AKcH5xaJW211m4Z1b7DGLPGWntfrq833TUA\npcB1XZ3sPa23zhyUPdOmt84c0NHu7L0PmVwWq9MtTR/URy6/XnNjdTmqFMifxvnVuu/ua/SFj6/U\nS28c189+8472Hjgz4TkpV3r39JDePX1WP23dpepYmVZcXud/1Kt58WxFIwy3BIBSVXIBTtJjktoy\n9HRtlHTOGLPDWrs9x9eb7hqAQHFdVx0DnTp07ogOdx5R27kjevtMm7rimSdwmMisspjWLXq/blqy\nTlfPNywFgJJUFg3rw6sX68OrF+vE2T49++oRPb/3mN49ceGvmZ7+If1m34mR4ZjRSEhXLK7VlY21\nalo0W02LZqtxfrUiYb52AKAUlFSA83u+Nkga18Nlre00xuz0900qPE3letNdA1DMXNdV12C32rtP\n6FjPCR3tPqn27uM63NmunnjvlK9bXTZL6xZfqxsaV2vlPKNIiN4EzBwN9bN07x3LdO8dy3TkZI9e\n3HtMz+85psPHuyd1/nAipf2HO8YsXRCNhLS0oVpLGmq0eF6VGudXa/G8KjXUzyLYAUDAlFSAk3SP\nv23Lsr9N0uYcX2+6awAKxnVd9Q71qWOgU2f7O3Wq74xO9Z31tr3e6/7hgUv+cxw5WlB5mZZWLNSy\nOc26fc0tChPaADXOr9anW4w+3WJ0/Eyfdr91Urta23TgWL+GEu6krzOcSOlAe5cOtHeNaY+EHV02\nJ6aGupjm18/S/LqY5tfFdNmcStXXVGpOTTkBDwCKTKkFuBZ/my08HZQkY8x6a+3OHF1vumsApo3r\nuoonh9Q71Ke+oX71DvWrJ96r7niPugZ71BXvUfdgr7ri3ero71THYJeGk9knVrgUi6obdNXcJl3T\nsEyr5i/X0bYj6u/vVywWI7wBGSyYO0sfu6lJTfVxdff06Uyvo7ODlXrzUIfefvechhKpi75mIunq\n+Jk+HT/TJ2n8zK+OI9VWlat+doXm1FSotqpcs/2P2qoy1VSVq6oyqupYmapjUcUqokyoAgA5VmoB\nrsnfdmTZ3+lvV0uaTHiayvWmuwbMACk3pWQqqWQqqUQqqUQqoYSbVCKZ0HAqoeHksL9NaDg1rKHk\nsIYSwxpKDmkoOax4ckiDibjiiSHFE3EN+h8DiUH1Dw9oYNjb9g8PKpFK5P3vVxEp1+VzGnVVfZPM\n3GZdNbdJNeet1XY071UBwRUJO2paENPHli+X5PWwHTzaqf2HvKGTbx/p1JnOS+8dd13pXE9c53ri\nkroueLzjSLGKqGIVEcXKIyOvK8u9j/KysCrKIqoo97Zl0bDKoyGVRcPe60hYkUhI0TEfYUXCjiJh\n7/NwOKRIOKQwQRHADFVqAa5W8p41u8Bx9Tm83nTXUBReP75Prxzdo4FEfGoXcDMP9XE1vj3jkRnO\nd0e27vjGUe2u3JF2V656enqUSCYUDodVdeZZb5c76ugxr71zvLbztq6r1OjXbkop+Vs3NdKW9D9P\nuSmlUqmRtmQ6tLlJuVn+fYJobqxOi2oadPmcRr2vtlGXz2nU/Kq5TD4C5FA0EtKypXVatrROd/tt\nXb1xHTrWpbajXWo72q3Dx7t09HSfEsmL76mbLNeV+gaG1TfBkgjTxXG8tfVCIS/MRcKOQiHHa3PS\nr0MKhbylG0Lpdsd5r81x5Djv7Zc0qs0b3i3Ha/NfynGckT9f8o7p7e1RMpVUJBxW9a+7xx2TPs5/\nMaot/XfJHEYztmZodDI0ZrnkhTnSsiVzdMvaRsUqWFsTKEalFuAuNK94ulesNofXm+4aCu6Vo3v0\nj88/XOgycmNycwLgPDXlVZo3a67mzapXQ/VlWlS9QItqGrSwep4qohWFLg+ApNlV5br2qnm69qp5\nI23JlKuTHX1qP9Wr9pO9aj/Vo5Md/TrZ0a/TnQNKpYLzZpLrekNAlSy2hc37Cl3AJXuutV1vHDyr\nBz6/rtClAMig1ALcjLZ///6cXHfnkV05uS6KT0iOYpFKzYrEVB2dpZrILFVHq1QTrVJNdJZml9Wo\nNlqt8nDZ2BMHpPhAnw6dPDTlP3tgYGBkm6v/y7g43JPiNB33pdqRljdIyxsqJFVIqlMy5aqrL6GO\nnmF19yXU1Z8Ys+0ZSKh3MKnhi5g8BcH10hvH+LoHilSpBbgOTdyzle4du9Dwxku53nTXMGn9/f3T\nfUlJ0uzQrJxcF7kRdSKKhiKKOlGVh8pUHoqqLJR+XaaKcJkqQuWqCFeoIlSmynC5YuFKxcIVqgiV\nZx3KI0lKScl4Qv3K3XN0ruvm7P8ypoZ7UpxycV8qwtLCWmlhbUTZfkUYSqTUN5hS32BSA0MpDcRd\nb+t/xIdTGhxKKT7sKj6cUjzhbYcTroYSbrYR9Sgy9TURvu6BIlVqAU6StxbbJJ5By+n1pruGyYjF\nYjm57s2V12nISWh/90ENpSb3XEOm8fgXY7Lnv5c13jt+9KvzWx1HSqVc77P08w8j+5zRR44c4/if\npZ+FSB+fPtdRaORZCcdxFEof7YTkSAo5If/YkPdajt/mtYedsELyt05IYSc08jrihBUOhRVxvI+w\nE1Y0FFEkFFHUiSgS8j93IioLRRUNRb1nNQJoYGBAruvKcRxVVlYWuhyIe1KsCn1fYpJqa6Z2ruu6\nSiS9IDeU8EJdIulth5OuhhMpJZKuEilXyaR3bCLpKplKf3jDQJNJVynX+zzl70u53uuUK6VcV25K\nSrr+s8z+NuW/9rYaeebZ9c8Z9cj0yDmSRo5R+rloacyxqdTo5wrHfg92R71wM+zI9Cz4mPMu0Djp\nPDzZAx1p6bwKfXTtXMVi5ZO9+kUhGAKXptQCXDow1SlzD1e6Z+xgDq833TVM2nJ/NrJcuHrFypxd\nO9/2798/Ml19Lv/NcHHS96WyspL7UiS4J8WJ+1J8+LlycVpbWwtdAhBopTYtXHpa/mxDGNMzP76a\nw+tNdw0AAAAAIKn0AtwT/rYpy/4mSbLW7s7h9aa7BgAAAACQVGIBzg9FnZJashyyQdKj5zcaY5qM\nMVuNMWNC11SuN9UaAAAAAOBCSirA+TZJuscYM2YIozFms7xgtSXDOVsl3e9vp+N6UzkHAAAAACZU\napOYyFq73e9J+7kxZpOkNkn3yAtNt2WZGfIJSev13vDHS7reFGsAAAAAgAmVXICTJGvtQ8aYR+WF\npvWS2qy1zRMcv13S9um63lTPAQAAAICJlGSAkyS/l2vanjWbyvWmuwYAAAAAM1spPgMHAAAAACWJ\nAAcAAAAAAUGAAwAAAICAIMABAAAAQEAQ4AAAAAAgIAhwAAAAABAQBDgAAAAACAgCHAAAAAAEhOO6\nbqFrwCVqbW3lJgIAgEBZs2aNU+gagCCiBw4AAAAAAoIeOAAAAAAICHrgAAAAACAgCHAAAAAAEBAE\nOAAAAAAICAIcAAAAAAQEAQ4AAAAAAoIABwAAAAABQYADAAAAgIAgwAEAAABAQBDgAAAAACAgCHAA\nAAAAEBAEOAAAAAAICAIcAAAAAAQEAQ4AAAAAAoIABwAAAAABQYADAAAAgIAgwAEAAABAQEQKXQAA\noHgYY2olPSipSVKHpDpJO6y1jxa0MCAgjDGPyPua2V7oWgCUJgIcAEDSSHhrlbTVWrtlVPsOY8wa\na+19hatu5jLGNEnaKqlWXrBuk7SNUF18jDGrJW2WtKPQtQAoXQyhBACkPSapLUMw2ChpszFmQwFq\nmtGMMevlhbdN1toWa22zpG2SHjHGtBa2OmTwWKELAFD6CHDABIwxj/BLK2YCv/dtg7xwMIa1tlPS\nTkn0wOXfFmvtRv8eSJL8gL1F0mp/uB6KgDFms6RXC10HgNJHgAOyGDUUBgVijGkyxmzzh/Ad9Lfc\nk9y4x9+2ZdnfJml9nmqBRgJBxoBmrX3If7nZD98oIP8eNIuhkwDygAAHZMdQmAJi6FjetfjbbAHu\noDRyX5AfLZK2TTAKIH2v1uapHmS3VdLXC10EgJmBAAdkwFCYosDQsfxq8rcdWfan78PqPNSCsVqy\ntKfvCT1wBeS/qdE6+nsVAOQSAQ44D0NhCo+hYwVRK4087zaR+jzUAs8meW9YbMmyPx26s/WaIj82\nMiMogHwiwAHjMRSm8Bg6ln91F9if7pkjNOeJtbbTWvtQplDtP6NbK2/W0N35rw6SZIy5X97PDADI\nGwIcMApDYYoOQ8eAzB70t8wMWiD++nz11lp6QAHkFQt5A2NtZLHiorBJ0iuSsg1LYujY9OvQxIE4\n3UPHmxsF5r/RtEHSQ9banYWuZwbbws8LAIVAgAN8DIUpHn4P6EOZ9jF0LLeMMbX0QBcv/7nPbZIe\ntdZmezYOOeYP7+Y5aQAFwRBKQAyFCRiGjuVGOrRlexYu3Tt3MA+1ILttkn5Az0/BtVhrtxe6CAAz\nEz1wgIehMAHA0LGc2ilviYBswyjTs0+yvEaB+EtntPG9qrD870Prs6xHmR7evdUY86AkWWvX5K04\nADMCAQ6BZIzZJu8X+anYPfoHKkNhgoGhYzn3hKT75f0CmmloapMkMWy1MPwh3jo/vPlfF3WMHsgf\n/82j5kz7Rg3F30IPHYBcIcAhkKy1G6e6BliG53taeEf70k1nqM6CoWM5ZK3dbYzplDfzZ6ZfPDco\n+6QyyCG/x6c5y//9e+RN5kOAA4AZggCHwJqOiRYYCjN9pjlUj8HQsbzZJOkxY8yW0ffEX1i9U9kX\nlEaO+JP2TDQ7bou8+4bikB5qfKF1FQFgyhzXdQtdA1CURg2F2chQmMLx78O43geGjuWG/+/9aXmh\noE1eD88WeV8HDJ/MI///+KEJDqmVJGutk5+KkI0xZoe8N/2aRjW3SdrJG08Aphs9cACKFkPH8s9a\n+5Ax5lF5/77r5fV8ZnzeBzn3mC68WD2hughYa1sKXQOAmYMAB2THUJgCYuhY4fjDJ3nercCstRsL\nXQMAoPgwhBI4D0NhCo+hYwAAAJnRAwech6EwRYGhYwAAABnQAwcAAAAAAREqdAEAAAAAgMkhwAEA\nAABAQBDgAAAAACAgCHAAAAAAEBAEOAAAAAAICAIcAAAAAAQEAQ4AAAAAAoIABwAAAAABQYADAAAA\ngIAgwAEAAABAQBDgAAAAACAgCHAAAAAAEBAEOAAAAAAICAIcAAAAAAQEAQ4AAAAAAoIABwAAAAAB\nQYADAAAAgICIFLoAAEDxMMbcL6lZUp3ftMla22mM2SxpjaROSbWStlhrOwtUJgAAMxY9cAAASZIx\n5hFJO62191lrN/rN2/zw1mGtvU/SK5I2S3qwUHUCADCT0QMHAEj3vG2z1u4e1fyKpK2SOkcFuvv8\n7Y581gcAADwEOACAJLVYax86r63Z3z4xqm2jpDprbVt+ygIAAKMR4ABghjPG1ErakmHXWn+7M93g\nP/fGs28AABSI47puoWsAABQhY4wrqc1a23zBgwEAQF4wiQkAYBxjzGr/5c4JDwQAAHlFgAMAZLLe\n3zJZCQAARYQABwDIpMXfjuuBM8ZsyHMtAADAR4ADAMgY0zTqda28HrjO8xfr9teEAwAABUKAA4AZ\nzhhzTtJBP7hJ3kLdktSR4fAWa+32/FQGAADOR4ADgBnMD221knZaazv9z5vlrffWlA51xphaY8wj\nyrzcAAAAyBOWEQCAGc4fFrlmVNMWP8xtlhfk0ot2b2UBbwAACosABwAAAAABwRBKAAAAAAgIAhwA\nAAAABAQBDgAAAAACggAHAAAAAAFBgAMAAACAgCDAAQAAAEBAEOAAAAAAICAIcAAAAAAQEAQ4AAAA\nAAgIAhwAAAAABAQBDgAAAAACggAHAAAAAAFBgAMAAACAgCDAAQAAAEBAEOAAAAAAICAIcAAAAAAQ\nEAQ4AAAAAAgIAhwAAAAABAQBDgAAAAACggAHAAAAAAHx/+Cek8X4LEmtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cda4ef0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 288,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.plot(domain, px_class1, label='Class 1')\n",
    "plt.plot(domain, px_class2, label='Class 2')\n",
    "plt.xlabel('$x$'); plt.ylabel('$p(x|C_k)$');plt.legend(bbox_to_anchor=(1.37,1), fancybox=True);\n",
    "plt.title('Class conditional probability - $p(x|C_k)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Marginal distribution of $x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "px = [p_x(x, true_mu1, true_mu2, true_sigma, true_gamma) for x in domain]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qZfgnAewRQpQLIXLUoHUzgNU+qg3sgBLU7tDfIYRYp+aktgHYpjZvFEK0qe1P\n+OuPEGK3EKIeSmAMANuEEPVCiG3+tiOKZk+/eRxdXpOdAGBBSX7U5PT5kp6ahO89sszQ/vKHDTja\n0GJBjygW9Q+48JNnD0BXrhV3r5yB5WWTrOlUgApz0/EHv7fA0P7r1+vQwysPFAPsluMKAJBSbhVC\nbAewHsAaAA1SSp+jpGqwa5p36u++APviK22BKCadv9KB3b/Tjs4kJybge1GaIqC3qLQA9988C698\ndHq4zZMy8E9/djtSk235tUghZJYiUJCThq+bBITR6PMrZ+DDgxfw2anm4bb2zj68+F49vnSXsLBn\nRKOz3Yirh5SyXUq5XUq5lZOhiELn168fx5BuqOnhO+egeGKmRT0K3lfvm2+eMvAaUwbIP+kjReCP\n1i9FemqSBT0KnsPhwLcfXmz4ofnCuydxrbPPx1ZE0cG2gSsRhd6Js2346LOLmrbszGQ8eNtY0r6t\nk5qSyJQBClr/gAv/6CNFoFwUWtOpMZpamIW1N0zXtPX0ufBc9QmLekQUGAauRBSw/3ztmKFt/Zq5\nMTPS5M2TMuDNkzLQN+DysRXFs2d3y5hOEdD70l0CyYnaMOC1jxvR1MolSyl6MXAlooAckFdw6GSz\npq0wLx33rJppTYdCwFfKwG/eMV4Kpvh2/kpHzKcI6OVnp+H3btVWgRx0DeHpN5gyQ9GLgSsRjWpo\nyI1fmoy2Pvr5eUhKjL56lYHylTKwa88JXOGoE6ncbjeeevEIBl3aHIG7boy9FAG9dXfOQUaaNvB+\nt/Y8Tl80LmFLFA0YuBLRqD46dBH157UnsplFE3DbsqkW9Sh0FpUWGHL9+geH8LOXjXVqKT7tPXoZ\ntVK72EZ2ZrJpWalYk5mejMo752ja3G7gPzlRkaIUA1ci8mvQNYRfmVw6/Op982Oi/FUgHr93PjJ0\n67h//NklHDxxxccWFC/6Blymi208fu98ZKbFZoqA3v23liA/O1XTtr+uiRMVKSoxcCUiv6p/dxaX\nmrs0bQtK8lExL7YvkXrLyUrBl++eZ2jf/uJhDLqGTLagePGbd04Z0kbmTMvBmhXTfWwRe1KSnPjS\nXcbPv9lkTCKrMXAlIp9cQ27TCSlfu38+HA57jLZ63HfzLMyYnKVpO9fUiVc+bLCoR2S1K63d2LXH\nWB7qW1801kCNdWtWTMPUQm0t5mOnW1F3utWiHhGZY+BKRD797uhlXNSNtt4wfzLmzcizqEfh43Qm\nYNNDiw3BBygNAAAgAElEQVTtz7wp0Xa914IekdV+9vIR9A9qR9zX3jAdc6fnWtSj8HE6E/CVzxtH\nXV94jxU2KLowcCUin8xGWx++c7YFPYmMRbMLcMuSYk1bT98g/uNVXjKNNwdPXMHHn13StGWkJuLx\ne+db1KPwW7WoGEX5GZq2T49cwsXmTh9bEEUeA1ciMlV3uhV1jdrLhGJGLspm2m+01dvXf28hUpK1\nJb7e3n8O8gwvmcYLl2sI2180Tsj68ufnIScrxYIeRYYzwYEv6FbBc7uBl96rt6hHREYMXInIlNkl\nwodun2273Fa9iblpWL96rqH9F68cg9vtNtmC7KZ63zmca+rQtM2YnIX7bprlYwv7WL1iGrLSkzVt\n1fvO4Vpnn0U9ItJi4EpEBhebO/HpEe1l0sn56Vi5sMiiHkXWQ7eXGlbUOtrQgn3HmizqEUVKb98g\nnnnTWP5t40OL4HTa/5SZmpyIe2+eqWnrH3DhtY8bLekPkZ79/wqJKGgvvVcP/eDig58rhdNmM6l9\nSUp04vF7jLmM//HqMbhYHsvWXvqgHq3XtaOLy8smYfHsiRb1KPLuu3kWkhK14cGrHzWgb8BlUY+I\nRjBwJSKNa519qN53TtOWlZ6M1TfYp25lIG5eUow503I0beeaOgzvDdnHtc4+PP+2NkUmwQF87T77\nTsgyk5uVijuXT9O0Xevsxzv7+dkn6zFwJSKN1z5uRL9uZOXem2ciNTnRxxb2lJDgwB/cb1zS85k3\nj6O3f9CCHlG4PbtboqdPe2xXr5iOGUUTLOqRdR7UTdICgBffO4WhIeZ5k7UYuBLRsL4BF179SFtw\nPykxAffdbP9JKWYWzS7A8rJJmrbW67347ftclMBuLjZ34nVdHmdyktN0RbV4MLUwCzcumKxpu3C1\nC/uOXbaoR0QKBq5ENOyd/edwrbNf03bn8mnIzUr1sYX9fe2++dCn9u56+yRnWdvMr16rg0s3mviF\nz5WgICfNoh5Z76HbjTWbf2NS25kokhi4EhEAwO1249WPThvav/A54yXDeDKjaAJW69al7+kbxI5q\n41KgFJtOnG3Dh4cuatqy0pPx8B1zLOpRdJg/Kw9zp2vzvI+dbsXpi9cs6hERA1ciUp0424bGS9c1\nbSvmT8K0SVkW9Sh6fPnueUjWzbJ+/ePTuKRbDpdij9vtxi9eOWpo//21c5GRlmRBj6KHw+HAg7cZ\nR13f/PSMBb0hUjBwJSIA5ieje+Og4HogCnLS8IBu5HnQ5cYzbx23qEcUKgfkVRypb9G0TcpLxz03\nzbSmQ1Fm1aIiw2ph79ac4wRFsgwDVyJCV88A3j94QdNWkJOGZaLQoh5Fn3V3zjGsKPRe7XmcuXzd\nxxYU7dxuN371hnGxgcfuKUNSotNki/iT6EzAGl2qTFfvID7SpVYQRQoDVyLCewfOo69fWwLrrhtn\nxM2CA4HISEvCuju1OY9uN/D0Gxx1jVWfHrmEU+faNW2ziifg1qVTLOpRdLrrxhmGNqYLkFUYuBLF\nObfbjTc+adS0JTiAtXG24EAg7rtlFvImaC+bfnLYGPxQ9HMNufFrkx8dj95ThgT+YNMoKsjA0jna\nlcPqGltx5hKvNlDkMXAlinMnz7Xj9EXtCWh52eS4LgPkS0qSE+vXCEO72eVmim4fHLyAs5c7NG1i\nRi5W6Or2kuLuVSajrns56kqRx8CVKM69ZXLyMTtJkeKuG2egMFcb1Ncev4KjDS0+tqBoM+gawjNv\nGkdbH7unDA4HR1vN3LigCNmZ2hzvt/efQ59ulT2icGPgShTHunsH8F7teU1bQXYqKjgpy6ekxAR8\n6S7jqOuv36iD283lMGPB2/vPGUqZLZ5dgCW6y+E0IinRZJJWzwAnaVHEMXAlimPvH7iAXt2krLU3\nzoDTya8Gf+6omIYpEzM0bUfqW3DwxFWLekSBGhh04dnd0tD+2D1lFvQmtphP0mqMfEcorvHsRBTH\n9CcdhwNYw0lZo3I6E0zXsP/V6xx1jXZvfHIGV9t6NG3LyyZh3sw8i3oUO4onZmLx7AJN27HTrTjL\nknAUQQxcieLUqfPtOHVeu3RjxbxJKMxNt6hHseWWJVMws2iCpu3kuXbsPXrZoh7RaHr7B/HcHuNS\nvRxtDdzdK42jrm/tPWtBTyheMXAlilNvmdRhNDspkbmEBAce/bxx1PWZN49jaIijrtHotY8a0d7R\np2m7eUkxSqZkW9Sj2LNqUZFhIY63959FPydpUYQwcCWKQ/0DLrx/QDspK29CCksBBemGBZMxd3qO\npu30xev45Mgli3pEvvT0DeL5d05q2hIcwFdMUj7It6REJ1avmKZp6+gewL5jTRb1iOINA1eiOLSv\nrgldvdq1xlevmM5JWUFyOBz4yt3Gy8wcdY0+r3zYgOtd/Zq2z5VPxbRJWRb1KHaZTdJ6t/acBT2h\neMSzFFEc0pfAApSZ8hS8ZWIiynQTe85e7mCZoCjS3TuAF949pWlLSHDgS2uNZc1odNMmZWH2NO2V\nhv11Tejo7vexBVHoMHAlijMd3f2Gy3qzp2Zz5GmMHA4HvmKW6/rWcbg46hoVXv6gAR3dA5q2Oyum\noXhipkU9in13lE/V/P+gy40P+WONIoCBK1Gc+ejQRQy6hjRtt3O0dVwWzy7AwtJ8Tdv5K5344IBx\nZJsiq7NnAC+8V69pcyY48MjauRb1yB5uXTYFCQnaVcberWG6AIUfA1eiOPOuLk0gwQF8bukUi3pj\nDw6Hw7Su63+9JeHS/UigyPrt+/Xo6tGOtq65YTom52f42IICkZuViqVztSuNHTvdiqbWbot6RPGC\ngStRHLnS2o2jDS2atiVzJiJ3QqpFPbKPRaUFWDJHW5z9YnMX3uOoq2U6uvvx0vva0dZEpwPrV3O0\nNRRu16ULAOb580ShxMCVKI6YBVFMEwgds1HXZ986YUjNoMh48b16dOuqZ6y9cQYK87jIRiisXFiE\nlGSnpu3d2nNcPY7CioErUZxwu914R5eDlpLsxKpFRRb1yH7mz8pHuSjUtF1q6cLb+5n7F2nXOvvw\n8gf60dYEjraGUFpKIlYt1H5/nGvqRMOFaz62IBo/Bq5EcaLhwjWca+rUtK1cUIS0lESLemRPX77b\nWGJpx26JgUGOukbSC++eQk+fdjWnz6+agYKcNIt6ZE+3VxjTBfR59EShxMCVKE6YnUzMTjo0PmJG\nHpbrViC70taD6t8Zl9il8Gjr6MUrH53WtCUnJmDdnXMs6pF9LZ0zETmZKZq29w+cZyk4ChtbDrUI\nIXIAbAFQAqAVQB6A3VLK7SHYdxWA+tH2JYQoAVAFIEftRwOAnaHoA1GwXENuwxKv2ZnJhlnBFBpf\nuXse9tdpa+XuqD6B1SumIznJ6WMrCpVdb59EX792tPWem2YhP5ujraHmdCbg1mVT8PIHDcNtrdf7\ncPjUVSydW+hnS6Kxsd2Iqxq01kAJLiullJuklJUAKoUQ28ax33IhxG4AT0AJRv09dg2UoHWDlHKt\nlLIUwE4A24QQNWPtA9FYHT51Fa3X+zRtty6dgkQu8RoWs6flYOXCyZq2lmu9eOPTRms6FEdarvXg\n9Y8bNW0pyU6OtoaRWXWBd2qYLkDhYcez1lMAGkxGNisBbBRCrAtmZ0KIKjXYfARAbYCbbVaD5nZP\ng9qfzQDKxxNAE42F2UmES7yGl1mFgZ17TqK3f9Dk0RQqO/ecNOQT33/zLORkpfjYgsZrzrQcTJmo\nrYv7yeGL/KxTWNgqcFVHW9dBGd3UUIPIagCbgtmnlHKzlLJCSrkZwL4A+rARgGlgKqXcqv7nRrWv\nRGHXP+DCJ4cvadqKCjIwZxo/guE0qzgbNy8p1rS1d/ThtY8arelQHLjS1o03P9XmEqelOPHQ7bMt\n6lF8cDgcuK1c+0O4p89lWFqaKBRsFbgCWK/eNvi4vwHAmjD3YS2AnX5Gdj19Wx7mfhABAA7IK+jp\n04583F4+FQ6Hw8cWFCpfvktA/zY//85JdPcOmG9A4/JctbFm7gO3liI7k6Ot4WaWLvDRZxct6AnZ\nnd0C17Xqra/AtR4YzkGNVF/0POkDHO6iiDA7edzKJV4jYvrkCbhtmfaEfr2rH6/qZrzT+F1u6UL1\n785q2jJSE/HgbaUW9Si+FBVkYPbUbE3b/rompgtQyNktcC1Rb1t93O8JGsvD2IcNUHJZN/u439NH\nX8E1UcgMDLqw9+hlTdu0SVmYNinLoh7Fny/dJZCQoB12/c07p9DVw1HXUHp2tzSUYHrw9tnITE+2\nqEfx56bF2tSYvn4Xao5fsag3ZFd2C1xzgOF8Vn/yw9UBKWW7lHKrWR+EEOVQ+tggpQx0ohfRmB08\ncdWw5OUturxLCq/iiZm4UzcRrrNnAL99v97HFhSsC1c78Y5udbKs9CQ8cGuJjy0oHPQ53QDw8SGm\nC1Bo2a2Oa94o93tGYq26TL9FvQ1qglig6urqwrFb2+np6Rm+tft79tr7lw1tRZm9Ufm67Xxclpc4\n8fZ+wHtA8Pl3TmJO4SAyUqO3rmusHJOn374Efb37WxZk48zpU9Z0KMyi+bgU56fgYstI6b1Pj17E\nZ4ePIinRbuNkWtF8TOzGboFr1FLzatcB2CqlrA7Hc3R3d4djt7bldrtt/Z4Nutw40tihaSuYkIis\nlEF0d7t8bGU9Ox6XVCewrDQDNae6htv6Bobw1v4m3F0e/enu0XxMLrX241CD9nOenpKApTOTo7bP\noRKNx2XeFG3g2j/gxmf1bSibFh+LP0TjMbEbuwWurfA/muoZkR0tlSCk1NJXOwFsV8tqhUV6enq4\ndm0rPT09cLvdcDgcSEuz75epPNeF3gHtMNSSkgnIyMjwsYW17H5c7l6RhEOnGzHoGjkm+0524Y5l\nE5GTkWRhz3yLhWPy7vvGKQ1rluUjNzvTgt5ERjQflwqRiLc/u65pO3GxHxUibBl6USGaj0k0Gk9w\nb7fAFYASKAaQ5xpJOwE8J6UMS4qAR1lZWTh3bxt1dXXo7u5GWlqard+z3Z8dMLR9YfVizCrONnm0\n9eLhuNx/MQEvvjeS2zrocmN/wxD+aH10vt5oPyZH6pshz5/QtE3MTcPXHroRSYnRm4IxXtF8XMoA\n7PywFY2XRoLX4+d7UDp7rq2XO47mYxKNamrGvoio3ZJOPMGqr1xXz2hsxGZFqKtkNYQ7aCXyNuga\nwqdHtIsOFBdkYGbRBIt6RACw7s45SEvRjhdU7zuLC1c7LepR7HK73fjP14y5hF++S9g6aI0F+uoC\nPX2DOHjiqkW9IbuxW+DqyR31lS7guVaxPwJ9gRDiCQDQB61CiBwhBKe7UtgcPtWMjm5tuaWblxRz\n0QGLZWem4It3aFdxGhpy49evczJHsPbVNaGuUZsmMG1SJpcyjgJmlUu4GAGFit0C1x3qra+gsAQA\nIlGKSp2MVepjpHU9fPeRaNzMThI3L2YZrGjwwK0lyM7U1hb98NBFnDofTdlN0W1oyI1fmYy2Pvr5\nMjiddjutxR6zWtF7j1zCwGD0Tgql2GGrv3A1IG2H71Wr1gHYrm8UQpQIIapCNQqq1mut9JMesBYR\nGvWl+ONyDeGTw9o0gcn56SiZEp25rfEmPTUJ61fPNbT/iqOuAXv/wHlNDiUAzJmWg1WLiizqEenp\nfyh39Q7i0Mlmi3pDdmKrwFW1AcB6dSb/MCHERihBrdms/ioAT6i3/nhyZ32uIag+7x61D20m/9wA\n1kXZ5DGykSP1Lbje1a9pu3kx0wSiyT03zcTEXO3M49rjV3C4nif20QwMDuHpN48b2h+/t4yf8Shi\nli7w4aELFvSE7MZ2gauUcheAJwHsEUKUq/mkG6EErKt9BIw7oAS1O/R3CCHWCSFqhBBtALapzRvV\nILTGk8fq5SkoOba+/gEAV82isDFNE+BqWVElKdGJL981z9D+y1ePwe12m2xBHm992ojLLdpSOkvm\nFGDp3EKLekRmpk/OwpSJ2pJknx65jIHBIYt6RHZhy3JYUsqtQojtUHJJ10CZ1e9zlFQNdncFe5+P\nx1cG2V2ikHENuQ1pAoV56Zg9NfqL3MebO5ZPw2/ePYlzTSMVBeSZNnx46CJuXTrFwp5Fr66eATzz\nljS0P37vfAt6Q/44HA7cvKQYz1WPlCvr6hnAZ6euomLeJAt7RrHOdiOuHlLKdinldinlVjX4JLK9\n442taO/s07QxTSA6ORMceOweY73HX756DP0DnMRiZueeE4Y0mFWLijB3eq5FPSJ/zNIFPj1iXIaa\nKBi2DVyJ4tHeo8aTwk2csBK1Vi4swvxZ2rLTTa3deOXDBot6FL0ut3Thpfe174szwYGv3cfR1mg1\ns2gCJudrV3T83dFLGBpiOgyNHQNXIptwu93Yq1t0ICcrhaNRUczhcOAbDyw0tO+oPoFrupHzePfL\nV49h0KXNj7zvllkonmjfpV1jncPhwI0LtD+cW6/3sfQbjQsDVyKbOH+lExebuzRtN8yfjIQEpglE\ns7nTc3F7xVRNW3fvIJ4xmTkfr+pOt+LDQ9pJh5lpSfj9tcKiHlGgblw42dCmX9WPKBgMXIlswuxk\nYHbSoOjz+D3zkZyo/Tp+49MzONfUYVGPoofb7cbPfnvE0P77dwlkpSebbEHRZP7MPGSlJ2namOdK\n48HAlcgm9PmtKclOLJkz0aLeUDAm5qbhoduNS8H+/OWjFvUoenxw8ALk2TZNW1FBBu69aZZFPaJg\nOJ0JWDFf+wP6XFMHLjZ3+tiCyD8GrkQ20Ha9Fyd0J/dyUYiUJKdFPaJgPXznHORmpWja9tc14YC8\nYlGPrNc34MJ/vHrM0P4H9y9AUiJPX7HixgXGKz97OepKY8S/fCIb+N2xy9DXrTc7WVD0SktJxKMm\n5bF+/vJRuFzxWbT9pffqcbWtR9O2sDQfK5kCE1OWiULDDw2zCihEgWDgSmQD+pyxBAewvIxFvmPN\n6hXTMbNogqat8dJ1vByH5bEut3Rhh1fxegBwOIBvPLCQdYljTFpKoiFtqe50Cytn0JgwcCWKcT19\ngzh08qqmrWxWPrIzU3xsQdHKmeDANx5YYGh/+o3jhpFHO3O73dj2wmHDQgx3VEzjKnAxSj9KPuQG\n9h1rsqg3FMsYuBLFuAPyimH9b15KjV1L5xbiZt2KQ739Ljz10mGLehR5nxy+hP112qAmIzWRiw3E\nsBvmT4Z+oHzvUZbFouAxcCWKcWa5Yvqi3xRbNnxhIdJSEjVtnxy+hN/FQV5gd+8Atr9oDNIfv28+\nciekWtAjCoXcCamGxVAOnLiKPi5vTEFi4EoUw1yuIew7pg1mpk/OQlFBhkU9olDIz07Do/fMM7Rv\ne+Ez9PYNWtCjyHnmTYmWa72atrnTc3D3ypnWdIhCRj9htK/fhUMnrvp4NJE5Bq5EMexYYys6ugc0\nbSsXcrTVDu67aRZKp2Zr2q609eDZ3dKiHoVf/fl2vPxBvaYtwQF85+ElcHIFuJhn9t3EVbQoWAxc\niWKYWS1ElsGyB6czAd95eIkhL/DF9+px5tJ1azoVRq4hN376/CEM6cq63X9rCUo5IcsWpk3KwpSJ\n2qtB+441waU/6ER+MHAlilFut9swuSFvQipnXdvI3Om5uGfVTE2ba8iN/7frEIZsdrJ/89NGnDjb\nrmnLm5CKr9xtTJmg2KXPv2/v7MOJM20+Hk1kxMCVKEadberA5ZZuTduNCyYjgZdUbeWxe+cjR7ei\nVl1jK158r97HFrHnYnMnfmGyvO3GBxchPTXJZAuKVTeaVDxhdQEKBgNXohhlVgPxBqYJ2E5mWhK+\n+cBCQ/uvXj+G0xevWdCj0Bp0DeHvn65Fb792dnnFvELctJj52nYjZuQhOzNZ07avjvVcKXAMXIli\nlL7OZUqyE4tnF1jUGwqnzy2bYlgJbdDlxo9+XRPz5YSeqz4BeVZ7qTgtJRHffngJV8iyIWeCAxXz\ntJ/ls5c7cKW128cWRFoMXIliUEd3P+pOt2jals6ZiOQkp0U9onByOBz43iNLDSNV55o68MtXj1nU\nq/E73tiKHSZVEr71xcWYlJduQY8oElbMNy5HzVFXChQDV6IYVHv8imH2tX5EjuwlNysV33tkmaH9\n5Q8aUHv8igU9Gp/u3gH8+Jkaw+f4liXFuKNiqjWdoohYNrfQUN5MX4+ayBcGrkQxSJ8mADBwjQc3\nzJ9sqDIAAP/4bC2udfZFvkPj8NSLRwyTCwuyU/GH65giYHcZaUmYPytf03b4VDN6++29uAaFBgNX\nohjjGnKjRjfCVlKcjYKcNIt6RJH09d9bYKiF2dbRh3/ZeRBud2yUyPros4uo3nfW0P4nXypHZnqy\nyRZkN/p0gf7BIXx2qtmi3lAsYeBKFGNOnGlDR3e/pm25Sc4Y2VNqSiL++1cqDJdaPz1yGTv3nLSo\nV4FrvHQdP3n2gKH9wdtKsWTORAt6RFYwu0K036RSCpEeA1eiGLOvzpgLtoJpAnFlzrRcfNmkMP+v\nXq/Dh4cuWNCjwLR19OKvfvYpevq0l4RnFk3A4/eWWdQrssLUwkxMztdOwNtX1xQzVw3IOgxciWKM\nvn7rhIxkzJmea1FvyCoP3zkHC0ryDe3/8EwtTpyNvpWI+gZc+Jtf/A5X2no07clJTvzZVyqQlMiK\nGPHE4XAYRl2b23tw5nKHRT2iWMHAlSiGXG3rQaNunfryecYZumR/zgQHtnx1haFsVP/gEP7653tx\npS166mK63W7807MHIHVLezocwJ99pRwziiZY1DOy0ooy44IprC5Ao2HgShRD9h835oAxTSB+ZWem\n4C+/cSPSUxM17W0dffirn+1Fd++ART3TeuZNifcPGlMYvnrvfKxaVGxBjygaLCzNR0qydqTdrGIK\nkTcGrkQxRD95ISHBgXJRaFFvKBpMnzwBmx9fgQTdqHvjpev40a9rMOgasqhnirf3n8OzJosMrL1h\nOr54x2wLekTRIjnJiaW6CXnHG1txvavfxxZEDFyJYkbfgAuHTl3VtJXNzGP5IEK5KMSmhxYZ2vfX\nNeGvf74XvX3W1Md8/ZNG/OOztYb2RaUFXNKVABjLYg25gVoZewtqUOQwcCWKEYdPNaOvX7suPdME\nyOPem2bhgVtLDO01x6/gL7Z9bCihFk5utxvP7pb46a5D0E8SLy7IwJavrUBSIk8/xLJYFDx+cxDF\nCNPVsli/lbx8/YGFpuvAyzNt2PwvH6K5vcdkq9AaGnJj+wuH8fQbxw33ZaYl4S+/uRJZvEpAqvzs\nNJQUZ2vaamUTXPq1gIlUDFyJYoDb7cY+XeBamJuG6ZOyLOoRRSNnggM/eHwFVi40ztY+19SB7//z\nBzjXFL5yQwODQ/jx0zV45aPThvtys1Lww+/cjCkTM8P2/BSb9D/AO7oHIM+0WtQbinYMXIliwLmm\nDlxp1ZY3WjF/MnMEySA5yYkfPL4Ca2+Ybrivub0HT/zzB6j+3ZmQF3pvvHQdW376oWn1gKKCDGz9\no1sxSzeyRgQY81wBVhcg3xi4EsWA/XXGyQpmuWFEAOB0JuCP1i9F5eo5hvs6ewbwkx0HseWnH4Vk\n9LW3bxD/8cpR/Mnfv2uo0woApVOzsfW7t2Jyfsa4n4vsac60XEzI0KaPMHAlXxi4EsWAWqn9Ek9O\nTMCi2QUW9YZigcPhwOP3zseGLyw0vf9oQwu+9+N38KvX69A34DJ9zGj21zXhD//uHTz/zinTnMTF\nswvww2/fjJyslDHtn+KDM8GB8nnasn6nL15Hy7Xw52RT7Ekc/SFEZKWevkEcbdDmey2aXYCUJC6R\nSaN74HOlmJCZgn/acQADg9qaroMuN56rPoG39p7BqoVFWLmwCItmF/ic8e92u3GuqQOfHrmMT45c\nwqlz7T6f99alU/CnX1rGpVwpIBXzJuHdmvOatgPyCtbcMMOiHlG0YuBKFOUOn2o2FJHXj04Q+XN7\n+VTMnZaDnz5/CIdONhvub+/ow+ufNOL1TxqRnpqI5WWTMHViJq42t2BgYABJST346MQR7K+7jAtX\nu/w+V25WCjY8uAi3LClmDjYFbNnciXA4oCmfVnOcgSsZMXAlinJmy7wun8f8VgpO8cRM/NWmm/Be\n7Xn8+2+P4FqneV3X7t5BvH/AOMEKaPG7f4cDuGfVTDx273xkpiWFoMcUT7IzUzBnWg5OnB0ZxT9w\n4ipcriE4ncxqpBEMXImimNvtRs1x7cSsyfnpKCrgRBcKnsPhwO0V01BRNgm/fPUY3vz0TEj2O7No\nAr5buQRiRl5I9kfxqVxM0gSuXT0DOHG2HWWz+LmiEQxciaLYhaudhjJYFfMm8RIsjUtWejK+W7kU\n96yaiXdrz+OTw5fQpPucjSY12YmKskm4eVExblpcxFExGreKskI8u1tq2mqONzFwJQ0GrkRRrPa4\nsQwW81spVEqn5qB0ag6+/nsL0HjpOj49fAmfHLmE0xevmz4+OzMZN8yfjJWLirB0zkQkc4IghdCc\nabnISk9CR/fAcFuNvIJH7ymzsFcUbWwZuAohcgBsAVACoBVAHoDdUsrtIdh3FYD60fYVzj5Q/NCn\nCSQ6E7C4lGWwKLQcDgdmFWdjVnE2vnT3PPQPuDDoGoKUEt09PUhPS4MQAmkpiRztp7BxJjiwbG6h\nZhGLU+fa0d7Rx5JqNMx213bUgLEGSnBZKaXcJKWsBFAphNg2jv2WCyF2A3gCQI4VfaD40jfgwpF6\n7QzwhSX5SE2x5e9NiiLJSU6kpyYhNdmJ1KQEpCYr/8+glcLN7IrSgRPGK08Uv2wXuAJ4CkCDychm\nJYCNQoh1wexMCFElhKgB8AiAWiv6QPHp8Klm9OvqblaUMU2AiOzLLHCtMVk5kOKXrQJXdaRzHYCd\n+vuklO0AqgFsCmafUsrNUsoKKeVmAPus6APFp1ppkt8qGLgSkX3lZqWidGq2pq1WXjFdmY3ik60C\nVwDr1dsGH/c3AFgTB30gG6jRrdVdkJOGaZOyLOoNEVFk6H+gd3T3o/6871XaKL7YLXBdq976Chrr\nAcQarCgAACAASURBVEAIEc7AMRr6QDHuUnMXLjZrVyiqmFfIHEMisr0KkwVW9BNVKX7ZLXAtUW9b\nfdzv+clWbvM+UIyrNVktq4JlsIgoDsybkYuMVO0k1BqT70SKT3YLXHOA4VxSf/Jt3geKcTW6/FZn\nggNL5ky0qDdERJHjdCZg6VztD/WTZ9twvct8mWKKL3YLXEdbXsMzCuq3nJUN+kAxrH/Ahc9Oactg\nlc3KQ3oq138novigry4w5AYOsiwWwaYLEMSruro6q7sQE3p6eoZvo/E9O3mhC339Lk3btDxHVPY1\nlKL9uMQjHpPoFA/HZYJzwND29t6TmJjaYUFvRhcPxyRa2C1wbYX/kUzPaGg4pyda1ofu7uDWGo93\nbrc7Kt+zI6evGdpmFCREZV/DIVqPSzzjMYlOdj4uSQ6gMCcJV9pHAtjj5zrR1dUV1ZNU7XxMooXd\nAlcASi3VAHJMbdeH9PT0SD5dzOrp6YHb7YbD4UBaWprV3TE43aS9HJaV7sSs4uyo/rIOhWg/LvGI\nxyQ6xctxKZuWiSvtbcP/39U7hGu9iSjOj77lX+PlmITKeIJ7uwWunkAxD+Yjmp6R0Ho79qGsrCzU\nu7Sluro6dHd3Iy0tLeres5ZrPbjcdkLTtmJ+MebPn29RjyInmo9LvOIxiU7xclz6nQV47/DHmrb2\n/gysLptjUY98i5djEio1NTVj3tZuk7Oq1Vtfl+o9M/n327wPFKMOyKuGNq6WRUTxaH5JHlKSnZo2\nsxUFKb7YLXDdod6W+Li/BACklLU27wPFqAO6L2WHA1g6l2WwiCj+JCU6sai0QNN27HQrevsGLeoR\nRQNbBa5qMNiOkdWr9NYB2K5vFEKUCCGqhBC+gs2w94HINeTGgRPaEdfSKdnIzoy+fC4iokhYpvvh\nPugawpGGFot6Q9HAVoGragOA9UIIzaV6IcRGKAHlZpNtqgA8od7646kIUBqGPlCcqz/fjo5ubYHt\nZUwTIKI4ZvYdyHSB+Ga3yVmQUu5SR073CCE2AGgAsB5KsLjax0z/HQDWYOQy/zAhxDoAW6Bc4vcE\nohuFEOvVfe+QUm4NQR8ozh0wKa7N/FYiimdTCzMxMTcNV9t6httqjzNwjWe2C1wBQEq5VQixHUqw\nuAZAg5TS5yiplHIXgF3B3hfKPhDpJ2alpSRi3szRFmIjIrIvh8OBclGINz89M9x24WonrrR2ozCP\nJSDjkS0DVwBQRzUtzSWNhj5QbOjuHcDxxlZN2+LZBUh02jGbh4gocMt0gSugpAt8ftVMazpEluJZ\nkSgKHDrZDNeQW9PG/FYiImDJ7AIk6NZfMUutovjAwJUoCujLYAHMbyUiAoDM9GTMnZ6raTt04ipc\nriGLekRWYuBKFAX0owdF+RkoKsiwqDdERNFF/0O+q3cQJ85ynnM8YuBKZLGLzZ243KJdt3mZ4KID\nREQey+axLBYpGLgSWeyASWkXpgkQEY2YMy0XGWlJmjazFCuyPwauRBar1ZXBciY4sGh2gY9HExHF\nH2eCA0vnaK9EnTzXZli0heyPgSuRhQYGh3C4Xhu4zpuZh/TUJB9bEBHFJ32llSE3cOjkVR+PJrti\n4EpkoeNnWtHT59K0MU2AiMjI7LuRq2jFHwauRBZiGSwiosBMzE3DtEmZmrYD8grcbrePLciOGLgS\nWUgfuE7ISEbJlGyLekNEFN2WzdX+sG++1ovzVzot6g1ZgYErkUWudfah/sI1TdvSuRORoF8ihoiI\nAJivKMhVtOILA1cii3x2shn6K1z60QQiIhqxsCQfiU5t6HJAcoJWPGHgSmQRs1ECLjxARORbakoi\n5s/K07Qdrm/GwKDLxxZkNwxciSzgdrsN+a3TJ2chPzvNoh4REcUGfbpAX78LxxvbLOoNRRoDVyIL\nnL/SieZrvZo2pgkQEY1u2VzjlSnmucYPBq5EFjArg7XU5MuYiIi0ZhVnIzszWdPG5V/jBwNXIgsc\nOKGdTJDoTMDCknyLekNEFDsSEhxYolv+tf7CNVzr7LOoRxRJDFyJImxg0IXD9c2atvmz8pCakmhR\nj4iIYos+tcrN5V/jBgNXogira2xFX792BqxZbUIiIjJnVoGFZbHiAwNXoggz+3I1m2xARETm8rPT\nMH1ylqbtwAku/xoPGLgSRdhB3ezX7MxkzCrmMq9ERMHQpwu0cPnXuMDAlSiCTJd5nVPIZV6JiIJk\nni7A6gJ2x8CVKIIOnbxqXOaVq2UREQVtgdnyryeY52p3DFyJIsgsv5X1W4mIgpeanIgFJVz+Nd4w\ncCWKELfbbVjdhcu8EhGN3dK5xuVf6xpbLeoNRQIDV6IIOdfUgRYu80pEFDKmy7+yLJatMXAlihCz\n3CvmtxIRjZ3p8q8nOEHLzhi4EkWIfrZrojMBC7jMKxHRmCUkOLB0jvbKVf15Lv9qZwxciSJAWea1\nRdM2f1YeUpO5zCsR0XiYXbk6yOoCthW2s6YQYimANQBWACgBkAMgT70FgHYADeq/fQCqpZQHw9Uf\nIivVNbaif0A707Wcy7wSEY2bWWWWgyeu4rbyqRb0hsItpIGrEGImgE0ANkIJUB0YCU5PA2iFErB6\nB7GlACoBuIUQ7QB2AKiSUp4JZd+IrGS6zCsDVyKiccvPTsOMyVk4c7ljuM2z/KvDwcVd7CYkgasQ\nYgKArVAC1moAfwtlBPVAEPsoB7AawFoADUKInQA2SCk7/G9JFP30kwWyM5Mxs2iCRb0hIrKXpXML\nNYFry7VenGvqwPTJ/J61m3HnuAohHgbQCMANoFRKeZeU8kfBBK0AIKWsVbe7C8AcANcANAohHhpv\nH4msdK2zD/XnucwrEVG4mC7/yjxXWxpX4CqE+Fsoo6yzpJTfllKeDkWnpJQNUspNUNII/ocQ4oeh\n2C+RFcwmCbAMFhFR6Jgt/8oJWvY05sBVCLEBQIuU8m4p5bVRNxgDKWW7lHI5gAQhxDfD8RxE4Wb2\n5cllXomIQofLv8aP8Yy47pdS/ihkPfFDSvkDADWReC6iUOIyr0REkcHlX+PDmAPXYHNYxyvSz0cU\nClzmlYgoMrj8a3zgAgREYcRlXomIIsNs+deDXP7VdsIauAohsoUQTwoh7gjn8xBFKy7zSkQUGabL\nv17g8q92E+4R1yoAmwFUq4sTaAghHhZCfDHMfSCyxMCgC0catMu8LijhMq9EROGiv6LldgOHTjJd\nwE7CHbi2Q1kVaw+UVbM0pJTPA8gXQuwwC2yJYlldYyv6+rUzWvWTB4iIKHR8Lf9K9hHuoZ9sNTh9\n3tcDpJRPAXhKCPFvQoi/lVI2jvdJhRA5ALYAKIESMOcB2C2l3B6p/anbVKmPBZTlbXdLKbeOpQ8U\ne0yXeWUZLCKisMnPTsP0yVk46738q+Tyr3YS7hHX2iBSATar/8ZFDRhrANRLKSullJuklJUAKoUQ\n2yKxP3WbnQCq1G0qpZRr1ftY1itOmC3zOqs426LeEBHFB33lluZrvTh/pdOi3lCohTVwVUdTPakA\nDwkhfC4aHMJFDJ4C0GAyGloJYKMQYl0E9rcTQKWUssG7UR1t3S+EqAqyDxRjuMwrEZE1TJd/lawu\nYBfhriowAUqAVwlgF4A2IcRJIcS/CiG+6B3Iqv9dMs7nywGwDkrgqCGlbAdQDWBTBPa3XL3fzE4A\nawLtA8Ums8kAXC2LiCj8zJZ/NStNSLEp3KkC/w5lgtZmKCOXBwGUQgn2dkIJZFuEECcBtMEkQAzS\nevW2wcf9DQguaAx6f0KIcgA5atBLcco0v5X1W4mIwi41ORHzZ3H5V7sK+wIEUsr1UsofSSm/JaWs\nkFImAKgA8AMAbwPIhTLSWiml/PdxPt1a9dZXoFkPAEKIQIPXsezP89g9PoLXtVBGasmmuMwrEZG1\nlgku/2pX4Q5cTT8lUsoDajC7FkrgugXAWn85sAHypBr4+nR6Lt+Xh2t/aorALrXttHcOrDoau0ZK\nOe5JaBS9zJZ5ZZoAEVHkcPlX+wp34FovhFjq7wFSymvqpKUtUMpHjUeOuk9f+aUegS5dNNb9bQBQ\nq26/UwixUwixEcprXB3gc1OMqjX5ciwXrN9KRBQpZsu/6q+EUWwKd1WBHwH4lhDiTn+PE0JMUIPD\n8U65zhvlfs/IaaD5p2Pan5SyXUpZAcBTiWAdgG0AtgUQBFOM0385JiVymVciokgyXf71PJd/tYOw\nrz0ppfyWEOL7QojNADZLKQ963y+EmAXglBCiGr5zSWOOmvdaAmVi2haoCxAIIbaGK1Wgrq4uHLu1\nnZ6enuHbUL9nA4NDOKyrKDCzMBWn60+G9HnsKJzHhcaGxyQ68bgEZvKEQUPbq+8cxLLZ481KNOIx\niZyILJqujrz+SAhhqL4upTwthLgOZdLSxnE+VSv8j6Z6RlADHfUc0/7UtADvRQe2Q6mqsA7AE0II\nhCN47e7uDvUubc3tdof8Pau/3IsBl1vTNrMwiccmCOE4LjQ+PCbRicfFv6l5xou4x85chygOX+jD\nYxJ+EQlcPXwtMiClzBVCZIdqEQIhRE4oL8kHsz91AlYVgFmeNnXbSjWg3QYleN2mX6BgvNLT00O5\nO9vq6ekZXv4vLS20M/3PXu0ytC2clYP09JSQPo8dhfO40NjwmEQnHpfApKcDk3NbcLmtf7itoakP\naWlpIV/+lcckOOMJ7iMauPoToqDVE1zmwXxU1TN6Wh/G/W0BsN0s0JVSbhdCNADYDaX+q341rnEp\nKysL5e5sq66uDt3d3UhLSwv5e/avr13W/H9OVgruuHkJ18gOQDiPC40Nj0l04nEJ3KolQ3jh3VPD\n/9/R7UJ67lTMLAptugCPSXBqamrGvO2YJ2eFoHRVOJ7PUx/V1+V9zwyZ/QE+7Vj2twbAPl87lFJW\nQ6k4UBpgHyhGtF3vxemL1zVty+ZOZNBKRGQR87JYrC4Qy8ZTVeDPR6sWECrq82wJ4KE71FtfS8eW\nAICUsjbApx7L/howejWCBgQ+6ksxwmxJQZbBIiKyzvySfCQn6pZ/ZeAa08YcuEopfwDgB0KIH4aw\nPwZCiL+FUo1g1MBVDSDbMbLild46mFyeF0KUCCGqhBCaAHWM+6v283iPcnD1LNsxqxG4hAsPEBFZ\nJiXJiYWlBZq2ow0t6Bvg8q+xalx1XKWUdwHIF0KcFEJ8I0R9AgAIIb4ohDgJIFtKeXcQm24AsF6/\n3Ko6MaodSnkqvSoAT8B8AYRg9/ckgHL1fgMhxDYAVaGemEXWGhpy46BuxLWkOBu5WakW9YiIiABg\nmdAOIPQPDuFoQ4tFvaHxGvfkLCnlJrVm6b8JIbZCmTW/Q0p5KNh9qatsPQKlLFYrgG9JKfcE2Z9d\n6sjpHiHEBiiX5ddDCTBX+6gOsANKbuoO/R3B7k9K2S6EWAtgmxCiEsBOdZsSAJUAdkopQzopi6zX\neOk62ju0ha31X5ZERBR5y+YWAjiqaTsgrzCVK0aFpKqAOuFothBiHQBPCoEbyiSk/VBGJlvU21Yo\nOaA5UCY35QBYDuXyOQAcAPADKeVT4+jPVrV26nooAWmDlNLnZCgp5S4Au0K4vwYAa9WAt1z9Vwul\ntitXzrIhs5ypZfxSJCKy3PTJWcibkIrW673DbcxzjV0hLYflCQDV1bDWQskBfQT+i/g3qP9+AGCX\nlPJ0iPrSjhCWmxrL/tQAlikBcUCf35qS7MT8WaPN0SMionBzOBxYJiZiz75zw21nLneg5VoP8rNZ\nczXWhKWOqxp8bodXoKcGs4ASxLaHKkAlslpv3yD+f3t3Hhzlfed5/NO6QEIgIYn7loAftwFh7PiI\nYwPO6cwkAWYyx25NsobsTG3V1EyVWe/fW+XCU7W1NXtMGWenZqpmNutAMskkk8QBx/EZ2yBuLH4c\nMvchQIhLErp6/+hHwNP9tNQS3f0c/X5Vpdr8uvvRN3qQ+PTv+T3f35GWNtfY0oY6lZYU+1QRAOBB\nK+ZPdAVXSdpnr2jt6pk+VYSRytsGBARVRNXhlmvq7et3jXn1DgQA+GP5/AmKxaT4Azty7zvWSnAN\noYfqKgDAuw0W61sBIDiqKkepYVqVa2z/sSvq74+neQeCKi8zrk63gFVK7BZ1TdJea+1v8vG1gVxL\nXuRfV12u6RMrfaoGAOBlhZmoE+fu7y5/8063Ws7f0NwZg92Gg6DJ+YyrMeaHkpqUWO+6RYleqTuN\nMb3GmL/O9dcHcunK9U6dvXzbNcY2rwAQPIm2WG576S4QOjkNrs6uV9WSvqdED9Mtkn4k6TPna/+N\nMeaqMebZXNYB5IrXL72VC1gmAABBs2B2jcpHuW+aJbiGT66XCtQ7u2ulcLoMbJC0WdIuY8x6a+2/\n5LgeIKv22suuPxfFpOXzuDELAIKmtKRIy+ZO0MdHLt0bO3qqTR1dPaoYXepjZRiOXC8VaEv3hLX2\nM2vtq04j/5eV6P86K8f1AFnT19evA0nbvM6fOV6VFWU+VQQAGEzyjbN9/XEdOH7Vp2owErkOru3G\nmHFDvcha+6qkL0p6Ncf1AFljz1zXna5e1xhbCAJAcDV6LOViuUC45Dq4vqLEzVhDcraN5Y4WhMbe\no6xvBYAwmVw7RlPqxrjG9h69rHictlhhkdPgaq29IWmbMWZ3hjdg8TcHoZH8KX1sRanmzhjvUzUA\ngEw0Jl0Za73eqfNXbqd5NYImpzdnGWPWSNrp/HGXMaZd0h5nbJe1dv8Dr/2WEt0GgMC7cfuuTpxr\nd40tnz9RxUVcNACAIFuxYKJ+/oE7buw92qrpE8f6VBGGI9ddBbYq0QJLSmw+sFbSOud/cWOMJO2S\nVK9EkP2PXgcxxrxprf1ijmsFMrb/2BUlX1laaegmAABBt7ShTiXFRa6tuvfaVn398w0+VoVM5Tq4\n7rHW/s2DA8aYKiV20Xpe94OsJDUYYzZJ2qv7s7JN1trTzuuAwPBazM82rwAQfOWjSrRoTo0Onrjf\nTeDQyWvq7ulTWWnxIO9EEOQ6uO40xrwi6TVr7Snp3rrXt5z/SZKMMSuUCKfPS1ojqVHSJue5HJcI\nDE9/fzwluM6eMk61VeU+VQQAGI7GBRNdwbW7p09HWq4xARECub4560dKbPX6PWPM3xljvpnmdfus\ntX9jrV1nrS1SIrh+T9KPRacBBMypizfVfuuua4w2WAAQHisXTEoZoy1WOOR6xlXW2s8k/edhvmef\npH2SXjfGVGuQjQyAfPPc5pXgCgChMWvyWNWMG622m133xvbaVn3Xx5qQmVz3cX1o1tp2STv8rgMY\nkNy/dVRZsRbV1/hUDQBguGKxWMqEw5lLt3TleqdPFSFTgQ+ukmSt3eh3DYAkdXT1qPnUNdfY0oY6\nlZawoB8AwsTrStm+YywXCLpQBFcgKA6duKrePncfLK8tBAEAwfbI/AlKbr3ttSMigoXgCgwD61sB\nIBrGjSnTvKTdDvcfv6K+B/q7IngIrsAwJAfXybUVKfteAwDCYWXSFbM7nT06dqY9zasRBARXIEMX\nrtzWpWsdrrEVZqJiMTq2AUAYeV0xazp62YdKkCmCK5ChPc2pv8waWSYAAKE1b+Z4VZaXusYIrsFG\ncAUy1JS0aL+kuEjL5k3wqRoAwMMqLoql7JZ14twNXb/VleYd8BvBFchAV3evDp286hpbUl+r8lE5\n38MDAJBDqxZ6tMViF63AIrgCGTh04qp6et13mjZ6/LIDAIRL8oyrJO1pJrgGFcEVyEDyMgFJavTY\n6xoAEC7jx47W3BnVrrF9tpW2WAFFcAWGEI/HUxbrT6yp0PSJlT5VBADIpuSNZG7TFiuwCK7AEM57\ntMFqXEAbLACIilUeV9D20F0gkAiuwBC8lgmsWsgyAQCIinkzx2tsBW2xwoDgCgyhKal/a0lxkZY1\n1PlUDQAg27zaYp08d0PXb9IWK2gIrsAguu726tDJa66xpQ21Gk0bLACIFK8raV5X3OAvgiswiIMn\nr6q3L7kNFssEACBqVpqJSr51geUCwUNwBQbhuc3rAvq3AkDUVFWO0tzpSW2xjl2hLVbAEFyBNBJt\nsNyXiSbXVmjaBNpgAUAUJS8XuNPZo6Onr/tUDbwQXIE0zrXeVmtbchusSbTBAoCI8rqixnKBYCG4\nAml4/bKiDRYARNfcGeM1bkyZa6yJ7V8DheAKpJH8y6q0pEhLGmp9qgYAkGvFRTGtTGqL1XLhhtpo\nixUYBFfAQ+fdXh1uSW6DVafRZbTBAoAo81wu4HGjLvxBcAU8HDh+xaMNFt0EACDqVni0xWL71+Ag\nuAIedn/qsb7VYy9rAEC0VFWO0vyZ411j+2yrenppixUEkbzuaYyplvSypHpJbZJqJO201m7L9/GM\nMZskbZDU7gy1WGu3jKQO5Ed/f1x7mi+5xqZNqNRU2mABQEF4dNEk2QfaYHXe7dORlqtaPp8rb36L\n3IyrEzKbJJ201m6w1m621m6QtMEY81q+jmeMqTbGNElqtNauc967QdLukdSB/Gk5f0NtN++6xh5d\nxGwrABSK1Ysmp4x5XYlD/kUuuEp6XYlZzeTZ0A2SNhlj1ufpeG9J2mOt3Tww4ITg7ZI2DrMG5NHu\nTy+ljHn9EgMARNPsKeNUVzXaNfbJp5cUj8d9qggDIhVcnWC4Xolw6GKtbZe0S9Lm5OeyfTxjzEuS\nVkra4vGeFud9CKhPku4eHTO6RAvn1PhUDQAg32KxmB5NmrC4dK1D51pv+1QRBkQquOr+TGZLmudb\nJK3Nw/FelrTDCaou1toGZ8kAAqjtZpdOnHWftpULJqmkOGo/KgCAwXgtEWO5gP+i9q/xOucxXdA8\nKUnGmEzD67CP5ywdqJa0O8OvgQDx6tXH+lYAKDxL59aprMQdk/bQz9V3UesqUO88tqV5fmAqbaUy\nu1w/kuMNhN29xph63V9KUK3EDV6vZvB14ZPdSb+UimJK2UUFABB9o8tKtGzeBFdYPfLZNd3u7FFl\neamPlRW2qM24Vkv31pIOJtN9O0dyvFUPvHeztXaL87/Nkh41xuzM8Gsjz3p6+7TPurd5NbNqVFU5\nyqeKAAB+Wp10xa2/P659R1vTvBr5ELUZ16HuoBmYOa3O4fEGZmn/wGMt64uSrhtjtuail2tzc3O2\nDxlJnZ2d9x4f/J4dO3dHXd19rtfOnlDE9zVP0p0X+IdzEkycl/ypLu1JGdv1kVXd6JuuMc5J/kQt\nuAZJyrpYa227MWaXpJeMMa9kMJM7LB0dHdk8XOTF43HX9+xgy42U18yeUMz3Nc+Szwv8xzkJJs5L\n7pUVSZOqS3W5/X6AbT5zR7dv31FRUSzl9ZyT3ItacG3T4LOpAzOomQbGhzleupuzBgLtWkk7Mqwj\nIxUVFdk8XGR1dnYqHo8rFoupvLxcUuKXzYmL7vWt4ytLNHvKOMWSN61GTnidF/iLcxJMnJf8Wjx7\nrC7vv3+rS2d3v67eLtLsyfe/95yT4XmYcB+14Cop0X81m7OZwzzeQNhN9/qB8fo0z4/YwoULs33I\nSGpublZHR4fKy8vvfc/OXLqptlvHXa974pEZWrRokR8lFiSv8wJ/cU6CifOSX7GKNv1m/3uusdaO\n0fryA997zsnwNDU1jfi9Ubs5ayAUplubOjB7ejKHx0vXOitZpjeIIQ+8evPRBgsAMG/GeFVVlrnG\nvHZYRH5ELbgOtKRKd3l/ICzuyeHx9g7xngGZhmfkQXIbrFFlxVraUOdTNQCAoCguiqlxgXsi4/Sl\nW7rcxlpWP0QtuL7hPKa7DF8vSdbavWmez8bxMnqPMg/PyLFbHd1q/uyaa2z5vAkqKy32qSIAQJCs\nTtr+VZL2MOvqi0gFVydAtuv+JgDJ1kvaljxojKk3xmx1Ngx4qOM572kZ5D1rJe0aRnhGjjU1X1Z/\n3D2WvEc1AKBwrTATVJzUReATtn/1RaSCq+NFSRuNMa5L9caYTUqEUK/+qVslveQ8ZuN4myWtTd5a\n9oHtYDd7vAc++ehI6qfmVQvZLQsAkFAxulRLGty3phw8cUUdXal9XpFbkesqYK3d4cycvmWMeVGJ\n2c+NSgTMNWm6A7yhxEzoG8lPjOR41tpdxpgNkrYbY15RYt3rOiVmaButtZnewIUc6+nt096j7k/N\n82ZUq7aKdiYAgPtWL56sA8ev3vtzb19cTc2tenrFNB+rKjxRnHGVtfZVSWuU2H51k6Q2a21Dusvz\n1tod1trx1lrPvqrDPd7AMSXNUSLorpT0xlDvQf4dOH5VnXfdu2U9toRlAgAAt8cXT0kZ++jIRR8q\nKWyRm3Ed4MyEpqxnzefxnPdkdZMBZNfHHssEHl+S+ssJAFDYJtZUqH5qlVou3N9lsan5snr7+n2s\nqvBEcsYVyER/PK5Pkj4tT6kdo5mTxvpUEQAgyJKvyN3p6tXhk1fTvBq5QHBFwTp3pUttN++6xh5b\nMpktXgEAnh5bnLqU7OPDtMXKJ4IrCtaR03dSxrx+KQEAIEn106o0Ybz75t2PjlxSPB5P8w5kG8EV\nBevT07ddfx5bUaaFs9Pt7gsAKHSxWEyPJfX5vtreqfPX7qZ5B7KN4IqCdO1mjy63d7vGVi+epOJi\nfiQAAOl53cCbPBGC3OFfaRSko+e7UsYe82h1AgDAgxY31GpMealrzGvpGXKD4IqCZM91uv5cVlKk\nFfMn+FQNACAsSoqLtGrBJNfYxba7un6716eKCgvBFQXndmevzl51LxNYPn+iRo+KbFtjAEAWeW1U\nY893erwS2UZwRcFpPntHyTeAslsWACBTjQsmqqTY3Trx6LnUJWjIPoIrCs6RU+5F9LGYtHoRwRUA\nkJmK0aVaNs+9vOx06111dPWleQeyheCKgtLV3avj5ztcYwtm1ah67CifKgIAhNHjSX2/43Hp6Flu\n0so1gisKyv5jV9TT514n8DjLBAAAw7TaY8OaI2doi5VrBFcUlN8dupgy9phHTz4AAAZTW1WueTOq\nXWP27B11ddNdIJcIrigYPb39+viwO7jOmDRW0yZU+lQRACDMPrfUPfHR3RvXPtvqUzWFgeCKYwxP\nygAAH2RJREFUgnHwxBXd6XJ/En5iGbOtAICReWLZ1JSxDw+mXtlD9hBcUTC8fpk86fFLBwCATEyb\nUKnZU8a5xj759JJ6eukukCsEVxSEvr5+fZS0TKB2XGnKLxwAAIbjiaTlAh1dvTpw/KpP1UQfwRUF\n4XDLNd28494ta+nsSsVisTTvAABgaF7LBT44cMGHSgoDwRUF4cODqb9Els4Z60MlAIAomTl5rCZU\nlbrGPj5yUb19/T5VFG0EV0Ref388pQ1WVUWxptex6QAA4OHEYjEtne2eCLnV0aPDJ1kukAsEV0Re\n86k2Xb911zW2cEY5ywQAAFmxZE5qW8UP6C6QEwRXRN6Hh1KXCSyaWe5DJQCAKJpWO0rVY4pdYx8d\nuqi+/niad2CkCK6ItHg8dZnA2IpiTa8r86kiAEDUxGKxlAmR9tt31fzZNZ8qii6CKyLt+Nl2Xbne\n6RpbMqtSRSwTAABk0cIZqVfyPvTYZhwPh+CKSKObAAAgH6bVlqmqosQ19uHBC+pnuUBWEVwRWfF4\nPGW3rHFjyjRnMutbAQDZVRSLpdykde1Gl46dve5TRdFEcEVknbp4Uxev3XGNPb5kioqLWCYAAMi+\npbNTuwt4bTeOkSO4IrK8di55YtkUj1cCAPDwZk8qV3Wlu0f4BwcvKB5nuUC2EFwRSfF4XO/uP+8a\nG1NeqmVzJ/hUEQAg6oqKYvrcUvcESWtbh46dYblAthBcEUknz93QxavuZQKfWzJFpSX8lQcA5M5T\ny6emjCVPpGDk+FcckeT1S+LpFdN8qAQAUEgW19dp/Fj3coH3959nM4IsIbgicvr743ovKbhWVZbp\nkbl1PlUEACgUxUUxPbXcPVHSdvOuPmUzgqwguCJyjp5u09V296YDTy6bquJi/roDAHLv8x5X+N7d\nx3KBbOBfckTOex6/HD6/YroPlQAACpGZOV4Tx7t7hn9w4IJ6+/p9qig6CK6IlL6+fr2f1Aarrmq0\nFs6u8akiAEChicViejppucCtjm4dOH7Fp4qig+CKSDl08qrab991jT21fJqK2HQAAJBHXlf6WC7w\n8AiuiBSvXwpea40AAMilOVPHadoE905aHx2+qO6ePp8qigaCKyKjp7dfHx5yb603pXaM5k6v9qki\nAEChisViKRMnHV29ajp62aeKooHgisjYd6xVdzp7XGNPr5imWIxlAgCA/Ete5yqxXOBhEVwRGZ7d\nBDx+aQAAkA8zJo1V/dQq19gnn15W591enyoKP4IrIqGru1cfH3EvE5g1eaxmTRnnU0UAAKTu2tjd\n06dPjlzyqZrwK/G7gFwwxlRLellSvaQ2STWSdlprt/l5PGPMa877doykDqS3p/myOu+6F7yzxSsA\nwG9PL5+mf/y3T11j7+47r2dW0l98JCI34+qEzCZJJ621G6y1m621GyRtcIKjL8czxqyUtGm4Xx+Z\n8Voz5LW2CACAfJpUUyEza7xrbK+9rJt3un2qKNwiF1wlvS6pxWM2dIOkTcaY9T4d7/Vhfl1k6Oad\nbu3+1H3ZZe6Mak2tq0zzDgAA8if5fovevrjeP8BNWiMRqeDqzI6ul7Q9+TlrbbukXZI25/t4xphN\nkvZk+nUxPO/tP6/evrhr7NlGLsEAAILh6RWpG+H8Zs9Zn6oJt0gFV0kbnceWNM+3SFqbz+M54bdB\n0s5hfF0Mw9tJP/zFRTF9fjnBFQAQDOPHjtZKM9E1Zk9f1/krt32qKLyiFlzXOY/pguZJSTLGZBpe\ns3G8rZJeyfDrYZjOtd6SPXPdNda4YJKqx47yqSIAAFI9t2pGyljyxAuGFrXgWu88tqV5vt15XJmP\n4zmBtslZVoAceLvpXMqY1y8HAAD8tHrxZI0Z7W7m9HbTWfX3x9O8A16iFlyrpXvrTwdTm6fjbRhp\nCy4Mrb8/rreb3J9Wx5SX6tFFk3yqCAAAb6NKi/VU0k1ardc7deSzaz5VFE5RC641Qzw/MHOa6eb1\nIz6eMeYlJZYJIEeOtFzTleudrrGnl09TWWmxTxUBAJDes40sF3hYkdyAwG/GmHpJtdbadGtjc6K5\nuTmfX853P343deeR+rq+Ib8PnZ2d9x4L7XsWZJyX4OGcBBPnJXgyPSexeFw1Y0vVdqvn3ti7+87p\nmUVlKiuJ2lxibkQtuLZp8NnUgRnUTNecjvR4W6y1GbfdypaOjo58f0nfdPf262DLLdfY+MpiTajs\nz/j7EI/HC+p7Fhacl+DhnAQT5yV4MjknS2eN1juH7wfXuz392nesTUtnV+S6vEiIWnCVlGhBlc0b\nooZzPGdDAl9aX1VUFM5f+qMnbqq7172gfdX8ao0ZM2bI93Z2dioejysWi6m8vDxXJWKYOC/BwzkJ\nJs5L8AznnDy+qETvHHZPvBw606XHFtXlssRAeZgPXFELrgPhskbes6oDs6cnc3i8dX7MtkrSwoUL\n/fiyvvjBux+mjG380gpNrh06uDY3N6ujo0Pl5eUF9T0LOs5L8HBOgonzEjzDPSf/+slNNZ+637Do\nxPkOTZw6W7VVhfFBpKmpacTvjVpw3aVEa6p0l/cH7v7PdBerYR3PaX+11hjjdUYGWmttNca8LEnW\n2sYM68ADrt3o1IHjV1xji+trMwqtAAD47blVM1zBtT8uvbP3vL757FwfqwqHqAXXNyS9pERI3Ovx\nfL0kWWu9nnvo41lrdymxS1aKB7oMbLHW7sjw68PDO3vPKbntndedmgAABNFTj0zVtp8cUk9v/72x\n3+w5o298oUGxWGyQdyJSt7A5AbJd93e8SrZeUkpfVWNMvTFmq9MN4KGPh9yJx+PatdvdOqS0pEhP\nPTLVp4oAABieyooyrV482TV2+tItnTx3w6eKwiNSwdXxoqSNxhjX5X1jzCYlQugWj/dsVWJm1avv\n6kiO52VgWcFQvWExiKOnruvsZfei9seXTNGY8lKfKgIAYPi8dnn89cenfagkXKK2VEDW2h3OzOlb\nxpgXJbVI2qhEwFyTpjvAG5LWOo/ZON49xpidSiwpGJjNfc0Ys0XSLr9u4gqzX310KmVs3eqZ+S8E\nAICH0GgmqmbcaLXd7Lo39tu95/RnLyxW+ajIxbOsieR3xlr7qjFmmxIBc62kFmut59pT5/U7JKVd\ndzrc4yW9N90yAwzT7c4evX/ggmtsUk2FHpk3waeKAAAYmeLiIq1dPVM/3HXs3ljn3V69v/+81j02\ny8fKgi2SwVWSnJnQrK0/zfbxMHzv7D2n7p4+19i6x2aqqIiF7ACA8FmXFFwl6c2PTxNcBxHFNa6I\noHg8rl9/5F77U1QU09pHWSYAAAinybVjtHy++6qhPX1dpy/e9Kmi4CO4IhROnGtXywX33ZaPLpxU\nMM2aAQDR9KXHZ6eMvclNWmkRXBEKb36U+kP8/ONcSgEAhNvqxZNVVVnmGnt7z9mUpXFIILgi8Drv\n9urdfedcY7VVo9VoJvpUEQAA2VFaUqQ1q9zL3m539ujDgxfSvKOwEVwReO/tP6/Ou+5PnmtXz1Rx\nMX99AQDh53UFkeUC3viXH4GXfFNWLCY9v5plAgCAaJg2oVJLGmpdY4dPXtP5K7d9qii4CK4ItFMX\nb8qeue4aW2EmamJNhU8VAQCQfV/0aIGVPHEDgisC7k2PnbK8frgBAAizJ5ZNVWXS9uVv7Tmjnt5+\nnyoKJoIrAqvrbq/e3nPWNVY9dpRWL57sU0UAAORGWWmxnls1wzV243a3fneIm7QeRHBFYL3ddFZ3\nunpdY2tWzVAJN2UBACLI6yatn7//mQ+VBBcJAIEUj8f18w/cP6yxmPSlz832pyAAAHJs1uRxWlzv\nvkmr+VSbTpxr96mi4CG4IpAOnriqM5duucZWL5qsybVjfKoIAIDce+Hp+pSxn7/f4kMlwURwRSD9\n7L3UH9IXnkr9YQYAIEoeXzxZddXu7czf3XdeN27f9amiYCG4InAuXbuj3Z9eco3NmDRWy+bV+VQR\nAAD5UVxcpK88Mds11tPb77n1eSEiuCJwfvHhKfXH3WMvPDVHsVjMn4IAAMij5x+bpdISd0T7xYef\nqbeP1lgEVwRKV3evdiZtczdmdIm+0DgjzTsAAIiWqspRembFdNfYtRtd+ujwRZ8qCg6CKwLlnb3n\ndLuzxzW2dvUslY8q8akiAADy72tPzUkZozUWwRUBEo/HU27KisWkrz6Z+sMLAECUNUyv1qI5Na6x\nIy3X1HL+hk8VBQPBFYFx+OQ1nU5qgbVq4SRNqaMFFgCg8HzNo5tOobfGIrgiMH7m8cPo9UMLAEAh\n+NzSKaqtGu0a++3ecwXdGovgikC4ePWOPk5adD5tQqWWz5vgU0UAAPirpLhIX07aMbKnt1+//N0p\nP8oJBIIrAuFffnsipQXW156ao6IiWmABAArXFx+frZJid1z72Xst6uru9akifxFc4bvrt7q0a/cZ\n19jYilKtfXSmTxUBABAM1WNH6blV7paQN+90661PzqR5R7QRXOG7n73Xop5ed1Plrz5Zr9G0wAIA\nQN98dq6S9+D58Tsn1VeAGxIQXOGrjq4e/eLDU66xstJiz/51AAAUomkTKvX4kimusda2Dr1/4IJP\nFfmH4ApfvfnRad1J2nDg+cdmqqpylE8VAQAQPOufm5cy9qO3jysej3u8OroIrvBNT2+ffvLOSddY\nUVFMv//MXJ8qAgAgmObPHK+lDXWusc8u3NQ+e8WnivxBcIVvftt0Tm03u1xjn18+TZNqKnyqCACA\n4Eo361pICK7wRX9/XD96+0TK+DefZbYVAAAvK8wE1U+tco0dPHFVx85c96mi/CO4whcfH7mk81du\nu8ZWLZykOUk/kAAAICEWi3lO8BTSrCvBFXkXj8c9f8i+xWwrAACDeuqRqSlL6n536GLKZFBUEVyR\ndweOX5E97b6sYWaN1+L6Wp8qAgAgHIqLi/SNZxpcY/G49MNdx3yqKL8IrsireDyuf/rV0ZTxbz07\nT7Hk7soAACDFmtUzVVVZ5hr7bdNZnWu95VNF+UNwRV41HW1NmW2dPWWcHls82aeKAAAIl9FlJfpG\nUuvI/rj0g19bnyrKH4Ir8iYej+uf30ydbf2jLy5QURGzrQAAZOqrT85RddJmPe/tP6/Tl276VFF+\nEFyRNx8fuaQTZ9tdYw3Tq/T4EmZbAQAYjtGjSvStpL6u8bj0gzejPetKcEVe9PfH9X89Zlv/+IsL\nWNsKAMAIfPmJ2aoZ5551/eDgBbWcv+FTRblHcEVe/O7QRX12wX35wswcr1ULJ/lUEQAA4TaqtFgb\n1sxPGfeaKIoKgityrq/fe23rH3+J2VYAAB7GFx+fpbqq0a6xj49c0vGz0dxNi+CKnHt//3mdvexu\n0bFoTo2Wz5/gU0UAAERDaUmxNq4zKeP/7NF6MgoIrsipvr5+/eDXqT88f/Klhcy2AgCQBWsfnamJ\nSbtpNR1tVfNnbT5VlDslfheQC8aYakkvS6qX1CapRtJOa+22fB3PGFMvaaukaud9LZK2j7SGsNq1\n+4zOX7njGls2t05L59b5VBEAANFSWlKkP1w7X3/7w/2u8X/8xad65c+fjNREUeRmXJ2Q2STppLV2\ng7V2s7V2g6QNxpjX8nE8Y8xaJULri9baddbaBknbJb1mjGka6f+3sOno6tE//dJ7bSsAAMie51bN\n0JS6Ma6xIy3X9OGhiz5VlBuRC66SXpfU4jGzuUHSJmPM+jwcb4sTcu81LXXev0XSypEE6DDa8Zvj\nar991zX26KJJWjSn1qeKAACIpuLiIv3plxamjP/Dz4+op7fPh4pyI1LB1ZkdXa/E7KaLEyJ3Sdqc\ny+MZYzZJ8gym1tpXnf/c5Bw7slrbOvSTd066xoqLYvrOC4t9qggAgGh7avlULZg13jV26VqHfv7+\nZz5VlH2RCq6SNjqPLWmeb5G0NsfHWydp+yAzuwPHWjWMOkLnH3/xqXp6+11jX35itqZPHOtTRQAA\nRFssFtN3f29JyvgbO61uJF0BDauoBdd1zmO6oHlSurcGNdfHW+cxJkkDywciO+N69HSb3t133jU2\nprxU336eta0AAOTSglk1+vyKaa6xO129+sGvo7EVbNSCa73zmK7/w0BoXJnD472oxFrWLUMcM10Y\nDrV4PK7v//RwyvgfrpuvcWPKfKgIAIDC8u+/skilJe6I98vfnUrpqR5GUQuu1dK99aeDyfTuoGEf\nz1rbbq191es9xpiVzjFbrLV7M6whVN7ff0H2tHu3jim1Y/TVJ+f4VBEAAIVlYk2Ffv+ZBtdYf39c\nf/+zIz5VlD1RC641Qzw/MHOa6WX6bB/vZecx4xvEwqS7p0//8G+pPxR/9sIilZYU+1ARAACFaf1z\n81RdOco1tqf5svbZVp8qyo5IbkAQRM462PWSXrXW7srF12hubs7FYTP266arar3e6RqbM7lcVcXt\nam6+4VNVqTo7O+89+v09w32cl+DhnAQT5yV4gnpO1iyv0o/edwfV//lGk/7ymzNVUhzOucuoBdc2\nDT77OTCDOtSl/6wez2l9tV3SNmtturWvD62joyNXhx7SlRs9evtA6lLgdcvH3vuBDpp4PO7r9wze\nOC/BwzkJJs5L8ATtnCyeXqr3qkvV2t5zb6z1Rrd27mnVM0vH+VjZyEUtuEpKBMUM1qXm83jbJf3Q\nWpvTJQIVFRVDvygH4vG4fvmba+pzd7/So/PHae704DVP6OzsVDweVywWU3l5ud/lwMF5CR7OSTBx\nXoInyOfk95+YpG2/OOcae+/TW1q1oEYTqvy5afphwn3UgutAuKyR9yzoQIo66fFcTo7n7JLVkuvQ\nKkkLF6bumJEPuz45rZZL7lnVcWPK9Jd/8mQgOwk0Nzero6ND5eXlvn3PkIrzEjyck2DivARPkM/J\nwoXSidaYfrPn7L2x3r643tx3W//1e08oFovlvaampqYRvzecCxzSG1g7mm6ab+Du/z35OJ4x5iVJ\nSg6txphqY0y913vC5sbtu553KX7360sCGVoBACg033lhscZWlLrGDp64qrebzqZ5R3BFLbi+4Tym\nC4X1kjSMVlQjPp5zM1ZDmpnWjYMcM1T+/mdHdKujxzW2bG6dnm2c7lNFAADgQVWVozy3XP/+T4+E\nbketSAVXJ0C2K/2uVeslbUseNMbUG2O2Js+CPsTxVkraMMjygHXKfNY3sA4cv+K69CBJpSVF+ov1\nj/hy6QEAAHhb8+hMLWlwt7G/1dGtf/j5pz5VNDKRCq6OFyVtdO7kv8cYs0mJEOp1V/9WSS85jw91\nPOd1bznvue7xv7ik9dm8ecwP3T19+t87DqSM/8Ha+Zo6odKHigAAQDqxWEx//q1HUtpg7dp9RodO\nXPWpquGLXHC11u6Q9Iqkt4wxK531pJuUCJhr0gTGN5QIoW8kPzGC472uxJrYdP+TpNDvmvVPvzqq\nC1fvuMZmTKrUN5+d61NFAABgMDMmjdWGNfNSxv/2h/vUebfXh4qGL2pdBSRJ1tpXjTHblFhLulaJ\nu/obBnn9Dkk7snE8a+2Ghyo+BA6duKqfvHMiZfzPv/UIO2QBABBg65+bp3f3ndP5K/cnny5d69D3\nf3pY/2njch8ry0wkg6skOTOhKetPg3K8sLrd2aP/9oO9isfd488/NktLGur8KQoAAGSkrLRYf7F+\nuf7L333gGv/1x6e1etEkPbZkik+VZSZySwWQW6/9+KCutrt7tk6urdB3v556tyIAAAiepXPr9Huf\nT71w/D+279f1W10+VJQ5gisy9t6+8/rtXvfuG0Ux6a++3aiK0aVp3gUAAILm331loWZNHusau3G7\nW3/7xn7Fky+rBgjBFRm52t6p//Wj1C4C69fM18I5NT5UBAAARqqstFh//ceNKV0G9jRf1q8+Ou1T\nVUMjuGJI/f1x/ff/t1d3Ot0bDcydXqVvP298qgoAADyMOVOr9KdfXpAy/n/+9bDOX7ntQ0VDI7hi\nSO/tP68Dx9093spKi/VXf5T6SQ0AAITH7z0zV0uTbq6+292nbT855FNFgyN1YEh7mi+njH3na4s0\nY9JYj1cDAICwKC6K6S+/vUJjRrsbTR04dkU9vX0+VZUewRVDaphe5frzygUT9ZUn5/hUDQAAyKaJ\n4yv0vW8uc43NmjwukL3ZI9vHFdnzlSfmqO3mXR08cUVzp1frP3x9iWKxmN9lAQCALPlC4wxJ0k/f\na9G4ijJt+sZSnyvyRnDFkMpKi/WdF+jTCgBAlH2hcca9ABtULBUAAABAKBBcAQAAEAoEVwAAAIQC\nwRUAAAChQHAFAABAKBBcAQAAEAoEVwAAAIQCwRUAAAChQHAFAABAKBBcAQAAEAoEVwAAAIQCwRUA\nAAChQHAFAABAKBBcAQAAEAoEVwAAAIRCLB6P+10DHlJTUxMnEQAAhEpjY2NsuO9hxhUAAAChwIwr\nAAAAQoEZVwAAAIQCwRUAAAChQHAFAABAKBBcAQAAEAoEVwAAAIQCwRUAAAChQHAFAABAKBBcAQAA\nEAoEVwAAAIQCwRUAAAChQHAFAABAKBBcAQAAEAoEVwAAAIQCwRUAAAChQHAFAABAKBBcAQAAEAol\nfhcAAAgOY0y1pJcl1Utqk1Qjaae1dpuvhQEhYYx5TYmfmR1+1xJFBFcAgKR7obVJ0lZr7ZYHxnca\nYxqttZv9q65wGWPqJW2VVK3EB4oWSdv5MBE8xpiVkjZJ2ul3LVHFUgFgEMaY14wx6/2uA8iT1yW1\neASiDZI28bOQf8aYtUqE1hetteustQ2Stkt6zRjT5G918PC63wVEHcEVSOOBT87wiTGm3hiz3Znx\nO+k8ck5ywJltXa9EKHKx1rZL2iWJGdf822Kt3eCcA0mS88Fii6SVzmVpBIDzu2mP33VEHcEVSI9P\nzj5ipinvNjqPLWmeb5G0Nk+1QPeCkGcwtda+6vznJudDB3zknIMGsUQg5wiugAc+OQcCM035tc55\nTBdcT0r3PlAgP9ZJ2j7IEo2Bc7UqT/Ugva2SXvG7iEJAcAWS8MnZf8w0+aLeeWxL8/zAB4iVeagF\nbuvSjA+cE34OfOR8mGt68EM2cofgCqTik7P/mGnKv2rp3nrWwdTmoRYkvKjEFYYtaZ4f+LCRbpYc\n+bGBDg/5Qzss4AEPfnI2xvhdDhIB1qsXIjNN2VczxPMDM7F8z/PE+RDxqtdzzs2j1Up0gdib18Jw\njzHmJSUmO5AnBFfAbQO9KgPhRUm7JaWbxWCmCYXuZeeR31c+cfrr1lpr+T2URwRXwMEn5+BgpskX\nbRp8NnVgRpZ1fD5zrgytl/SqtXaX3/UUsC1MdOQfa1wB8ck5ZJhpyiFueAs25/xsl7Ttwd3NkF/O\n+ntu4PUBwRVI2MI/AsHHTFNODcykplvrOhBoT+ahFqS3XdIPmenz3Tprrdf6e+QYSwUQSsaY7UoE\nmJHYa61tfOBYfHIOAWaacm6XEq2u0s24DnQToL+xT5zexS2EVn85H6DXptkIZWD9/VZjzMuS9OC/\nN3h4BFeEkrV2w0gvaXq0+1nHPwQPL5sfJtJgpim33pD0khL/8HqtHa6XJNYV+8NZg6/kv//O78Ea\nljnlj3O1p8HruQfuldjCjGxuEFwRWtlo9swn5+zJ8ocJF2aacs9au9cY0670LcjWK32XB+SQ83uq\nIc3f/41KdNcguKIgEFxR0PjknF252DmGmaa8elHS68aYLQ+eS2cns3alb4SPHHG6aAzWpm+dEucN\nwTCwpGaovsgYIYIrgMBipim/rLU7nA4bbxljXlTie7tRicC6hi0t88v5cPaW898bPV4ysNvZhnzW\nhVTGmJ1KXKUbuFL3mjFmi6RdXCnKLoIrkB6fnH3ETJM/rLWvGmO2KRFY1yqxRMPzqgRy7nUNvVMZ\na44DwFq7zu8aCkUsHo/7XQMQKB6fnKXEzBOfnPPEmWn6bJCXDMw0xfJTEQAgCJhxBZLwyTkQmGkC\nAKRgxhUAAAChwM5ZAAAACAWCKwAAAEKB4AoAAIBQILgCAAAgFAiuAAAACAWCKwAAAEKB4AoAAIBQ\nILgCAAAgFAiuAAAACAWCKwAAAEKB4AoAAIBQILgCAAAgFAiuAAAACAWCKwAAAEKB4AoAAIBQILgC\nAAAgFAiuAAAACAWCKwAAAEKhxO8CAADBYYx5SVKDpBpn6EVrbbsxZpOkRkntkqolbbHWtvtUJoAC\nxYwrAECSZIx5TdIua+1ma+0GZ3i7E1rbrLWbJe2WtEnSy37VCaBwMeMKABiYad1urd37wPBuSVsl\ntT8QZDc7jzvzWR8ASARXAEDCOmvtq0ljDc7jGw+MbZBUY61tyU9ZAHAfwRUACpwxplrSFo+nVjmP\nuwYGnHWtrG0F4ItYPB73uwYAQAAZY+KSWqy1DUO+GADygJuzAAApjDErnf/cNegLASCPCK4AAC9r\nnUduwgIQGARXAICXdc5jyoyrMWZ9nmsBAEkEVwCAJGNM/QP/Xa3EjGt78iYDTk9XAPAFwRUACpwx\n5rqkk05glRIbDEhSm8fL11lrd+SnMgBwI7gCQAFzwmq1EjtmtTt/blCiX2v9QJg1xlQ7O2t5tc0C\ngLygHRYAFDjn8n/jA0NbnBC7SYkAO7DZwFY2HgDgJ4IrAAAAQoGlAgAAAAgFgisAAABCgeAKAACA\nUCC4AgAAIBQIrgAAAAgFgisAAABCgeAKAACAUCC4AgAAIBQIrgAAAAgFgisAAABCgeAKAACAUCC4\nAgAAIBQIrgAAAAgFgisAAABCgeAKAACAUCC4AgAAIBQIrgAAAAgFgisAAABCgeAKAACAUCC4AgAA\nIBT+P1M7x4tnpzC9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cda4b38>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 288,
       "width": 343
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.plot(domain,px)\n",
    "plt.xlabel('$x$');plt.ylabel('$p(x)$');plt.title('Marginal distribution - $p(x)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Posterior distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pc1x, pc2x = [], []\n",
    "for x in domain:\n",
    "    pck = p_Ckx(x, true_mu1, true_mu2, true_sigma, true_gamma)\n",
    "    pc1x.append(pck[0]); pc2x.append(pck[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Tr1H94jRTYBXrwpy282iRn6TPR7iwaZqMtBcxPSfi8xZPC72ATn0J6GWrRT/+TFOvJPLa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\nlGgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d099470>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 288,
       "width": 340
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.plot(domain, pc1x, label='Class 1')\n",
    "plt.plot(domain, pc2x, label='Class 2')\n",
    "plt.xlabel('$x$');plt.ylabel('$p(C_k|x)$');plt.title('Posterior distributions - $p(C_1|x)$ and $p(C_2|x)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Or model is ready, let's generate some data and test it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789) # do not do this in real life\n",
    "num_samples = 100\n",
    "x = np.zeros(num_samples)\n",
    "t = np.zeros(num_samples)\n",
    "pcx = np.zeros(num_samples)\n",
    "n1 = 0\n",
    "nae = 0\n",
    "assignment_epsilon = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Assigning `x` to `1` for **class 1** and `0` for **class 2**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(num_samples):\n",
    "    rv = np.random.uniform()\n",
    "    x[i] = inv_cdf(rv, true_mu1, true_mu2, true_sigma, true_gamma)\n",
    "    pcx1 = p_Ckx(x[i], true_mu1, true_mu2, true_sigma, true_gamma)\n",
    "    pcx2 = pcx1[1]\n",
    "    pcx1 = pcx1[0]\n",
    "    #we don't want a perfect dividing line for our domain, otherwise why would we need a learning algorithim?\n",
    "    if math.fabs(pcx2-pcx1) <= assignment_epsilon:\n",
    "        nae = nae + 1\n",
    "        if np.random.uniform() <= 0.5:\n",
    "            t[i] = 1\n",
    "            n1 = n1 + 1\n",
    "        else:\n",
    "            t[i] = 0\n",
    "    elif pcx1 > pcx2:\n",
    "        t[i] = 1\n",
    "        n1 = n1 + 1\n",
    "    else: t[i]=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot the simulated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+sjmBk88+iQfWL3xf/a/ZC5j+8qrdxs87tpbyySkXQosF2mL1YfgkoqXgRPQL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\n2CIYHHPbaa4DFaSqjttSBwAwNJAAAJQqDQxkzPDcwYSafDauJitVGst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9p3+MlEDNaaDm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d560e48>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 336
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.scatter(x, t, marker='x', alpha=0.5)\n",
    "plt.axvline(0, linestyle='--')\n",
    "plt.xlabel('$x$');plt.ylabel('Class ($t$)'); plt.title('Simulated training data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Estimating the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n2 = num_samples - n1\n",
    "e_gamma = n1/num_samples # Python 3! fix this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "e_mu1 = 0\n",
    "for x_i, t_i in zip(x,t): \n",
    "    if t_i == 1:\n",
    "        e_mu1 += x_i\n",
    "    # e_mu1 += x_i*t_i\n",
    "e_mu1 /= n1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "e_mu2 = 0\n",
    "for x_i, t_i in zip(x,t):\n",
    "    if t_i == 0:\n",
    "        e_mu2 += x_i\n",
    "    # e_mu2 += x_i*(1-t_i)\n",
    "e_mu2 /= n2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def Sn(Z, ck, mu=(e_mu1,e_mu2)):\n",
    "    idx = 1-int(ck)\n",
    "    return (Z[0]-mu[idx]) * (Z[0]-mu[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "e_sigma = 0\n",
    "for x_i, t_i in zip(x,t): \n",
    "    e_sigma += Sn((x_i, t_i), t_i)\n",
    "e_sigma /= float(num_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of inputs in C1 is 49\n",
      "The number of inputs that were assigned based on the assignment factor is 12\n",
      "True model parameters: gamma=0.5, µ1=-2.0, µ2=2.0, ∑=2.0\n",
      "Estimated model parameters: gamma=0.49, µ1=-2.1627582966950736, µ2=2.028003758731953, ∑=1.6660489752832408\n"
     ]
    }
   ],
   "source": [
    "print('The number of inputs in C1 is {0}'.format(n1))\n",
    "print('The number of inputs that were assigned based on the assignment factor is {0}'.format(nae))\n",
    "print('True model parameters: gamma={0}, µ1={1}, µ2={2}, ∑={3}'.format(true_gamma, \n",
    "                                                                       true_mu1, true_mu2, \n",
    "                                                                       true_sigma))\n",
    "print('Estimated model parameters: gamma={0}, µ1={1}, µ2={2}, ∑={3}'.format(e_gamma, e_mu1, \n",
    "                                                                            e_mu2, e_sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Probabilistic discriminative models\n",
    "\n",
    "Probablistic discriminative models assume the same generalized linear model\n",
    "\n",
    "$$y(\\phi(\\vec{x})) = f(\\vec{w}^\\intercal\\phi(\\vec{x}))$$\n",
    "\n",
    "as in the probabilistic generative models. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* Instead of formulating models for the *class-conditional* densities, $p\\left(\\phi(\\vec{x})\\right|\\left.C_k\\right)$, and the *class priors*, $p(C_k)$, \n",
    "* the discriminative approach explicitly models the *class posterior* probabilities, $p\\left(C_k\\right|\\left.\\phi(\\vec{x})\\right)$ with model parameters $\\vec{w}$. \n",
    "* As in the probabilistic generative approach, maximum likelihood is used to estimate the model parameters given some training data set, $\\vec{t}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The **key difference** is the form of the likelihood function. \n",
    "* In the **probabilistic generative case**, the likelihood function is a function of the joint probability,\n",
    "$p\\left(\\phi(\\vec{x}),C_k\\right)=p\\left(\\phi(\\vec{x})\\right|\\left.C_k\\right)p(C_k)$. \n",
    "* In the **probabilistic discriminative approach**, the likelihood function is a function of the conditional class posteriors, $p\\left(C_k\\right|\\left.\\phi(\\vec{x})\\right)$ only."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "*Note*: The section on probablistic generative models focused on models that used the input, $\\vec{x}$, directly. However, as noted previously, those models, and the results, hold equally well for input that undergoes a **fixed** transformation using a set of basis functions, $\\phi()$. In this section, we will focus on the inclusion of an input transformation via the basis functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logistic Regression\n",
    "\n",
    "* Logistic regression is one specific example of discriminative modeling, for the case of **two classes**. \n",
    "* It assumes a model for the class posterior probabilities, $p(C_k|\\phi(\\vec{x}))$, in the form of the logistic sigmoid\n",
    "\n",
    "$$p\\left(C_1\\right|\\left.\\phi(\\vec{x})\\right) = f(a) = \\sigma\\left(\\vec{w}^\\intercal\\phi(\\vec{x})\\right)$$\n",
    "\n",
    "with \n",
    "\n",
    "$$p\\left(C_2\\right|\\left.\\phi(\\vec{x})\\right) = 1 - p\\left(C_1\\right|\\left.\\phi(\\vec{x})\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* We apply maximum likelihood to obtain the model parameters. \n",
    "* Assume that our training set is of the form $\\left\\{\\phi(\\vec{x}_i),t_i\\right\\}$ where $t_i \\in \\{0,1\\}$,\n",
    "and $i=1,\\ldots, m$. \n",
    "* The likelihood function of the training data is then\n",
    "$$p(\\vec{t}|\\vec{w}) = \\prod_{i=1}^m \\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i))^{t_i} (1 - \\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i)))^{(1-t_i)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Defining the error function, $E(\\vec{w})$, as the negative of the log-likelihood function, and taking the gradient with respect to $\\vec{w}$, we obtain\n",
    "$$\\bigtriangledown E(\\vec{w}) = \\sum_{i=1}^m \\left[\\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i)) - t_i\\right] \\phi(\\vec{x}_i).$$\n",
    "\n",
    "* this error function looks the same as that obtained for **linear** regression under the assumption of a Gaussian noise model which had a closed form solution.\n",
    "* the nonlinearity of the *sigmoid* function, $\\sigma\\left(\\vec{w}^\\intercal \\phi(\\vec{x}_i)\\right)$ prevents a closed form solution in the **logistic** regression problem. \n",
    "* We must apply an iterative method to obtain a numerical solution for the parameters, $\\vec{w}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we will consider the *Newton-Raphson* method for which minimizing the error function takes the form\n",
    "\n",
    "$$\\vec{w}(t+1) = \\vec{w}(t) - \\vec{H}^{-1}\\bigtriangledown E(\\vec{w}),$$\n",
    "\n",
    "where $\\vec{H}$ is the *Hessian* matrix composed of the second derivatives of the error function\n",
    "\n",
    "$$\\vec{H} = \\bigtriangledown \\bigtriangledown E(\\vec{w}) = \\Phi^\\intercal \\vec{R} \\Phi,$$\n",
    "\n",
    "where $\\Phi$ is the $n \\times m$ design matrix whose $n$-th row is given by $\\phi(\\vec{x_n})^\\intercal$ and $\\vec{R}$ is an $n \\times n$ diagonal matrix with elements.\n",
    "\n",
    "$$R_{i,i} = \\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i)) \\left[1-\\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i))\\right].$$ \n",
    "\n",
    "This can be reduced to a form equivalent to that of localy weighted linear *regression* as follows\n",
    "\n",
    "$$\\vec{w}^{\\tau+1} = \\left( \\Phi^T \\vec{R} \\Phi \\right)^{-1} \\Phi^T \\vec{R} \\vec{z}$$\n",
    "\n",
    "where $\\vec{z}$ is an $n$-dimensional vector defined by\n",
    "\n",
    "$$\\vec{z} = \\Phi \\vec{w}^{\\tau} - \\vec{R}^{-1}(\\vec{y} - \\vec{t})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2>Example 2</h2>\n",
    "Let's consider an example with two classes and 2D input, $\\mathbf{x_n} = (x_n^{(1)},x_n^{(2)})$. \n",
    "*  As an experiment, you can try increasing the number of training points, `N`. \n",
    "* Eventually, the training points will overlap so that it will not be possible to completely seperate them with the transformation provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# preparing training dataset\n",
    "np.random.seed(123456789) # fixing for reproducubility\n",
    "N = 100 #number of data points\n",
    "D = 2   #dimension of input vector\n",
    "t = np.zeros(N) #training set classifications\n",
    "X = np.zeros((N,D)) #training data in input space\n",
    "sigma = .25\n",
    "mu0 = 0.0\n",
    "mu1 = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def create_scatter(X, t, ax):\n",
    "    'Generates a two-class scatter plot'\n",
    "    C1x, C1y, C2x, C2y = [], [], [], []\n",
    "    for i in range(len(t)):\n",
    "        if t[i] > 0: \n",
    "            C1x.append(X[i,0])\n",
    "            C1y.append(X[i,1])\n",
    "        else: \n",
    "            C2x.append(X[i,0])\n",
    "            C2y.append(X[i,1])\n",
    "    ax.scatter(C1x, C1y, c='b', alpha=0.5)\n",
    "    ax.scatter(C2x, C2y, c='g', alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Generating test data\n",
    "\n",
    "* Pick a value from a uniform distribution on $[0,1]$. \n",
    "* If it is less than 0.5, assign class 1 and pick $x_1, x_2$ from a $\\mathcal{N}(\\mu_0,\\sigma)$ \n",
    "* otherwise assign class 2 and pick $x_1,x_2$ from $\\mathcal{N}(\\mu_1,\\sigma)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(N):\n",
    "    #choose class to sample for\n",
    "    fac = 1\n",
    "    if np.random.rand() <= 0.5:\n",
    "        thismu = mu0\n",
    "        t[i] = 1\n",
    "    else: \n",
    "        thismu = mu1\n",
    "        t[i] = 0\n",
    "        if np.random.rand() < 0.5: fac = -1\n",
    "    X[i,0] = fac * np.random.normal(thismu, sigma)\n",
    "    X[i,1] = fac * np.random.normal(thismu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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SiMQi8Dg9OLLvCJ4/+HxFvyfKjYGWiIiINvG6vOju6EZ3R/d2X4ppXpcXz93/HL5f832s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\np9JebmceFoIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111311320>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 341,
       "width": 346
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5)); ax =fig.gca()\n",
    "ax.set_xlabel('$x_1$'); ax.set_ylabel('$x_2$'); ax.set_title('Training data set')\n",
    "create_scatter(X,t,ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The training data does not have a linear boundary in the original input space.\n",
    "* So lets apply a tranformation, phi to try to make it linearly seperable\n",
    "* *Note*: This transformation is not the only one that works. \n",
    "    * For example try switching the values of $\\mu_1$ and $\\mu_2$. \n",
    "    * The result will be a different mapping that is still linearly seperable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def phi(x,mu,sigma):\n",
    "    detSigma = np.linalg.det(sigma)\n",
    "    fac = math.pow(2*math.pi, len(mu)/2.0) * math.sqrt(detSigma)\n",
    "    arg = -0.5 * np.dot((x-mu).T, np.dot(np.linalg.inv(sigma), x-mu) )\n",
    "    return math.exp(arg) / fac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "phiX = np.zeros((N,D))\n",
    "MU1 = np.ones(D)*mu0\n",
    "MU2 = np.ones(D)*mu1\n",
    "SIGMA = np.diag(np.ones(D))*sigma\n",
    "for i in range(N):\n",
    "    phiX[i,0] = phi(x=X[i,:], mu=MU2, sigma=SIGMA)\n",
    "    phiX[i,1] = phi(x=X[i,:], mu=MU1, sigma=SIGMA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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HwteCimYiYY+53MI5nUF1NBazSub8cBqJ2PUlq5JGoxZCJWly0n7fv7/1nwsAAKwubRNA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\nuAcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d334390>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 324,
       "width": 336
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5)); ax =fig.gca()\n",
    "ax.set_xlabel('$x_1$'); ax.set_ylabel('$x_2$')\n",
    "create_scatter(phiX,t,ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now, lets apply machine learning to determine the boundary!\n",
    "\n",
    "* We will assume M = 3, i.e. that there are 3 free parameters,\n",
    "* that is $\\vec{w} = [w_0, w_1, w_2]^\\intercal$ and,\n",
    "* `phi_n = [1, phiX[0], phiX[1]]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = 3\n",
    "Phi = np.ones((N,M))\n",
    "Phi[:,1] = phiX[:,0]\n",
    "Phi[:,2] = phiX[:,1]\n",
    "w = np.zeros(M)\n",
    "R = np.zeros((N,N))\n",
    "y = np.zeros(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def sigmoid(a):\n",
    "    return 1.0 / (1.0 + math.exp(-a))\n",
    "\n",
    "def totalErr(y,t):\n",
    "    e = 0.0\n",
    "    for i in range(len(y)):\n",
    "        if t[i] > 0:\n",
    "            e += math.log(y[i])\n",
    "        else:\n",
    "            e += math.log(1.0 - y[i])\n",
    "    return -e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Starting Newton-Raphson. \n",
    "\n",
    "* As a stopping criteria we will use a tolerance on the change in the error function and a maximum number of iterations\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "max_its = 100\n",
    "tol = 1e-2\n",
    "w0 = [w[0]] \n",
    "w1 = [w[1]]\n",
    "w2 = [w[2]]\n",
    "err = []\n",
    "error_delta = 1 + tol\n",
    "current_error = 0\n",
    "idx = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from functools import reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "while math.fabs(error_delta) > tol and idx < max_its:\n",
    "    #update y & R\n",
    "    for i in range(N): \n",
    "        y[i] = sigmoid(reduce(lambda accum, Z: accum + Z[0]*Z[1], zip(w, Phi[i,:]), 0))\n",
    "        R[i,i] = y[i] - y[i]*y[i]\n",
    "    #update w\n",
    "    z = np.dot(Phi,w) - np.dot(np.linalg.pinv(R),y-t)\n",
    "    term_1 = np.linalg.pinv(np.dot(np.dot(Phi.T,R),Phi))\n",
    "    term_2 = np.dot(np.dot(term_1, Phi.T),R)\n",
    "    w = np.dot(term_2, z)\n",
    "    w0.append(w[0])\n",
    "    w1.append(w[1])\n",
    "    w2.append(w[2])\n",
    "    idx += 1\n",
    "    temp = totalErr(y,t)\n",
    "    error_delta = current_error - temp\n",
    "    current_error = temp\n",
    "    err.append(error_delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The total number of iterations was 13\n",
      "The total error was 0.003482221426895694\n",
      "The final change in error was 0.00577180168397616\n",
      "The final parameters were [ -17.844  -14.062  163.065]\n"
     ]
    }
   ],
   "source": [
    "print('The total number of iterations was {0}'.format(idx))\n",
    "print('The total error was {0}'.format(current_error))\n",
    "print('The final change in error was {0}'.format(error_delta))\n",
    "print('The final parameters were {0}'.format(w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our decision boundary is now formed by the line where $\\sigma(a) = 0.5$, i.e. where $a = 0$, which for this example is where $\\phi_2 = -\\frac{w_1}{w_2}\\phi_1$, i.e. where $\\vec{w} \\cdot\\vec{\\phi} = 0.5$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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JhZ3w4XC+ez3YFz6bXbqRaXbWGp/6+60T/stftpDa3287KQXSaemFF6QXX7TF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\nlvB8lAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d06db00>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 324,
       "width": 336
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5)); ax =fig.gca()\n",
    "ax.set_xlabel('$x_1$'); ax.set_ylabel('$x_2$')\n",
    "create_scatter(phiX,t,ax)\n",
    "\n",
    "bdryx = (-0.2,1.1)\n",
    "bdryy = (-(w[0]+w[1]*bdryx[0])/w[2], -(w[0]+w[1]*bdryx[1])/w[2])\n",
    "ax.plot(bdryx, bdryy, linestyle='--');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZWVlZSE1NBVAXGp0pLCxEQkKCpG3x4sXQ6/XsTSQiImoGgyL5JLPZLAl627dvR3Ky9L0S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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d06d0b8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 324,
       "width": 325
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.plot(w0, 'bo-', label='$w_0$')\n",
    "plt.plot(w1, 'rx-', label='$w_1$')\n",
    "plt.plot(w2, 'gs-', label='$w_2$')\n",
    "plt.plot(err, 'm*-', label='error delta')\n",
    "plt.legend(loc='upper left', frameon=True)\n",
    "plt.xlabel('Newton-Raphson iterations');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<h1>Readings</h1>\n",
    "<ul>\n",
    "    <li>Bishop: 4.2.0-4.2.4, 4.3.0-4.3.4, 4.4, 4,5</li>\n",
    "    <li>Ng: Lecture 2 pdf</li>\n",
    "    <li>Ng: Lecture 5 pdf</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<hr/>\n",
    "<div class=\"container-fluid\">\n",
    "  <div class='well'>\n",
    "      <div class=\"row\">\n",
    "          <div class=\"col-md-3\" align='center'>\n",
    "              <img align='center'alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\"/>\n",
    "          </div>\n",
    "          <div class=\"col-md-9\">\n",
    "              This work is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n",
    "          </div>\n",
    "      </div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]"
        },
        {
         "module": "IPython",
         "version": "5.3.0"
        },
        {
         "module": "OS",
         "version": "Darwin 16.5.0 x86_64 i386 64bit"
        },
        {
         "module": "scipy",
         "version": "0.19.0"
        },
        {
         "module": "numpy",
         "version": "1.12.1"
        },
        {
         "module": "matplotlib",
         "version": "2.0.0"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]</td></tr><tr><td>IPython</td><td>5.3.0</td></tr><tr><td>OS</td><td>Darwin 16.5.0 x86_64 i386 64bit</td></tr><tr><td>scipy</td><td>0.19.0</td></tr><tr><td>numpy</td><td>1.12.1</td></tr><tr><td>matplotlib</td><td>2.0.0</td></tr><tr><td colspan='2'>Sat Apr 08 17:04:07 2017 -03</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)] \\\\ \\hline\n",
       "IPython & 5.3.0 \\\\ \\hline\n",
       "OS & Darwin 16.5.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "scipy & 0.19.0 \\\\ \\hline\n",
       "numpy & 1.12.1 \\\\ \\hline\n",
       "matplotlib & 2.0.0 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Sat Apr 08 17:04:07 2017 -03} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.1 64bit [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]\n",
       "IPython 5.3.0\n",
       "OS Darwin 16.5.0 x86_64 i386 64bit\n",
       "scipy 0.19.0\n",
       "numpy 1.12.1\n",
       "matplotlib 2.0.0\n",
       "Sat Apr 08 17:04:07 2017 -03"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext version_information\n",
    "%version_information scipy, numpy, matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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       "}\n",
       ".text_cell_render h4 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 17pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h5 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 15pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       "div.text_cell_render{\n",
       "line-height: 120%;\n",
       "font-size: 100%;\n",
       "font-weight: 400;\n",
       "text-align: justify;\n",
       "margin-left:0em;\n",
       "margin-right:0em;\n",
       "}\n",
       ".reveal div.text_cell_render{\n",
       "line-height: 120%;\n",
       "font-size: 74%;\n",
       "font-weight: 400;\n",
       "text-align: justify;\n",
       "margin-left:0em;\n",
       "margin-right:0em;\n",
       "}\n",
       "\n",
       ".reveal h2 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal h3 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal h4 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal .code_cell {\n",
       "    font-size: 83%;\n",
       "}\n",
       ".reveal code {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       ".reveal pre {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       "code {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       "pre {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       ".CodeMirror{\n",
       "font-family: \"Inconsolata\", monospace;\n",
       "}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this code is here for cosmetic reasons\n",
    "from IPython.core.display import HTML\n",
    "from urllib.request import urlopen\n",
    "HTML(urlopen('https://raw.githubusercontent.com/lmarti/jupyter_custom/master/custom.include').read().decode('utf-8'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}