{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "  var password,\n",
       "      teacher_mode,\n",
       "      isHtml;\n",
       "      \n",
       "  var class_output,\n",
       "      class_input,\n",
       "      class_answer;\n",
       "      \n",
       "  function code_toggle(e) {\n",
       "    var orig_e = e;\n",
       "    while (!e.closest(class_output).previousElementSibling.classList.contains(class_input)) {\n",
       "      e = e.closest(class_output).previousElementSibling;\n",
       "    }\n",
       "    var target = e.closest(class_output).previousElementSibling;\n",
       "    if (target.getAttribute(\"style\") == \"\" || target.getAttribute(\"style\") == null) {\n",
       "      target.style.display = \"none\";\n",
       "      orig_e.innerHTML = 'show code';\n",
       "    }\n",
       "    else {\n",
       "      target.style.removeProperty(\"display\");\n",
       "      orig_e.innerHTML = 'hide code';\n",
       "    }\n",
       "  }\n",
       "  \n",
       "  function hide_comment(e) {\n",
       "    teacher_mode = 1;\n",
       "    var target = e.closest(class_answer).nextElementSibling;\n",
       "    //e.closest(class_output).previousElementSibling.style.display = \"none\";\n",
       "    if (target.getAttribute(\"style\") == \"\" || target.getAttribute(\"style\") == null) {\n",
       "      //target.style.display = \"none\";\n",
       "      e.innerHTML = 'show comment';\n",
       "      answer_block = target;\n",
       "      //if (isHtml) {\n",
       "          while (answer_block.innerHTML.indexOf(\"blacksquare<\") == -1) {\n",
       "              answer_block.style.display = \"none\";\n",
       "              answer_block = answer_block.nextElementSibling;\n",
       "          }\n",
       "      //}\n",
       "      answer_block.style.display = \"none\";\n",
       "    }\n",
       "    else if (teacher_mode) {\n",
       "        e.innerHTML = 'hide comment';\n",
       "        //target.style.removeProperty(\"display\");\n",
       "        answer_block = target;\n",
       "        //if (isHtml) {\n",
       "          while (answer_block.innerHTML.indexOf(\"blacksquare<\") == -1) {\n",
       "              answer_block.style.removeProperty(\"display\");\n",
       "              answer_block = answer_block.nextElementSibling;\n",
       "          }\n",
       "        //}\n",
       "        answer_block.style.removeProperty(\"display\");\n",
       "    }\n",
       "  }\n",
       "  \n",
       "  function done() { \n",
       "    document.getElementById(\"popup\").style.display = \"none\";\n",
       "    var input = document.getElementById(\"password\").value;\n",
       "    if (input==password) { teacher_mode=1; alert(\"Unlocked!\");}\n",
       "    else { teacher_mode=0; alert(\"Wrong password!\");}       \n",
       "  };\n",
       "\n",
       "  function unlock() {\n",
       "    document.getElementById(\"popup\").style.display = \"block\";\n",
       "  }\n",
       "  \n",
       "  $(document).ready(function() {\n",
       "    $.ajax({\n",
       "      type: \"GET\",  \n",
       "      url: \"https://raw.githubusercontent.com/ming-zhao/ming-zhao.github.io/master/data/course.csv\",\n",
       "      dataType: \"text\",       \n",
       "      success: function(data)  \n",
       "      {\n",
       "        //var items = data.split(',');\n",
       "        //var url = window.location.pathname;\n",
       "        //var filename = url.substring(url.lastIndexOf('/')+1);\n",
       "        password='a';\n",
       "        //for (var i = 0, len = items.length; i < len; ++i) {\n",
       "        //    if (filename.includes(items[i].trim()) && i%2==0 && i<items.length) {\n",
       "        //        password=items[i+1].trim();\n",
       "        //        break;\n",
       "        //    }\n",
       "        //}\n",
       "        var code_blocks = document.getElementsByClassName('nbinput docutils container');\n",
       "        if (code_blocks[0]==null) { \n",
       "            isHtml=0;\n",
       "            code_blocks = document.getElementsByClassName('input');\n",
       "            class_output=\".output_wrapper\";\n",
       "            class_input=\"input\";\n",
       "            class_answer='.cell';\n",
       "        }\n",
       "        else { \n",
       "            isHtml=1;\n",
       "            class_output=\".nboutput\";\n",
       "            class_input=\"nbinput\";\n",
       "            class_answer=\".nboutput\";\n",
       "        }\n",
       "        \n",
       "        for (var i = 0, len = code_blocks.length; i < len; ++i) {\n",
       "          if (\n",
       "              code_blocks[i].innerHTML.indexOf(\"toggle\") !== -1 \n",
       "              || code_blocks[i].innerHTML.indexOf(\"button onclick\") !== -1\n",
       "             ) {\n",
       "            code_blocks[i].style.display = \"none\";\n",
       "          }\n",
       "        }\n",
       "        for (var i = 0, len = code_blocks.length; i < len; ++i) {\n",
       "          if (code_blocks[i].innerHTML.indexOf(\"hide_comment\") !== -1) {\n",
       "            code_blocks[i].style.display = \"none\";\n",
       "            if (isHtml) {\n",
       "              answer_block = code_blocks[i].nextElementSibling.nextElementSibling;\n",
       "              while (answer_block.innerHTML.indexOf(\"blacksquare\") == -1) {\n",
       "                  answer_block.style.display = \"none\";\n",
       "                  answer_block = answer_block.nextElementSibling;\n",
       "              }\n",
       "              answer_block.style.display = \"none\";\n",
       "            }\n",
       "            else{\n",
       "              //code_blocks[i].closest(class_answer).nextElementSibling.style.display = \"none\";\n",
       "              answer_block = code_blocks[i].closest(class_answer).nextElementSibling;\n",
       "              while (answer_block.innerHTML.indexOf(\"blacksquare\") == -1) {\n",
       "                  answer_block.style.display = \"none\";\n",
       "                  answer_block = answer_block.nextElementSibling;\n",
       "              }\n",
       "              answer_block.style.display = \"none\";              \n",
       "            }            \n",
       "          }\n",
       "        }\n",
       "      }\n",
       "    });\n",
       "  });\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%run ../initscript.py\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "from ipywidgets import *\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "\n",
    "import sys\n",
    "sys.path.append('modules')\n",
    "\n",
    "from DesignMat import Polynomial\n",
    "from Classifier import LeastSquares, Logistic\n",
    "\n",
    "from sklearn.linear_model import LinearRegression, LogisticRegression, BayesianRidge\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis, QuadraticDiscriminantAnalysis\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Models for Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We introduce 3 training datasets that will be used in this note."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(12321)\n",
    "x0 = np.random.normal(size=50).reshape(-1, 2) - 1\n",
    "x1 = np.random.normal(size=50).reshape(-1, 2) + 1\n",
    "x2 = np.random.normal(size=50).reshape(-1, 2) + 3.\n",
    "x_1 = np.random.normal(size=10).reshape(-1, 2) + np.array([11., 10.])\n",
    "\n",
    "train_data ={'2-class': (np.concatenate([x0, x1]), np.concatenate([np.zeros(25), np.ones(25)]).astype(np.int)),\n",
    "             '2-class_ex': \n",
    "             (np.concatenate([x0, x1, x_1]), np.concatenate([np.zeros(25), np.ones(30)]).astype(np.int)),\n",
    "             '3-class':\n",
    "             (np.concatenate([x0, x1, x2]), np.concatenate([np.zeros(25), np.ones(25), 2 + np.zeros(25)]).astype(np.int))}\n",
    "\n",
    "plt.figure(figsize=(15, 4))\n",
    "for i, (key, value) in enumerate(train_data.items()):\n",
    "    plt.subplot(1, 3, i+1)\n",
    "    x_train, t_train = value\n",
    "    plt.scatter(x_train[:,0], x_train[:,1], c=t_train, cmap=matplotlib.colors.ListedColormap(['red','green','blue']))\n",
    "    plt.title(\"{}\".format(key))\n",
    "plt.show()\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal in classification is to assign $p$-dimension $\\mathbf{x}$ to one of $K$ classes $\\mathcal{C}_k$. In general, there are two approaches to perform the task:\n",
    "\n",
    "- Nonprobabilistic approach constructs a **discriminant** function that directly assigns each vector $\\mathbf{x}$ to a specific class.\n",
    "\n",
    "- Probabilistic approach models the conditional probability distribution $p(\\mathcal{C}_k|\\mathbf{x})$ in an **inference** stage, and then subsequently uses this distribution to make optimal decisions.\n",
    "\n",
    "We define target vector as \n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{t} = (t_k: k = 1, \\ldots, K)^\\intercal\n",
    "\\end{align*}\n",
    "\n",
    "where the value of $t_k$ is interpreted as the probability that the class is $\\mathcal{C}_k$. For example, $\\mathbf{t} = (0, 1, 0, 0, 0)^\\intercal$ indicates a pattern from class 2 out of 5 classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discriminant Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When $K=2$, consider a linear discriminant function $y(\\mathbf{x}) = \\mathbf{w}^\\intercal \\mathbf{x} + w_0$ assigns $\\mathbf{x}$ to \n",
    "\n",
    "- class $\\mathcal{C}_1$ if $y(\\mathbf{x}) \\ge 0$, and\n",
    "\n",
    "- class $\\mathcal{C}_2$ otherwise.\n",
    "\n",
    "where $\\mathbf{w}$ is called a weight vector, and $w_0$ is a bias. The negative of the bias is sometimes called a threshold.\n",
    "\n",
    "When $K>2$, it is tempting to build a $K$-class discriminant by combining two-class functions.\n",
    "\n",
    "![discriminant](https://github.com/ming-zhao/Optimization-and-Learning/blob/master/figures/discriminant.png?raw=true)\n",
    "\n",
    "- One-versus-the-rest: $K-1$ classifiers each of which solves a two-class problem of separating points in a particular class $\\mathcal{C}_k$ from points not in that class.\n",
    "\t\t\n",
    "- One-versus-one: $K(K-1)/2$ binary discriminant functions, one for every possible pair of classes.\n",
    "\n",
    "- Both approach lead to regions of input space that are ambiguously classified.\n",
    "\n",
    "A single $K$-class discriminant comprising $K$ linear functions of the form:\n",
    "\n",
    "\\begin{align*}\n",
    "y_k(\\mathbf{x}) = \\mathbf{w}_k^\\intercal \\mathbf{x} + w_{k0}\n",
    "\\end{align*}\n",
    "\n",
    "$\\mathbf{x}$ is assigned to class $\\mathcal{C}_{k^\\ast}$ if $y_{k^\\ast}(\\mathbf{x}) > y_j(\\mathbf{x})$ for all $j \\ne k^\\ast$, i.e. class \n",
    "\n",
    "\\begin{align*}\n",
    "k^* = \\text{argmax}_k \\{y_k(\\mathbf{x}): k = 1,\\ldots,K\\}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a training data set $\\{\\mathbf{x}_i, \\mathbf{t}_i\\}$ where $i = 1,\\ldots,n$. The least squares approach is to find $\\mathbf{w}_k$, $k = 1, \\ldots, K$ such that \n",
    "\n",
    ">the sum-of-squares error between $\\mathbf{y}(\\mathbf{x_i}) = (y_1(\\mathbf{x}), \\ldots, y_K(\\mathbf{x}))$ and $\\mathbf{t}_i$ is minimal.\n",
    "\n",
    "- The least squares is equivalent to maximum likelihood of a Gaussian conditional distribution ($p(y|\\mathbf{x}, \\mathbf{w}, \\beta) = \\mathcal{N}(y | f(\\mathbf{x}, \\mathbf{w}), \\beta^{-1})$),\n",
    "\n",
    "- However, binary target vectors clearly have a distribution that is far from Gaussian.\n",
    "\n",
    "- When, for most of $\\mathbf{x} \\in \\mathcal{C}_k$, there always exists $j$ such that $y_{k}(\\mathbf{x}) < y_j(\\mathbf{x})$ for many, class $\\mathcal{C}_k$ is masked by others because the nature of linear function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Least squares solution**\n",
    "\n",
    "We can conveniently group those linear models together using vector notation so that\n",
    "\\begin{align}\n",
    "\\mathbf{y}(\\mathbf{x}) = \\tilde{\\mathbf{W}}^T \\tilde{\\mathbf{x}} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{align}\n",
    "\\tilde{\\mathbf{W}} = \\left( \\begin{array}{lll}\n",
    "w_{10} & \\cdots & w_{K0} \\\\\n",
    "\\mathbf{w}_1^\\intercal & \\cdots & \\mathbf{w}_K^\\intercal\n",
    "\\end{array} \\right) =\n",
    "\\left( \\begin{array}{lll}\n",
    "w_{10} & \\cdots & w_{K0} \\\\\n",
    "w_{11} & \\cdots & w_{K1} \\\\\n",
    "\\vdots & \\ddots & \\vdots \\\\\n",
    "w_{1d} & \\cdots & w_{Kd} \\\\\n",
    "\\end{array} \\right)_{(p+1) \\times K},~\n",
    "\\tilde{\\mathbf{x}} = \\left( \\begin{array}{l}\n",
    "1  \\\\\n",
    "x_{1}  \\\\\n",
    "\\vdots  \\\\\n",
    "x_{p}  \\\\\n",
    "\\end{array} \\right) \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "Consider a training data set $\\{\\mathbf{x}_i, \\mathbf{t}_i\\}$ where $i = 1,\\ldots,n$ and define\n",
    "\n",
    "\\begin{align}\n",
    "\\mathbf{T} =\n",
    "\\left( \\begin{array}{l}\n",
    "\\mathbf{t}_1 \\\\\n",
    "\\mathbf{t}_2 \\\\\n",
    "\\vdots \\\\\n",
    "\\mathbf{t}_n \\\\\n",
    "\\end{array} \\right)_{n \\times K} \\text{ and }\n",
    "\\tilde{\\mathbf{X}} =\n",
    "\\left( \\begin{array}{l}\n",
    "\\tilde{\\mathbf{x}}^\\intercal_1 \\\\\n",
    "\\tilde{\\mathbf{x}}^\\intercal_2 \\\\\n",
    "\\vdots \\\\\n",
    "\\tilde{\\mathbf{x}}^\\intercal_n \\\\\n",
    "\\end{array} \\right)_{n \\times (p+1)} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "where $\\mathbf{t}_i = (0, \\ldots, 0, \\underbrace{1}_{k}, 0, \\ldots, 0 )_{K \\times 1}$ indicates $\\mathbf{x}_i \\in k$-class. Minimizing the sum-of-squares error function\n",
    "\n",
    "\\begin{align}\n",
    "\\mathbb{SSE} \\left[ \\tilde{\\mathbf{W}} \\right] = \\frac{1}{2} \\text{Tr} \\left\\{ \\left( \\tilde{\\mathbf{X}}\\tilde{\\mathbf{W}} - \\mathbf{T}\\right)^\\intercal \\left( \\tilde{\\mathbf{X}}\\tilde{\\mathbf{W}} - \\mathbf{T}\\right) \\right\\} \\text{ gives } \\tilde{\\mathbf{W}} = \\left( \\tilde{\\mathbf{X}}^\\intercal \\tilde{\\mathbf{X}} \\right)^{-1} \\tilde{\\mathbf{X}}^\\intercal \\mathbf{T} \\nonumber\n",
    "\\end{align} \n",
    "\n",
    "<span style=\"float:right\"> $\\blacksquare$ </span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots demonstrate the least squares method for classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1_test, x2_test = np.meshgrid(np.linspace(-5, 12, 100), np.linspace(-5, 12, 100))\n",
    "x_test = np.array([x1_test, x2_test]).reshape(2, -1).T\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "for i, (key, value) in enumerate(train_data.items()):\n",
    "    plt.subplot(1, 3, i+1)\n",
    "    x_train, t_train = value\n",
    "    t = LeastSquares().fit(x_train, t_train).predict(x_test)\n",
    "    plt.scatter(x_train[:,0], x_train[:,1], c=t_train, cmap=matplotlib.colors.ListedColormap(['red','green','blue']))\n",
    "    plt.contourf(x1_test, x2_test, t.reshape(100, 100), alpha=0.3, levels=np.array([0., 0.5, 1.5, 2.]), \n",
    "                 cmap=matplotlib.colors.ListedColormap(['yellow','green','purple']))\n",
    "    plt.xlim(-5, 12)\n",
    "    plt.ylim(-5, 12)\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    plt.title(\"{}\".format(key))\n",
    "    \n",
    "plt.show()\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Least squares fails on many aspects:\n",
    "\n",
    "- lacks roubustness: highly sensitive to outliers \n",
    "\n",
    "- gives poor classification: assign small region to the middle cluster\n",
    "\n",
    "The failure of least squares should not surprise us when we recall that it corresponds to maximum likelihood under the assumption of a Gaussian conditional distribution, whereas binary target vectors clearly have a distribution that is far from Gaussian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a serious problem with the least squares approach when $K \\ge 3$ where classes can be masked by others. Consider an extreme situation with simulated dataset as follows.\n",
    "\n",
    "The middle class is mostly masked (dominated) by other two classes as many points of the middle class are assigned colors of other two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "size = 100\n",
    "np.random.seed(123)\n",
    "x0 = np.random.multivariate_normal([-4, -4], np.eye(2), size)\n",
    "x1 = np.random.multivariate_normal([ 0,  0], np.eye(2), size)\n",
    "x2 = np.random.multivariate_normal([ 4,  4], np.eye(2), size)\n",
    "x = np.concatenate((x0, x1, x2))\n",
    "x_tilde = np.hstack((np.ones((size*3, 1)), x))\n",
    "t1, t2, t3 = np.eye(3)\n",
    "t = np.vstack((np.tile(t1, (size, 1)),\n",
    "               np.tile(t2, (size, 1)),\n",
    "               np.tile(t3, (size, 1))))\n",
    "\n",
    "reg = LinearRegression().fit(x, t)\n",
    "y = reg.predict(x)\n",
    "t_pred = y.argmax(axis=1)\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.pipeline import Pipeline\n",
    "polyreg = Pipeline([('poly', PolynomialFeatures(degree=2)),\n",
    "                  ('linear', LinearRegression())])\n",
    "poly_y = polyreg.fit(x, t).predict(x)\n",
    "\n",
    "plt.figure(figsize=(12, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x0[:,0], x0[:,1], 'o', color='C0', markersize=3)\n",
    "plt.plot(x1[:,0], x1[:,1], 'o', color='C1', markersize=3)\n",
    "plt.plot(x2[:,0], x2[:,1], 'o', color='C2', markersize=3)\n",
    "plt.xlabel('$x_1$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.title('Simulated Data')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(x[t_pred == 0][:,0], x[t_pred == 0][:,1], 'o', color='C0', markersize=3)\n",
    "plt.plot(x[t_pred == 1][:,0], x[t_pred == 1][:,1], 'o', color='C1', markersize=3)\n",
    "plt.plot(x[t_pred == 2][:,0], x[t_pred == 2][:,1], 'o', color='C2', markersize=3)\n",
    "plt.xlabel('$x_1$')\n",
    "plt.ylabel('$x_2$')\n",
    "plt.title('Classification using Linear Regression')\n",
    "\n",
    "plt.show()\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each simulated point $(x_1, x_2)$, we have its $y$ (or $\\hat{y}$) value based on linear (or degree 2 polynomial) regression  equation, where $y$ (or $\\hat{y}$) has three components corresponding to three probabilities for each class.\n",
    "\n",
    "The `plot(x, y[:, 0], 'o', color='C0', markersize=2)` function plots two points $(x_1, y_0)$ and $(x_2, y_0)$ where $y_0$ is the probability that this point is in the first class.\n",
    "\n",
    "The classified class is defined as\n",
    "\n",
    "\\begin{align*}\n",
    "k^* = \\text{argmax}_k \\{y_k(\\mathbf{x}): k = 1,\\ldots,K\\}\n",
    "\\end{align*}\n",
    "\n",
    "or `t_pred = reg.predict(x).argmax(axis=1)`.\n",
    "\n",
    "Because of this `argmax` operator, the middle class cannot be identified in linear regression model, but can be identified in a polynomial regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = plt.figure(1, figsize=(12, 5))\n",
    "ax1 = fig.add_subplot(1, 2, 1)\n",
    "ax1.plot(x, y[:, 0], 'o', color='C0', markersize=2)\n",
    "ax1.plot(x, y[:, 1], 'o', color='C1', markersize=2)\n",
    "ax1.plot(x, y[:, 2], 'o', color='C2', markersize=2)\n",
    "y_floor, _ = ax1.get_ylim()\n",
    "ax1.plot(x0, [y_floor]*size, 'o', color='C0', markersize=2)\n",
    "ax1.plot(x1, [y_floor]*size, 'o', color='C1', markersize=2)\n",
    "ax1.plot(x2, [y_floor]*size, 'o', color='C2', markersize=2)\n",
    "ax1.set_title('Linear Regression')\n",
    "\n",
    "ax2 = fig.add_subplot(1, 2, 2)\n",
    "ax2.plot(x, poly_y[:, 0], 'o', color='C0', markersize=2)\n",
    "ax2.plot(x, poly_y[:, 1], 'o', color='C1', markersize=2)\n",
    "ax2.plot(x, poly_y[:, 2], 'o', color='C2', markersize=2)\n",
    "y_floor, _ = ax2.get_ylim()\n",
    "ax2.plot(x0, [y_floor]*size, 'o', color='C0', markersize=2)\n",
    "ax2.plot(x1, [y_floor]*size, 'o', color='C1', markersize=2)\n",
    "ax2.plot(x2, [y_floor]*size, 'o', color='C2', markersize=2)\n",
    "ax2.set_title('Polynomial(deg=2) Regression')\n",
    "plt.show()\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Discriminant Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear Discriminant Analysis (LDA) is most commonly used as dimensionality reduction technique in the pre-processing step for pattern-classification and machine learning applications. The goal is to project a dataset onto a lower-dimensional space with good class-separability in order avoid overfitting (\"curse of dimensionality\") and also reduce computational costs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For optimal classification, we need to know the class posteriors $p(\\mathcal{C}_k | \\mathbf{x})$ of our observation $\\mathbf{x}$:\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathcal{C}_k | \\mathbf{x}) = \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{p(\\mathbf{x})} = \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{\\sum_{j}p(\\mathbf{x}|\\mathcal{C}_j)p(\\mathcal{C}_j)}\n",
    "\\end{align*}\n",
    "\n",
    "Assume class-conditional densities are Gaussian with common covariance matrix $\\Sigma$. \n",
    "\n",
    "\\begin{align}\n",
    "p(\\mathbf{x}|\\mathcal{C}_k) = \\frac{1}{(2\\pi)^{D/2}} \\frac{1}{\\lvert \\Sigma \\rvert ^{1/2}} \\exp \\left( -\\frac{1}{2} (\\mathbf{x} - \\mathbf{\\mu}_k)^\\intercal \\Sigma^{-1} (\\mathbf{x} - \\mathbf{\\mu}_k) \\right) \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "If $p(\\mathbf{x}|\\mathcal{C}_k)$ has its own covariance matrix $\\Sigma_k$, then we will obtain $y_k(\\mathbf{x})$ as a quadratic discriminant function of $\\mathbf{x}$, giving rise to a quadratic discriminant analysis.\n",
    "\n",
    "When comparing two classes $k$, $\\ell$ by $p(\\mathcal{C}_k | \\mathbf{x}) - p(\\mathcal{C}_\\ell | \\mathbf{x})$, it is sufficient to consider\n",
    "\n",
    "\\begin{align}\n",
    "\\ln p(\\mathcal{C}_k| \\mathbf{x}) - \\ln p(\\mathcal{C}_\\ell | \\mathbf{x}) &= \\ln \\frac{p(\\mathcal{C}_k | \\mathbf{x})}{p(\\mathcal{C}_\\ell | \\mathbf{x})} = \\ln \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{p(\\mathbf{x}|\\mathcal{C}_\\ell)p(\\mathcal{C}_\\ell)} \\nonumber \\\\\n",
    "& = \\mathbf{x}^\\intercal \\Sigma^{-1} (\\mu_k - \\mu_\\ell) - \\frac{1}{2} (\\mu_k+\\mu_\\ell)^\\intercal \\Sigma^{-1} (\\mu_k - \\mu_\\ell) + \\ln \\frac{p(\\mathcal{C}_k)}{p(\\mathcal{C}_\\ell)} \\tag{LDA} \\\\\n",
    "& \\equiv \\ln \\frac{y_k(\\mathbf{x})}{y_\\ell(\\mathbf{x})} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "The discriminant function\n",
    "\\begin{align*}\n",
    "y_k(\\mathbf{x}) = \\ln p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k) &= \\mathbf{w}^\\intercal_k \\mathbf{x} + w_{k0} \\text{ where}\\\\\n",
    "\\mathbf{w}_k &= \\Sigma^{-1} \\mu_k \\\\\n",
    "w_{k0} &= - \\frac{1}{2} \\mu^\\intercal_k \\Sigma^{-1} \\mu_k + \\ln p(\\mathcal{C}_k)\n",
    "\\end{align*}\n",
    "\n",
    "The parameters of the Gaussian distributions are estimated through training data\n",
    "\n",
    "- $p(\\mathcal{C}_k) = n_k / n$ where $n_k$ is the number of class-$k$ observations\n",
    " \n",
    "- $\\mu_k = \\sum_{j \\in \\mathcal{C}_k} \\mathbf{x}_j / n_k$\n",
    "\n",
    "- $\\Sigma = 1/n \\sum_{k=1}^{K} \\sum_{j \\in \\mathcal{C}_k} (\\mathbf{x}_j - \\mu_k)^\\intercal (\\mathbf{x}_j - \\mu_k)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fisher's Linear Discriminant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fisher derived LDA via a route without referring to Gaussian distributions.\n",
    "\n",
    "Fisher's idea is to maximize a function that\n",
    "\n",
    "- give a large separation between the projected class means\n",
    "\n",
    "- give a small variance within each class\n",
    "\n",
    "thereby minimizing the class overlap.\n",
    "\n",
    "![fisher](https://github.com/ming-zhao/Optimization-and-Learning/blob/master/figures/fisher.png?raw=true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a two-class problem with $n_1$ points of class $\\mathcal{C}_1$ and $n_2$ points of class $\\mathcal{C}_2$\n",
    "\n",
    "- We need reduce $p$-dimension $\\mathbf{x}$ to one dimension using $y = \\mathbf{w}^\\intercal \\mathbf{x}$\n",
    "\n",
    "- We choose $\\mathbf{w}$ to maximize $\\mathbf{w}^\\intercal(\\mathbf{m}_1-\\mathbf{m}_2) \\equiv m_1-m_2$, with scaler $\\sum_{i} w^2_i=1$.\n",
    "\n",
    "where the mean vectors of two classes\n",
    "\n",
    "\\begin{align}\n",
    "\\mathbf{m}_1 = \\frac{1}{n_1} \\sum_{i \\in \\mathcal{C}_1} \\mathbf{x}_i \\text{ and } \\mathbf{m}_2 = \\frac{1}{n_2} \\sum_{i \\in \\mathcal{C}_2} \\mathbf{x}_i \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "We can get\n",
    "\n",
    "\\begin{align}\n",
    "\\mathbf{w} \\propto S^{-1}_W(\\mathbf{m}_2-\\mathbf{m}_1) \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "where $S_W$ is the total within-class covariance matrix. Note $S^{-1}_W$ is equivalent to $\\Sigma^{-1}$ in (LDA). Hence, Fisher's method gives the same discriminant function as in (LDA)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fisher's method is to maximize\n",
    "\n",
    "\\begin{align}\n",
    "J(\\mathbf{w}) &= \\frac{(m_1 - m_2)^2}{\\sum_{k=1}^{2}\\sum_{i \\in \\mathcal{C}_k} (y_i-m_k)^2} = \\frac{\\text{between class variance}}{\\text{within class variance}} \\nonumber \\\\\n",
    "&= \\frac{\\mathbf{w}^\\intercal (\\mathbf{m}_2-\\mathbf{m}_1) \\bigg(\\mathbf{w}^\\intercal(\\mathbf{m}_2-\\mathbf{m}_1)\\bigg)^\\intercal}{\\sum_{k=1}^{2} \\sum_{i \\in \\mathcal{C}_k} \\mathbf{w}^\\intercal(\\mathbf{x}_i - \\mathbf{m}_1) \\bigg(\\mathbf{w}^\\intercal(\\mathbf{x}_i - \\mathbf{m}_1)\\bigg)^\\intercal} \\nonumber \\\\\n",
    "&= \\frac{\\mathbf{w}^\\intercal (\\mathbf{m}_2-\\mathbf{m}_1)(\\mathbf{m}_2-\\mathbf{m}_1)^\\intercal \\mathbf{w}}{\\mathbf{w}^\\intercal \\sum_{k=1}^{2} \\sum_{i \\in \\mathcal{C}_k} (\\mathbf{x}_i - \\mathbf{m}_k)(\\mathbf{x}_i - \\mathbf{m}_k)^\\intercal \\mathbf{w}} \\nonumber \\\\\n",
    "&\\equiv \\frac{\\mathbf{w}^\\intercal \\mathbf{S}_B \\mathbf{w}}{\\mathbf{w}^\\intercal \\mathbf{S}_W \\mathbf{w}} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "\\begin{align}\n",
    "J^\\prime(\\mathbf{w}) &= 0 \\Rightarrow \\left(\\mathbf{w}^\\intercal \\mathbf{S}_W \\mathbf{w}\\right) \\mathbf{S}_B \\mathbf{w} = \\left(\\mathbf{w}^\\intercal \\mathbf{S}_B \\mathbf{w}\\right) \\mathbf{S}_W \\mathbf{w} \\Rightarrow \\mathbf{w} \\propto S^{-1}_W(\\mathbf{m}_2-\\mathbf{m}_1) \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For general $K$, Fisher's method is to maximize so called Rayleigh quotient\n",
    "\n",
    "\\begin{align}\n",
    "\\max_{\\mathbf{w}} J(\\mathbf{w}) = \\frac{\\mathbf{w}^\\intercal \\mathbf{S}_B \\mathbf{w}}{\\mathbf{w}^\\intercal \\mathbf{S}_W \\mathbf{w}} = \\frac{\\text{between class variance}}{\\text{within class variance}} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "\n",
    "where\n",
    "\\begin{align*}\n",
    "S_B &=  \\sum_{k=1}^{K} n_{k} (\\mathbf{m}_k - \\mathbf{m}) (\\mathbf{m}_k - \\mathbf{m})^\\intercal \\\\\n",
    "S_W &= \\sum_{k=1}^{K} S_k \\text{ with } S_k = \\sum_{i \\in \\mathcal{C}_k} (\\mathbf{x}_i - \\mathbf{m}_k) (\\mathbf{x}_i - \\mathbf{m}_k)^\\intercal\t\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{m}_k &= \\frac{1}{n_k} \\sum_{i \\in \\mathcal{C}_k} \\mathbf{x}_i \\\\\n",
    "\\mathbf{m} &=  \\frac{1}{n} \\sum_{i=1}^{n} \\mathbf{x}_i = \\frac{1}{n} \\sum_{k=1}^{K} n_k \\mathbf{m}_k\n",
    "\\end{align*}\n",
    "\n",
    "and $n_k$ is the sample size of the class $k$.\n",
    "\n",
    "Because $J(\\mathbf{w})$ is invariant w.r.t. rescaling of $\\mathbf{w} \\leftarrow \\alpha \\mathbf{w}$, so that we can choose $\\alpha$ as to have a unit denominator $\\mathbf{w}^\\intercal S_W \\mathbf{w} = 1$ (since it is a scalar). Thus\n",
    "\n",
    "\\begin{align*}\n",
    "\\max_{\\mathbf{w}}~ J(\\mathbf{w}) = \\min_{\\mathbf{w}} - \\mathbf{w}^\\intercal S_B \\mathbf{w} ~\\text{ s.t. } \\mathbf{w}^\\intercal S_W \\mathbf{w} = 1\n",
    "\\end{align*}\n",
    "\n",
    "Let $\\mathbf{w}^\\ast = S_W^{1/2} \\mathbf{w}$ and $S^*_B = (S_W^{-1/2})^\\intercal S_B S_W^{-1/2}$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\min_{\\mathbf{w}^*}~ -(\\mathbf{w}^*)^\\intercal S^*_B \\mathbf{w}^* ~\\text{ s.t. } (\\mathbf{w}^*)^\\intercal \\mathbf{w}^* = 1\n",
    "\\end{align*}\n",
    "\n",
    "Note that let $M$ be the $K \\times p$ matrix of centroids $\\mu_k$. Then\n",
    "\n",
    "\\begin{align*}\n",
    "S_B &= M^\\intercal M \\\\\n",
    "S^*_B &= (M S_W^{-1/2})^\\intercal (M S_W^{-1/2})\n",
    "\\end{align*}\n",
    "\n",
    "The Lagrangien is\n",
    "\n",
    "\\begin{align*}\n",
    "L = -(\\mathbf{w}^{*})^{\\intercal}S_B^{*}\\mathbf{w}^{*} + \\lambda[(\\mathbf{w}^{*})^{\\intercal}\\mathbf{w}^{*}-1]\n",
    "\\end{align*}\n",
    "\n",
    "Its derivative gives\n",
    "\n",
    "\\begin{align*}\n",
    "S_B^{*}\\mathbf{w}^{*}=\\lambda \\mathbf{w}^{*}\n",
    "\\end{align*}\n",
    "\n",
    "The optimization becomes an eigendecomposition problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The relationship between LDA and linear regression**\n",
    "\n",
    "When $K=2$, there is a simple correspondence between LDA and linear regression:\n",
    "\n",
    "we adopt a different target coding scheme that\n",
    "\n",
    "- $t_i =n/n_1$ if the input $\\mathbf{x}_i$ is in class $\\mathcal{C}_1$ (the value approximates the reciprocal of the prior probability for class $\\mathcal{C}_1$) and;\n",
    "\n",
    "- $t_i = -n/n_2$ if the input $\\mathbf{x}_i$ is in class $\\mathcal{C}_2$,\n",
    "\n",
    "where $n$ is the total number observations and $n_k$ ($k=1, 2$) is the number observations in class $k$.\n",
    "\n",
    "Minimizing the sum of squares error function\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{1}{2} \\sum_{i=1}^{n} \\left(\\mathbf{w}^\\intercal \\mathbf{x}_i + w_0 - t_i \\right)^2 \\text{ gives } \\mathbf{w} \\propto S^{-1}_W(\\mathbf{m}_2-\\mathbf{m}_1) \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "<span style=\"float:right\"> $\\blacksquare$ </span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code demonstrate the implementation of Fisher's method for 2-class data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train, t_train = train_data['2-class']\n",
    "x1_test, x2_test = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.array([x1_test, x2_test]).reshape(2, -1).T\n",
    "\n",
    "X0 = x_train[t_train == 0]\n",
    "X1 = x_train[t_train == 1]\n",
    "m0 = np.mean(X0, axis=0)\n",
    "m1 = np.mean(X1, axis=0)\n",
    "cov_inclass = (X0 - m0).T @ (X0 - m0) + (X1 - m1).T @ (X1 - m1)\n",
    "w = np.linalg.solve(cov_inclass, m1 - m0)\n",
    "w /= np.linalg.norm(w).clip(min=1e-10)\n",
    "\n",
    "mu0 = np.mean(X0 @ w, axis=0)\n",
    "mu1 = np.mean(X1 @ w, axis=0)\n",
    "var0 = np.var(X0 @ w, axis=0)\n",
    "var1 = np.var(X1 @ w, axis=0)\n",
    "a = var1 - var0\n",
    "b = var0 * mu1 - var1 * mu0\n",
    "c = var1 * mu0 ** 2 - var0 * mu1 ** 2 - var1 * var0 * np.log(var1 / var0)\n",
    "threshold = (np.sqrt(b ** 2 - a * c) - b) / a\n",
    "\n",
    "t = (x_test @ w > threshold).astype(np.int)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t_train)\n",
    "plt.contourf(x1_test, x2_test, t.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3),\n",
    "             cmap=matplotlib.colors.ListedColormap(['yellow','green','purple']))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.gca().set_aspect('equal', adjustable='box')\n",
    "plt.show()\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LDA: Iris Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the famous \"Iris\" dataset which contains measurements for 150 iris flowers from three different species.\n",
    "\n",
    "The three classes ($K=3$) in the Iris dataset:\n",
    "\n",
    "- Iris-setosa (n=50)\n",
    "\n",
    "- Iris-versicolor (n=50)\n",
    "\n",
    "- Iris-virginica (n=50)\n",
    "\n",
    "The four features ($p=4$) of the Iris dataset:\n",
    "\n",
    "- sepal length in cm\n",
    "\n",
    "- sepal width in cm\n",
    "\n",
    "- petal length in cm\n",
    "\n",
    "- petal width in cm\n",
    "\n",
    "<img src=\"https://github.com/ming-zhao/Optimization-and-Learning/raw/master/figures/iris_petal_sepal.png\" width=\"300\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_dict = {i:label for i,label in zip(\n",
    "                range(4),\n",
    "                  ('sepal length in cm',\n",
    "                  'sepal width in cm',\n",
    "                  'petal length in cm',\n",
    "                  'petal width in cm', ))}\n",
    "df = pd.read_csv(\n",
    "    'https://raw.githubusercontent.com/ming-zhao/Optimization-and-Learning/master/data/iris.data',\n",
    "    header=None, sep=',')\n",
    "df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']\n",
    "df.dropna(how=\"all\", inplace=True) # to drop the empty line at file-end\n",
    "df.tail()\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define\n",
    "\n",
    "\\begin{align}\n",
    "\\pmb X = \\begin{bmatrix} x_{1_{\\text{sepal length}}} & x_{1_{\\text{sepal width}}} & x_{1_{\\text{petal length}}} & x_{1_{\\text{petal width}}}\\\\\n",
    "x_{2_{\\text{sepal length}}} & x_{2_{\\text{sepal width}}} & x_{2_{\\text{petal length}}} & x_{2_{\\text{petal width}}}\\\\\n",
    "...  \\\\\n",
    "x_{150_{\\text{sepal length}}} & x_{150_{\\text{sepal width}}} & x_{150_{\\text{petal length}}} & x_{150_{\\text{petal width}}}\\\\\n",
    "\\end{bmatrix}, ~~\n",
    "\\pmb y = \\begin{bmatrix} \\omega_{\\text{setosa}}\\\\\n",
    "\\omega_{\\text{setosa}}\\\\\n",
    "...  \\\\\n",
    "\\omega_{\\text{virginica}}\\end{bmatrix} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "We use the `LabelEncode` from the `scikit-learn` library to convert the class labels into numbers: 1, 2, and 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import LabelEncoder\n",
    "X = df[df.columns[:-1]].values\n",
    "y = df['class label'].values\n",
    "\n",
    "enc = LabelEncoder()\n",
    "label_encoder = enc.fit(y)\n",
    "y = label_encoder.transform(y) + 1\n",
    "\n",
    "label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\pmb y = \\begin{bmatrix}{\\text{setosa}}\\\\\n",
    "{\\text{setosa}}\\\\\n",
    "...  \\\\\n",
    "{\\text{virginica}}\\end{bmatrix} \\quad \\Rightarrow\n",
    "\\begin{bmatrix} {\\text{1}}\\\\\n",
    "{\\text{1}}\\\\\n",
    "...  \\\\\n",
    "{\\text{3}}\\end{bmatrix}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Histograms and feature selection\n",
    "\n",
    "To get a rough idea how the samples of three classes are distributed, let us visualize the distributions of the four different features in 1-dimensional histograms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12,6))\n",
    "\n",
    "for ax,cnt in zip(axes.ravel(), range(4)):  \n",
    "\n",
    "    # set bin sizes\n",
    "    min_b = np.floor(np.min(X[:,cnt]))\n",
    "    max_b = np.ceil(np.max(X[:,cnt]))\n",
    "    bins = np.linspace(min_b, max_b, 25)\n",
    "\n",
    "    # plottling the histograms\n",
    "    for lab,col in zip(range(1,4), ('blue', 'red', 'green')):\n",
    "        ax.hist(X[y==lab, cnt],\n",
    "                   color=col,\n",
    "                   label='class %s' %label_dict[lab],\n",
    "                   bins=bins,\n",
    "                   alpha=0.5,)\n",
    "    ylims = ax.get_ylim()\n",
    "\n",
    "    # plot annotation\n",
    "    leg = ax.legend(loc='upper right', fancybox=True, fontsize=8)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    ax.set_ylim([0, max(ylims)+2])\n",
    "    ax.set_xlabel(feature_dict[cnt])\n",
    "    ax.set_title('Iris histogram #%s' %str(cnt+1))\n",
    "\n",
    "    # hide axis ticks\n",
    "    ax.tick_params(axis=\"both\", which=\"both\", bottom=False, top=False,  \n",
    "            labelbottom=True, left=False, right=False, labelleft=True)\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "axes[0][0].set_ylabel('count')\n",
    "axes[1][0].set_ylabel('count')\n",
    "\n",
    "fig.tight_layout()       \n",
    "\n",
    "plt.show()\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From just looking at these simple graphical representations of the features, we can already tell that the petal lengths and widths (histogram \\#3 and \\#4) are likely better suited as potential features two separate between the three flower classes. \n",
    "\n",
    "In practice, instead of reducing the dimensionality via a projection (here: LDA), a good alternative would be a feature selection technique. For low-dimensional datasets like Iris, a glance at those histograms would already be very informative. Another simple, but very useful technique would be to use feature selection algorithms.\n",
    "\n",
    "LDA assumes normal distributed data, features that are statistically independent, and identical covariance matrices for every class. However, LDA can work reasonably well if those assumptions are violated.\n",
    "\n",
    "In practice, LDA for dimensionality reduction would be just another preprocessing step for a typical machine learning or pattern classification task."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing Mean Vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this first step, we will start off with a simple computation of the mean vectors $\\mathbf{m}_i$, $i=1,2,3$ of the 3 different flower classes:\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{m}_i = \\begin{bmatrix}\n",
    "\\mu_{\\omega_i (\\text{sepal length)}}\\\\\n",
    "\\mu_{\\omega_i (\\text{sepal width})}\\\\\n",
    "\\mu_{\\omega_i (\\text{petal length)}}\\\\\n",
    "\\mu_{\\omega_i (\\text{petal width})}\\\\\n",
    "\\end{bmatrix} \\; , \\quad \\text{with} \\quad i = 1,2,3\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Vector class 1: [5.006 3.418 1.464 0.244]\n",
      "\n",
      "Mean Vector class 2: [5.936 2.77  4.26  1.326]\n",
      "\n",
      "Mean Vector class 3: [6.588 2.974 5.552 2.026]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(precision=4)\n",
    "\n",
    "mean_vectors = []\n",
    "for cl in range(1,4):\n",
    "    mean_vectors.append(np.mean(X[y==cl], axis=0))\n",
    "    print('Mean Vector class %s: %s\\n' %(cl, mean_vectors[cl-1]))\n",
    "    \n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the Scatter Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will compute the two $4 \\times 4$ $(p \\times p)$-dimensional matrices: The within-class and the between-class scatter matrix.\n",
    "\n",
    "Within-class scatter matrix\n",
    "\\begin{align*}\n",
    "S_W = \\sum_{k=1}^{K} S_k\n",
    "\\end{align*}\n",
    "\n",
    "where\n",
    "\\begin{align*}\n",
    "S_k &= \\sum_{i \\in \\mathcal{C}_k} (\\mathbf{x}_i - \\mathbf{m}_k) (\\mathbf{x}_i - \\mathbf{m}_k)^\\intercal \\\\\n",
    "\\mathbf{m}_k &= \\frac{1}{n_k} \\sum_{i \\in \\mathcal{C}_k} \\mathbf{x}_i\n",
    "\\end{align*}\n",
    "\n",
    "and $n_k$ is the sample size of the class $k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "within-class Scatter Matrix:\n",
      " [[38.9562 13.683  24.614   5.6556]\n",
      " [13.683  17.035   8.12    4.9132]\n",
      " [24.614   8.12   27.22    6.2536]\n",
      " [ 5.6556  4.9132  6.2536  6.1756]]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
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       "<IPython.core.display.HTML object>"
      ]
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     "execution_count": 13,
     "metadata": {},
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   ],
   "source": [
    "S_W = np.zeros((4,4))\n",
    "for cl,mv in zip(range(1,4), mean_vectors):\n",
    "    class_sc_mat = np.zeros((4,4))                  # scatter matrix for every class\n",
    "    for row in X[y == cl]:\n",
    "        row, mv = row.reshape(4,1), mv.reshape(4,1) # make column vectors\n",
    "        class_sc_mat += (row-mv).dot((row-mv).T)\n",
    "    S_W += class_sc_mat                             # sum class scatter matrices\n",
    "print('within-class Scatter Matrix:\\n', S_W)\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total variance matrix\n",
    "\\begin{align*}\n",
    "S_T =  \\sum_{i=1}^{n} (\\mathbf{x}_i - \\mathbf{m}) (\\mathbf{x}_i - \\mathbf{m})^\\intercal\n",
    "\\end{align*}\n",
    "\n",
    "where $\\mathbf{m}$ is the mean of total data set\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{m} =  \\frac{1}{n} \\sum_{i=1}^{n} \\mathbf{x}_i = \\frac{1}{n} \\sum_{k=1}^{K} n_k \\mathbf{m}_k\n",
    "\\end{align*}\n",
    "\n",
    "\\begin{align*}\n",
    "S_T = S_W + S_B\n",
    "\\end{align*}\n",
    "\n",
    "where $S_B$ is between-class scatter matrix\n",
    "\n",
    "\\begin{align*}\n",
    "S_B =  \\sum_{k=1}^{K} N_{k} (\\mathbf{m}_k - \\mathbf{m}) (\\mathbf{m}_k - \\mathbf{m})^\\intercal\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "between-class Scatter Matrix:\n",
      " [[ 63.2121 -19.534  165.1647  71.3631]\n",
      " [-19.534   10.9776 -56.0552 -22.4924]\n",
      " [165.1647 -56.0552 436.6437 186.9081]\n",
      " [ 71.3631 -22.4924 186.9081  80.6041]]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
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   ],
   "source": [
    "overall_mean = np.mean(X, axis=0)\n",
    "\n",
    "S_B = np.zeros((4,4))\n",
    "for i,mean_vec in enumerate(mean_vectors):  \n",
    "    n = X[y==i+1,:].shape[0]\n",
    "    mean_vec = mean_vec.reshape(4,1) # make column vector\n",
    "    overall_mean = overall_mean.reshape(4,1) # make column vector\n",
    "    S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)\n",
    "\n",
    "print('between-class Scatter Matrix:\\n', S_B)\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solving the Generalized Eigenvalue Problem\n",
    "\n",
    "Next, we will solve the generalized eigenvalue problem for the matrix $S^{-1}_W S_B$ to obtain the linear discriminants where\n",
    "\n",
    "\\begin{align*}\n",
    "(S^{-1}_W S_B) v = \\lambda v\n",
    "\\end{align*}\n",
    "\n",
    "- $\\lambda$: eigenvalue\n",
    "\n",
    "- $v$: eigenvector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvector 1: \n",
      "[[-0.2049]\n",
      " [-0.3871]\n",
      " [ 0.5465]\n",
      " [ 0.7138]]\n",
      "Eigenvalue 1: 3.23e+01\n",
      "\n",
      "Eigenvector 2: \n",
      "[[-0.009 ]\n",
      " [-0.589 ]\n",
      " [ 0.2543]\n",
      " [-0.767 ]]\n",
      "Eigenvalue 2: 2.78e-01\n",
      "\n",
      "Eigenvector 3: \n",
      "[[-0.8844]\n",
      " [ 0.2854]\n",
      " [ 0.258 ]\n",
      " [ 0.2643]]\n",
      "Eigenvalue 3: 3.42e-15\n",
      "\n",
      "Eigenvector 4: \n",
      "[[-0.2234]\n",
      " [-0.2523]\n",
      " [-0.326 ]\n",
      " [ 0.8833]]\n",
      "Eigenvalue 4: 1.15e-14\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
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       "<IPython.core.display.HTML object>"
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     },
     "execution_count": 15,
     "metadata": {},
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   ],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))\n",
    "\n",
    "for i in range(len(eig_vals)):\n",
    "    eigvec_sc = eig_vecs[:,i].reshape(4,1)   \n",
    "    print('\\nEigenvector {}: \\n{}'.format(i+1, eigvec_sc.real))\n",
    "    print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))\n",
    "    \n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall from our linear algebra, both eigenvectors and eigenvalues are providing us with information about the distortion of a linear transformation: The eigenvectors are basically the direction of this distortion, and the eigenvalues are the scaling factor for the eigenvectors that describing the magnitude of the distortion.\n",
    "\n",
    "If we are performing the LDA for dimensionality reduction, the eigenvectors are important since they will form the new axes of our new feature subspace; the associated eigenvalues are of particular interest since they will tell us how \"informative\" the new \"axes\" are.\n",
    "\n",
    "Checking the eigenvector-eigenvalue calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(len(eig_vals)):\n",
    "    eigv = eig_vecs[:,i].reshape(4,1)\n",
    "    np.testing.assert_array_almost_equal(np.linalg.inv(S_W).dot(S_B).dot(eigv),\n",
    "                                         eig_vals[i] * eigv,\n",
    "                                         decimal=6, err_msg='', verbose=True)\n",
    "# print('ok')\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the New Feature Subspace\n",
    "\n",
    "We are interested in \n",
    "\n",
    "- projecting the data into a subspace that improves the class separability, \n",
    "\n",
    "- reducing the dimensionality of our feature space, where the eigenvectors will form the axes of this new feature subspace.\n",
    "\n",
    "So, in order to decide which eigenvector(s) we want to drop for our lower-dimensional subspace, we have to take a look at the corresponding eigenvalues of the eigenvectors (eigenvectors all have all the same unit length 1). \n",
    "\n",
    "Roughly speaking, the eigenvectors with the lowest eigenvalues bear the least information about the distribution of the data, and those are the ones we want to drop.\n",
    "\n",
    "The common approach is to rank the eigenvectors from highest to lowest corresponding eigenvalue and choose the top $C$ eigenvectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in decreasing order:\n",
      "\n",
      "32.27195779972981\n",
      "0.27756686384003953\n",
      "1.1483362279322388e-14\n",
      "3.422458920849769e-15\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
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       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make a list of (eigenvalue, eigenvector) tuples\n",
    "eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "\n",
    "print('Eigenvalues in decreasing order:\\n')\n",
    "for i in eig_pairs:\n",
    "    print(i[0])\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, these two last eigenvalues should be exactly zero. They are not because of floating-point imprecision.\n",
    "\n",
    "In LDA, the number of linear discriminants is at most $K-1$ where $K$ is the number of class labels, since the in-between scatter matrix $S_B$ is the sum of $K$ matrices with rank 1 or less. \n",
    "\n",
    "Now, let's express the \"explained variance\" as percentage:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance explained:\n",
      "\n",
      "eigenvalue 1: 99.15%\n",
      "eigenvalue 2: 0.85%\n",
      "eigenvalue 3: 0.00%\n",
      "eigenvalue 4: 0.00%\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
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       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "print('Variance explained:\\n')\n",
    "eigv_sum = sum(eig_vals)\n",
    "for i,j in enumerate(eig_pairs):\n",
    "    print('eigenvalue {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))\n",
    "    \n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first eigenpair is by far the most informative one, and we won't loose much information if we would form a 1D-feature spaced based on this eigenpair.\n",
    "\n",
    "Now choose $K$ eigenvectors with the largest eigenvalues\n",
    "\n",
    "After sorting the eigenpairs by decreasing eigenvalues, it is now time to construct our $p \\times C$-dimensional eigenvector matrix $W$ (here $4 \\times 2$: based on the 2 most informative eigenpairs) and thereby reducing the initial 4-dimensional feature space into a 2-dimensional feature subspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[-0.2049 -0.009 ]\n",
      " [-0.3871 -0.589 ]\n",
      " [ 0.5465  0.2543]\n",
      " [ 0.7138 -0.767 ]]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
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       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
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   ],
   "source": [
    "W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))\n",
    "print('Matrix W:\\n', W.real)\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transforming the samples\n",
    "\n",
    "We use $W$ to transform our samples onto the new subspace via the equation\n",
    "\n",
    "\\begin{align*}\n",
    "Y = X_{n \\times p} W_{p \\times C}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_lda = X.dot(W)\n",
    "assert X_lda.shape == (150,2), \"The matrix is not 150x2 dimensional.\"\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def plot_step_lda():\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X_lda[:,0].real[y == label],\n",
    "                y=X_lda[:,1].real[y == label],\n",
    "                marker=marker,\n",
    "                color=color,\n",
    "                alpha=0.5,\n",
    "                label=label_dict[label]\n",
    "                )\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title('LDA: Iris projection onto the first 2 linear discriminants')\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=False, top=False,  \n",
    "            labelbottom=True, left=False, right=False, labelleft=True)\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()\n",
    "\n",
    "plot_step_lda()\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter plot above represents our new feature subspace that we constructed via LDA. We can see that the first linear discriminant \"LD1\" separates the classes quite nicely. However, the second discriminant, \"LD2\", does not add much valuable information, which we've already concluded when we looked at the ranked eigenvalues is step 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PCA vs LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA) are linear transformation techniques that are commonly used for dimensionality reduction. \n",
    "\n",
    "- PCA can be described as an \"unsupervised\" algorithm, since it \"ignores\" class labels and its goal is to find the directions (the so-called principal components) that maximize the variance in a dataset. \n",
    "\n",
    "- LDA is \"supervised\" and computes the directions (\"linear discriminants\") that will represent the axes that that maximize the separation between multiple classes.\n",
    "\n",
    "Although it might sound intuitive that LDA is superior to PCA for a multi-class classification task where the class labels are known, this might not always the case. For example, comparisons between classification accuracies for image recognition after using PCA or LDA show that PCA tends to outperform LDA if the number of samples per class is relatively small ([PCA vs. LDA, A.M. Martinez et al., 2001](https://ieeexplore.ieee.org/document/908974?arnumber=908974)).\n",
    "\n",
    "\n",
    "In practice, often a LDA follows a PCA for dimensionality reduction (PCA can be performed before LDA to regularize the problem and avoid over-fitting).\n",
    "\n",
    "![lad_pca](https://github.com/ming-zhao/Optimization-and-Learning/raw/master/figures/lda_pca.png)\n",
    "\n",
    "There is a more convenient way to achieve the same via the LDA classifier (or PCA) implemented in the `scikit-learn`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA as sklearnPCA\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "sklearn_lda = LDA(n_components=2)\n",
    "X_lda_sklearn = sklearn_lda.fit_transform(X, y)\n",
    "def plot_scikit_lda(X, title):\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X[:,0][y == label],\n",
    "                    y=X[:,1][y == label] * -1, # flip the figure\n",
    "                    marker=marker,\n",
    "                    color=color,\n",
    "                    alpha=0.5,\n",
    "                    label=label_dict[label])\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title(title)\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=False, top=False,  \n",
    "            labelbottom=True, left=False, right=False, labelleft=True)\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()\n",
    "\n",
    "sklearn_pca = sklearnPCA(n_components=2)\n",
    "X_pca = sklearn_pca.fit_transform(X)\n",
    "def plot_pca():\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X_pca[:,0][y == label],\n",
    "                y=X_pca[:,1][y == label],\n",
    "                marker=marker,\n",
    "                color=color,\n",
    "                alpha=0.5,\n",
    "                label=label_dict[label]\n",
    "                )\n",
    "\n",
    "    plt.xlabel('PC1')\n",
    "    plt.ylabel('PC2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title('PCA: Iris projection onto the first 2 principal components')\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=False, top=False,  \n",
    "            labelbottom=True, left=False, right=False, labelleft=True)\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.tight_layout\n",
    "    plt.grid()\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "toggle()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_scikit_lda(X_lda_sklearn, title='Default LDA via scikit-learn')\n",
    "plot_pca()\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two plots above nicely confirm what we have discussed before: Where the PCA accounts for the most variance in the whole dataset, the LDA gives us the axes that account for the most variance between the individual classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generative Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider \n",
    "\n",
    "- the class-conditional density $p(\\mathbf{x}|\\mathcal{C}_k)$ with a specified parametric functional form, and\n",
    "\n",
    "- the class prior $p(\\mathcal{C}_k)$\n",
    "\n",
    "- then compute posterior probability $p(\\mathcal{C}_k|\\mathbf{x})$ through Bayes' theorem.\n",
    "\n",
    "The indirect (comparing to model $p(\\mathcal{C}_k|\\mathbf{x})$ directly) is an example of generative modeling, because we can generate synthetic data by drawing values of $\\mathbf{x}$ from $p(\\mathbf{x})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Continuous Features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider $K=2$, we have\n",
    "\\begin{align}\n",
    "p(\\mathcal{C}_1 | \\mathbf{x}) = \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)} = \\frac{1}{1+\\exp(-a)} = \\sigma(a)  \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "with\n",
    "\\begin{align}\n",
    "a = \\ln \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)} \\triangleq \\mathbf{w}^\\intercal \\mathbf{x} \\label{eqn_act}\n",
    "\\end{align}\n",
    "\n",
    "where $\\sigma(\\cdot)$ is the logistic sigmoid function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For general $K > 2$,\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathcal{C}_k | \\mathbf{x}) &= \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{\\sum_{j}p(\\mathbf{x}|\\mathcal{C}_j)p(\\mathcal{C}_j)} \\\\\n",
    "&= \\frac{\\exp(a_k)}{\\sum_{j}\\exp(a_j)} = \\text{softmax}_k (a)\n",
    "\\end{align*}\n",
    "\n",
    "where the activate function\n",
    "\n",
    "\\begin{align*}\n",
    "a_k = \\ln p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)\n",
    "\\end{align*}\n",
    "\n",
    "and softmax function represents a smoothed version of the \"max\" function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us assume that the class-conditional densities are Gaussian and then explore the resulting form for the posterior probabilities for $K=2$.\n",
    "\n",
    "With assumption\n",
    "\n",
    "\\begin{align}\n",
    "p(\\mathbf{x}|\\mathcal{C}_k) = \\frac{1}{(2\\pi)^{D/2}} \\frac{1}{\\lvert \\Sigma \\rvert ^{1/2}} \\exp \\left( -\\frac{1}{2} (\\mathbf{x} - \\mathbf{\\mu}_k)^\\intercal \\Sigma^{-1} (\\mathbf{x} - \\mathbf{\\mu}_k) \\right) \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "We have\n",
    "\n",
    "\\begin{align}\n",
    "p(\\mathbf{x}_i, \\mathcal{C}_1) &= p(\\mathcal{C}_1)p(\\mathbf{x}_i|\\mathcal{C}_1) = \\pi \\mathcal{N}(\\mathbf{x}_i|\\mathbf{\\mu}_1, \\Sigma) \\nonumber \\\\\n",
    "p(\\mathbf{x}_i, \\mathcal{C}_2) &= p(\\mathcal{C}_2)p(\\mathbf{x}_i|\\mathcal{C}_2) = (1-\\pi) \\mathcal{N}(\\mathbf{x}_i|\\mathbf{\\mu}_2, \\Sigma) \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "The parameters $\\pi$, $\\mathbf{\\mu}_1$, $\\mathbf{\\mu}_2$ and $\\Sigma$ can be obtained by maximizing the likelihood function\n",
    "\n",
    "\\begin{align}\n",
    "p(\\mathbf{t}|\\pi,\\mathbf{\\mu}_1,\\mathbf{\\mu}_2,\\Sigma) = \\prod_{i=1}^{n} \\left( \\pi \\mathcal{N}(\\mathbf{x}_i|\\mathbf{\\mu}_1, \\Sigma)\\right)^{t_i} \\left( (1-\\pi) \\mathcal{N}(\\mathbf{x}_i|\\mathbf{\\mu}_2, \\Sigma)\\right)^{1-t_i} \\nonumber\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LDA (or QDA) is generative model and its parameters are estimated by maximizing the likelihood function. However, this approach is not robust to outliers because the maximum likelihood estimation of a Gaussian is not robust to outliers (see Student-t Distribution)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discrete Features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we have discrete features, e.g., $x_j \\in \\{0,1\\}$. The class-conditional densities $p(\\mathbf{x}|\\mathcal{C}_k)$ cannot be Gaussian in the case of discrete feature values $x_i$.\n",
    "\n",
    "- We make naive Bayes assumption: feature values are independent\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathbf{x}|\\mathcal{C}_k) &= \\prod_{j=1}^{p} \\mu_{kj}^{x_j}(1-\\mu_{kj})^{1-x_j} \\\\\n",
    "a_k(\\mathbf{x}) &= \\ln p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k) = \\sum_{j=1}^{p} \\left\\{ x_j \\ln\\mu_{kj} + (1-x_j)\\ln(1-\\mu_{kj}) \\right\\} + \\ln p(\\mathcal{C}_k)\n",
    "\\end{align*}\n",
    "\n",
    "- $a_k(\\mathbf{x})$ is again linear functions of the input values $\\mathbf{x}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discriminative Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider $K=2$, recall the generative approach gives\n",
    "\n",
    "\\begin{align}\n",
    "p(\\mathcal{C}_1 | \\mathbf{x}) = \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)} = \\frac{1}{1+\\exp(-a)} = \\sigma(a) = \\sigma(\\mathbf{w}^\\intercal \\mathbf{x})  \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "The posterior probability is a logistic sigmoid acting on a *linear function* of $\\mathbf{x}$ for a wide choice of $p(\\mathbf{x}|\\mathcal{C}_1)$. For example, as long as the class-conditional densities $p(\\mathbf{x}|\\mathcal{C}_1)$ is in exponential family, the activation function $a$ is a linear function of $\\mathbf{x}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The linearity indicates a direct (discriminative) approach that \n",
    "\n",
    "- model $p(\\mathcal{C}_k | \\mathbf{x})$ directly by considering\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathcal{C}_k | \\mathbf{x}) = f(\\mathbf{w}^\\intercal_k \\mathbf{\\phi})\n",
    "\\end{align*}\n",
    "\n",
    "where $\\phi$ are basis functions.\n",
    "\n",
    "- In logistic regression, we set $f = \\sigma(\\cdot)$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For data set $\\{\\phi_{i} \\equiv \\phi(\\mathbf{x}_i),t_i\\}, i=1,\\ldots,n$ with $t_i \\in \\{0,1\\}$, the likelihood function\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathbf{t}|\\mathbf{w}, \\phi) = \\prod_{i=1}^{n} y_i^{t_i}(1-y_i)^{1-t_i} \\tag{Likelihood}\n",
    "\\end{align*}\n",
    "\n",
    "where $\\mathbf{t} = (t_1,\\ldots,t_n)^\\intercal$ and $y_i=p(\\mathcal{C}_1|\\phi_i) = \\sigma(\\mathbf{w}^\\intercal \\phi)$. Since we model $p(\\mathcal{C}_k | \\mathbf{x})$ directly, our likelihood function is different from the one in generative model and does not depend on joint distribution.\n",
    "\n",
    "The error function is\n",
    "\n",
    "\\begin{align*}\n",
    "E(\\mathbf{w}) &= -\\ln p(\\mathbf{t}|\\mathbf{w}) = -\\sum_{i=1}^{n} \\left( t_i \\ln y_i + (1-t_i) \\ln (1-y_i) \\right) \\nonumber \\\\\n",
    "\\nabla E(\\mathbf{w}) &= \\sum_{i=1}^{n} (y_i - t_i) \\phi_{i} \\tag{Error}\n",
    "\\end{align*}\n",
    "\n",
    "$\\mathbf{w}$ is estimated through **iterative reweighted least squares**:\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{w}^{\\text{new}} = \\mathbf{w}^{\\text{old}} - H^{-1} \\nabla E(\\mathbf{w}^{\\text{old}})\n",
    "\\end{align*}\n",
    "\n",
    "where $H$ is the Hessian matrix. \n",
    "\n",
    "The approach requires fewer adaptive parameters comparing to generative approach. Note that\n",
    "\n",
    "- LDA (or QDA) is based on generative approach, and logistic regression is based on discriminative approach\n",
    "\n",
    "- LDA and logistic regression have exactly same form that the posterior probability $p(\\mathcal{C}_k | \\mathbf{x}) = \\sigma(\\mathbf{w}^\\intercal_k \\mathbf{\\phi})$\n",
    "\n",
    "- LDA and logistic regression are different in how linear coefficients $\\mathbf{w}_k$ are estimated, especially logistic regression does not assume Gaussian class-conditional density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
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   ],
   "source": [
    "def comp_log_ls(data):\n",
    "    x_train, t_train = data\n",
    "    \n",
    "    x1_test, x2_test = np.meshgrid(np.linspace(-5, np.ceil(np.max(x_train)), 100),\n",
    "                                   np.linspace(-5, np.ceil(np.max(x_train)), 100))\n",
    "    x_test = np.array([x1_test, x2_test]).reshape(2, -1).T\n",
    "\n",
    "    t_ls = LeastSquares().fit(x_train, t_train).predict(x_test)\n",
    "    t_lr = Logistic().fit(x_train, t_train).predict(x_test)\n",
    "\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.scatter(x_train[:, 0], x_train[:, 1], c=t_train)\n",
    "    plt.contourf(x1_test, x2_test, t_ls.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3),\n",
    "                cmap=matplotlib.colors.ListedColormap(['yellow','green','purple']))\n",
    "    plt.xlim(-5, np.ceil(np.max(x_train)))\n",
    "    plt.ylim(-5, np.ceil(np.max(x_train)))\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    plt.title(\"Least Squares\")\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.scatter(x_train[:, 0], x_train[:, 1], c=t_train)\n",
    "    plt.contourf(x1_test, x2_test, t_lr.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3),\n",
    "                cmap=matplotlib.colors.ListedColormap(['yellow','green','purple']))\n",
    "    plt.xlim(-5, np.ceil(np.max(x_train)))\n",
    "    plt.ylim(-5, np.ceil(np.max(x_train)))\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "    plt.title(\"Logistic Regression\")\n",
    "    plt.show()\n",
    "    \n",
    "toggle()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "comp_log_ls(train_data['2-class_ex'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "comp_log_ls(train_data['3-class'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum likelihood estimate in logistic regression can exhibit severe over-fitting for data sets that are linearly separable. If the data set is linearly separable, any decision boundary separating the two classes have the property\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{w}^\\intercal \\phi_i \\left\\{\\begin{aligned}\n",
    "\\ge 0 & \\text{ if } t_i = 1 \\text{ or } \\mathbf{x} \\in \\mathcal{C}_1 \\\\\n",
    "< 0 & \\text{ if } t_i = 0 \\text{ or } \\mathbf{x} \\in \\mathcal{C}_2\n",
    "\\end{aligned}\\right.\n",
    "\\end{align*}\n",
    "\n",
    "In equation (Error), minimizing the negative log-likelihood will push $y_i \\triangleq \\sigma(\\mathbf{w}^\\intercal \\phi_i) = t_i$ for all $i$. It is possible in separable case by simply having the magnitude of $\\mathbf{w}$ goes to infinity. Thus, $\\sigma(\\mathbf{w}^\\intercal \\phi)$ becomes a Heaviside function. Maximal likelihood could provide any solution that separating two classes which does not have good predictive capability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Application: MNIST"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a set of 60,000 training images, plus 10,000 test images, assembled by the National Institute of Standards and Technology (NIST). Each image is a gray scale 28 $\\times$ 28 pixels handwritten digits. we're trying to classify images into their 10 categories (0 through 9)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b6e56635765b4418932a8807faaf32bf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(RadioButtons(description='Data:', options=('train', 'test'), value='train'), IntText(val…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from keras.datasets import mnist\n",
    "(train_images, train_labels), (test_images, test_labels) = mnist.load_data()\n",
    "train_images_reshape = train_images.reshape((60000, 28 * 28))\n",
    "test_images_reshape = test_images.reshape((10000, 28 * 28))\n",
    "\n",
    "def showimg(data, idx):\n",
    "    span = 5\n",
    "    if data=='train':\n",
    "        if idx+span<train_images.shape[0]:\n",
    "            images = train_images\n",
    "            labels = train_labels\n",
    "        else:\n",
    "            print('Index is out of range.')\n",
    "    if data=='test':\n",
    "        if idx+span<test_images.shape[0]:\n",
    "            images = test_images\n",
    "            labels = test_labels\n",
    "        else:\n",
    "            print('Index is out of range.')\n",
    "    plt.figure(figsize=(20,4))\n",
    "    for i in range(span):\n",
    "        plt.subplot(1, 5, i + 1)\n",
    "        digit = images[idx+i]\n",
    "        plt.imshow(digit, cmap=plt.cm.binary)\n",
    "        plt.title('Index:{}, Label:{}'.format(idx+i, labels[idx+i]), fontsize = 15)\n",
    "    plt.show()\n",
    "\n",
    "interact(showimg,\n",
    "    data = widgets.RadioButtons(options=['train', 'test'],\n",
    "                                value='train', description='Data:', disabled=False),\n",
    "    idx = widgets.IntText(value=7, description='Index:', disabled=False));\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We apply logistic regression on training datasets and predict testing images. We use the SAGA algorithm because it is fast when the number of samples is significantly larger than the number of features and is able to finely optimize non-smooth objective functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "92.51% of test data is predicted correctly!\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logisticReg = LogisticRegression(multi_class='multinomial',\n",
    "                         penalty='l1', solver='saga', tol=0.1)\n",
    "logisticReg.fit(train_images_reshape, train_labels)\n",
    "predictions = logisticReg.predict(test_images_reshape)\n",
    "\n",
    "score = logisticReg.score(test_images_reshape, test_labels)\n",
    "print(\"{}% of test data is predicted correctly!\".format(score*100))\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "749 in 10000 testing images are misclassified!\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x288 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = 0\n",
    "misclassifiedIndexes = []\n",
    "for label, predict in zip(test_labels, predictions):\n",
    "    if label != predict: \n",
    "        misclassifiedIndexes.append(index)\n",
    "    index +=1\n",
    "\n",
    "print(\"{} in 10000 testing images are misclassified!\".format(len(misclassifiedIndexes)))    \n",
    "plt.figure(figsize=(20,4))\n",
    "for plotIndex, badIndex in enumerate(misclassifiedIndexes[0:5]):\n",
    "    plt.subplot(1, 5, plotIndex + 1)\n",
    "    plt.imshow(np.reshape(test_images_reshape[badIndex], (28,28)), cmap=plt.cm.gray)\n",
    "    plt.title('Predicted: {}, Actual: {}'.format(predictions[badIndex], test_labels[badIndex]), fontsize = 15)\n",
    "    \n",
    "plt.show()\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we have a multi-class problem, the coefficient has shape (number of classes, number of features) = (10, 28 $\\times$ 28). Thus, each coefficient can be demonstrated as an image.\n",
    "\n",
    "Classification vector $k$ can be interpreted as follows: if a testing image has a high probability to be classified into class $k$, comparing to the class $k$ image below, then we expect to see more pixels at the blue area (high weight) and less pixels at the red area (low weight) in the testing image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 11 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "        <a href=\"#\" onclick=\"code_toggle(this); return false;\">show code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coef = logisticReg.coef_.copy()\n",
    "scale = np.abs(coef).max()\n",
    "\n",
    "fig, axes = plt.subplots(nrows=2, ncols=5, figsize=(15,6))\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    im = ax.imshow(coef[i].reshape(28, 28), interpolation='nearest',\n",
    "                   cmap=plt.cm.RdBu, vmin=-scale, vmax=scale)\n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())\n",
    "    ax.set_xlabel('Class %i' % i)\n",
    "\n",
    "plt.suptitle('Classification Vectors')\n",
    "fig.subplots_adjust(right=0.8)\n",
    "cbar_ax = fig.add_axes([0.85, 0.15, 0.05, 0.7])\n",
    "fig.colorbar(im, cax=cbar_ax)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probit Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen that the posterior class probabilities are given by $f(a)$ where\n",
    "\n",
    "- $f$ is a logistic (or softmax) transformation acting on $a$,\n",
    "\n",
    "- $a$ is a linear function of the feature variables.\n",
    "\n",
    "Is there other way to define $f(\\cdot)$ such that $f(a) =$ the posterior class probability $p(t=1|a)$? To answer the question, we want to model the posterior probability $p(t=1|a)$ directly instead of using Bayes' theorem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let target value\n",
    "\n",
    "\\begin{align*}\n",
    "t_i = \\left\\{ \\begin{aligned}\n",
    "1 & \\text{ if } a_i=\\mathbf{w}^\\intercal \\mathbf{\\phi}_i \\ge \\theta \\\\\n",
    "0 & \\text{ otherwise.}\n",
    "\\end{aligned}\\right.\n",
    "\\end{align*}\n",
    "\n",
    "If $\\theta$ has a probability density $p(\\theta)$ (assumed to be a standard Gaussian), then\n",
    "\n",
    "\\begin{align*}\n",
    "p(t=1|a) = \\int_{-\\infty}^{a} p(\\theta) d\\theta = \\int_{-\\infty}^{a} \\mathcal{N}(\\theta|0,1) d\\theta = \\Phi(a) = \\frac{1}{2} \\left(1+\\frac{1}{\\sqrt{2}}\\text{erf}(a) \\right)\n",
    "\\end{align*}\n",
    "\n",
    "The generalized linear model based on activation function\n",
    "\n",
    "\\begin{align*}\n",
    "f(a) = \\frac{1}{2} \\left(1+\\frac{1}{\\sqrt{2}}\\text{erf}(a) \\right)\n",
    "\\end{align*}\n",
    "\n",
    "is known as probit regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The tails of the logistic sigmoid decay asymptotically like $\\exp(-x)$ for $x \\to \\infty$\n",
    "\n",
    "- The tails of the probit decay asymptotically like $\\exp(-x^2)$ for $x \\to \\infty$\n",
    "\n",
    "- The probit model is significantly more sensitive to outliers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mislabelling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both the logistic and the probit models assume the data is correctly labelled. The effect of mislabelling is easily incorporated into a probabilistic model by introducing a probability $\\epsilon$ that the target value $t$ has been flipped to the wrong value, so \n",
    "\n",
    "\\begin{align*}\n",
    "p(t|\\mathbf{x}) = (1-\\epsilon) \\sigma(\\mathbf{x}) + \\epsilon (1-\\sigma(\\mathbf{x}))\n",
    "\\end{align*}\n",
    "\n",
    "where $\\epsilon$ may be set in advance, or it may be treated as a hyperparameter whose value is inferred from the\tdata."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exact Bayesian inference for logistic regression is intractable because the posterior distribution comprises a product of logistic sigmoid functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distribution over $\\mathbf{w}$ is\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathbf{w}|\\mathbf{t}) \\propto p(\\mathbf{t}|\\mathbf{w})p(\\mathbf{w})\n",
    "\\end{align*}\n",
    "\n",
    "with a Gaussian prior $p(\\mathbf{w}) = \\mathcal{N}(\\mathbf{w}|\\mathbf{m}_0, \\mathbf{S}_0)$. From equation (Likelihood),\n",
    "\n",
    "\\begin{align}\n",
    "\\ln p(\\mathbf{w}|\\mathbf{t}) & = -\\frac{1}{2} (\\mathbf{w}-\\mathbf{m}_0)^\\intercal \\mathbf{S}^{-1}_0 (\\mathbf{w}-\\mathbf{m}_0) \\nonumber \\\\\n",
    "& \\quad + \\sum_{i=1}^{n} \\left( t_i \\ln y_i + (1-t_i) \\ln (1-y_i) \\right) + \\text{const} \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "- The posterior distribution $p(\\mathbf{w}|\\mathbf{t})$ is not Gaussian due to the second term.\n",
    "\n",
    "- We seek a Gaussian representation \n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathbf{w}|\\mathbf{t}) = q(\\mathbf{w}) \\equiv \\mathcal{N}(\\mathbf{w}_{MAP}, \\mathbf{S}_N)\n",
    "\\end{align*}\n",
    "\n",
    "for the posterior distribution by using Laplace approximation."
   ]
  },
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    "hide_comment()"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Laplace Approximation** is to find a Gaussian approximation to a probability density $p(z)$\n",
    "\n",
    "\\begin{align*}\n",
    "p(z) &= \\frac{1}{Z} f(z) \\text{ where } Z = \\int f(z) dz \\\\\n",
    "p(z) & \\sim \\mathcal{N}(z|z_0, A^{-1}) \\text{ where $z_0$ is a mode of } p(z)\n",
    "\\end{align*}\n",
    "\n",
    "$f^\\prime (z_0) = 0$ and $A = - \\nabla \\nabla \\ln f(z_0)$. Laplace framework is based purely on the aspects of the true distribution at mode of the variable, and so can fail to capture important global properties. In Bayesian logistic regression,\t\n",
    "\\begin{align}\n",
    "\\mathbf{S}_N &= -\\nabla \\nabla \\ln p(\\mathbf{w}|\\mathbf{t}) = \\mathbf{S}^{-1}_0 \\sum_{i=1}^{n} y_i(1-y_i) \\phi_i \\phi_{i}^\\intercal \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "<span style=\"float:right\"> $\\blacksquare$ </span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predictive Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive distribution\n",
    "\n",
    "\\begin{align}\n",
    "p(\\mathcal{C}_1|\\phi,\\mathbf{t}) &= \\int p(\\mathcal{C}_1|\\phi,\\mathbf{w}) p(\\mathbf{w}|\\mathbf{t})dw \\approxeq \\int \\sigma(\\mathbf{w}^\\intercal \\phi) q(\\mathbf{w}) dw \\nonumber \\\\\n",
    "&= \\int \\sigma(a) \\left(\\int \\delta(a-\\mathbf{w}^\\intercal \\phi) q(\\mathbf{w})\\right) da \\equiv \\int \\sigma(a) p(a) da\\nonumber \\\\\n",
    "& \\approxeq \\int \\sigma(a) \\mathcal{N}(a|\\mu_a, \\sigma^2_a) da \\quad \\quad \\text{Apply Laplace approximation}\\nonumber\n",
    "\\end{align}\n",
    "\n",
    "where $\\delta$ is Dirac function, $a = \\mathbf{w}^\\intercal \\phi$, and\n",
    "\n",
    "\\begin{align}\n",
    "\\mu_a &= E(a) = \\int p(a) a da = \\int q(\\mathbf{w}) \\mathbf{w}^\\intercal \\phi dw = \\mathbf{w}^T_{MAP} \\phi \\nonumber \\\\\n",
    "\\sigma^2_a &= \\text{var}(a) = \\int p(a) (a^2 - \\mu_a^2) da = \\phi^\\intercal \\mathbf{S}_N \\phi \\nonumber\n",
    "\\end{align}\n",
    "\n",
    "- The predictive distribution is the convolution of a Gaussian with a logistic sigmoid, and cannot be evaluated analytically,\n",
    "\n",
    "- We can use probit function $\\Phi$, then the convolution can be expressed analytically."
   ]
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   "cell_type": "code",
   "execution_count": 31,
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    "x1_test, x2_test = np.meshgrid(np.linspace(-5, 12, 100), np.linspace(-5, 12, 100))\n",
    "x_test = np.array([x1_test, x2_test]).reshape(2, -1).T\n",
    "\n",
    "funcs = {'Linear Discriminant Analysis':'LinearDiscriminantAnalysis',\\\n",
    "        'Quadratic Discriminant Analysis':'QuadraticDiscriminantAnalysis',\\\n",
    "        'User Logistic':'Logistic', 'Logistic Regression':'LogisticRegression',\\\n",
    "        'Bayesian Ridge':'BayesianRidge'}\n",
    "\n",
    "from ipywidgets import interact, widgets\n",
    "widget_layout = widgets.Layout(width='270px', height='30px')\n",
    "@interact(method = widgets.Dropdown(description='Methods:',\\\n",
    "                                        style = {'description_width': 'initial'},\\\n",
    "                                        options=['User Logistic','Logistic Regression','Linear Discriminant Analysis',\\\n",
    "                                                'Quadratic Discriminant Analysis','Bayesian Ridge'],\\\n",
    "                                        value='User Logistic',\\\n",
    "                                        layout=widget_layout))\n",
    "\n",
    "def classify(method):\n",
    "    plt.figure(figsize=(16, 4))\n",
    "    for i, (key, value) in enumerate(train_data.items()):\n",
    "        plt.subplot(1, 3, i+1)\n",
    "        x_train, t_train = value\n",
    "        t = globals()[funcs[method]]().fit(x_train, t_train).predict(x_test)\n",
    "        plt.scatter(x_train[:,0], x_train[:,1], c=t_train, cmap=matplotlib.colors.ListedColormap(['red','green','blue']))\n",
    "        plt.contourf(x1_test, x2_test, t.reshape(100, 100), alpha=0.3, levels=np.array([0., 0.5, 1.5, 2.]),\n",
    "                    cmap=matplotlib.colors.ListedColormap(['yellow','green','purple']))\n",
    "        plt.xlim(-5, 12)\n",
    "        plt.ylim(-5, 12)\n",
    "        plt.colorbar()\n",
    "        plt.gca().set_aspect('equal', adjustable='box')\n",
    "        plt.title(\"{}\".format(key))\n",
    "    plt.show()\n",
    "    \n",
    "toggle()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Information Criterion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Akaike information criterion (AIC): \n",
    "\n",
    "$\\ln p(\\mathcal{D}|\\mathbf{w}_{\\text{ML}}) - M$, where $p(\\mathcal{D}|\\mathbf{w}_{\\text{ML}})$ is the best-fit log likelihood and $M$ is number of parameters in $\\theta$.\n",
    "\n",
    "- Bayesian Information Criterion (BIC):  \n",
    "\n",
    "$\\ln p(\\mathcal{D}|\\mathbf{w}_{\\text{MAP}}) - \\frac{1}{2} M \\ln n$, where $n$ is the number of data points."
   ]
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    "hide_comment()"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The intuition of Bayesian Information Criterion**\n",
    "\n",
    "Laplace approximate gives\n",
    "\n",
    "\\begin{align}\n",
    "Z &= \\int f(\\mathbf{z}) d\\mathbf{z} \\approx f(\\mathbf{z}_0) \\int \\exp \\left\\{ -\\frac{1}{2} (\\mathbf{z}-\\mathbf{z}_0)^\\intercal \\mathbf{A} (\\mathbf{z} - \\mathbf{z}_0)\\right\\} d\\mathbf{z} = f(\\mathbf{z}_0) \\frac{(2\\pi)^{M/2}}{|\\mathbf{A}|^{1/2}} \\label{eqn_bic}\n",
    "\\end{align}\n",
    "\n",
    "where\n",
    "\n",
    "\\begin{align*}\n",
    "\\mathbf{A} = - \\nabla \\nabla \\ln f(\\mathbf{z})|_{\\mathbf{z} = \\mathbf{z}_0}\n",
    "\\end{align*}\n",
    "\n",
    "From Bayes' theorem, the model evidence is\n",
    "\n",
    "\\begin{align*}\n",
    "p(\\mathcal{D}) & = \\int p(\\mathcal{D}|\\theta) p(\\theta) d\\theta\n",
    "\\end{align*}\n",
    "\n",
    "identifying $Z = p(\\mathcal{D})$ and $f(\\theta) = p(\\mathcal{D}|\\theta) p(\\theta)$), \\eqref{eqn_bic} gives\n",
    "\n",
    "\\begin{align*}\n",
    "\\ln p(\\mathcal{D}) &\\approx \\ln p(\\mathcal{D}|\\mathbf{w}_{\\text{MAP}}) + \\underbrace{\\ln p(\\mathbf{w}_{\\text{ML}}) + \\frac{M}{2} \\ln (2\\pi) - \\frac{1}{2} \\ln |A|}_{\\text{Occam factor}} \\nonumber \\\\\n",
    "&\\approx \\ln p(\\mathcal{D}|\\mathbf{w}_{\\text{MAP}}) - \\frac{1}{2} M \\ln n\n",
    "\\end{align*}\n",
    "\n",
    "\"Occam factor\" penalizes model complexity.\n",
    "\n",
    "<span style=\"float:right\"> $\\blacksquare$ </span>"
   ]
  }
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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
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     "0f53532b68474cd6ae0f17c39c3f76cc": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "0f5f790ff0cb4f4eb9b9aafc51b72f33": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "0fd66e2f98f64ebeba8a72eff1da42f8": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "103489a463ca4beb9d0d83ff9f7180f4": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_7b8a1686e93c413e94cb2983c79e2edd",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
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       "children": [
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     "2256d9b068964bdb94efe3008f11e47f": {
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     "241a58cd26e44bacad2eb11a4e742a7e": {
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     "246f91927c674f46a8686753325ba895": {
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      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_9892372756454a63952e394ace0c9e77",
       "outputs": [
        {
         "data": {
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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "24862b1bcd5645ffa475bac233800b55": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "272ef4fa385b4ff49e943c630bf1a8ce": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": "initial"
      }
     },
     "2767f50869c84a8eac978b8b97c809e5": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "2804fcb893b54ec3b41778a550fe0518": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "283b4320ff8c49ec947366e181336af2": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "292c6bae00864cbc93c4c765beaa688c": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_401d77962f934209b5ea59b78837f578",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
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      "model_module_version": "1.5.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_35f7286d64be4f3c95d9335f32f629b5",
        "IPY_MODEL_0b71da2ce19a4bcc9503a2cb5cf7ba52",
        "IPY_MODEL_a7a7b9c69a2b4bdea2af728cb6a2cfb9"
       ],
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     "2f0c8a4c02614b09974be1dedc203236": {
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      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": "initial"
      }
     },
     "2f904e6950c3415ea981750eab1a137b": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "IntTextModel",
      "state": {
       "description": "Index:",
       "layout": "IPY_MODEL_56c1547e0d6a417db9285e57aec7fc60",
       "step": 1,
       "style": "IPY_MODEL_00a88599edd3474c9b89f932b456cb5c",
       "value": 7
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     },
     "308faf4a25b64bbbafc1b824191d7b61": {
      "model_module": "@jupyter-widgets/base",
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      "model_name": "LayoutModel",
      "state": {
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       "width": "270px"
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     "3124b9a503454f3a97911d5217c46e1a": {
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      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 0,
       "layout": "IPY_MODEL_aff45f7e60454427976124940738b531",
       "style": "IPY_MODEL_080394ceffdd4e82aa1a9d22bc77e2d3"
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     "313e167e74b54f10995360085dc5c4c6": {
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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
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      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 1,
       "layout": "IPY_MODEL_6dd6f301b52e4ea68a6065058af9f8b6",
       "style": "IPY_MODEL_2f0c8a4c02614b09974be1dedc203236"
      }
     },
     "62888374cf674741afc43a6995f5e810": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "632ad85507e54c75908bd4c562bce0a5": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "IntTextModel",
      "state": {
       "description": "Index:",
       "layout": "IPY_MODEL_f57b52fdcb7f4e5d9e040b80ad636ab3",
       "step": 1,
       "style": "IPY_MODEL_aa796e1414be431b9bd7fc2b94686aa1",
       "value": 7
      }
     },
     "652c940fc84940babed439458bbdacda": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_c807ffecfb4645be82fc342b156202d1",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "6628ae39b48f438f940f5929f79e9f2c": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "height": "30px",
       "width": "270px"
      }
     },
     "664c937539b442a8995927de97fb473c": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_7eb8a439827b42da9d78a5330d413311",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "952f3a930fe0466785d91de9f7f8718a": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "954eb0d3f64b4815aba58147c7f08a1e": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "height": "30px",
       "width": "270px"
      }
     },
     "974c6b789e4044f38ec8f12618ef78f1": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 0,
       "layout": "IPY_MODEL_3301b40a277e4bcdb9faebf98496a34f",
       "style": "IPY_MODEL_676e253a87694f1987bcfd7db5790c02"
      }
     },
     "9892372756454a63952e394ace0c9e77": {
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      "model_name": "LayoutModel",
      "state": {}
     },
     "99bf2925deeb4b969e9c82ceb28ec716": {
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      "model_name": "LayoutModel",
      "state": {}
     },
     "9a42e6ff96ec48ff834108b49f28ff78": {
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      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 0,
       "layout": "IPY_MODEL_763985bc1a3742549727784dca315309",
       "style": "IPY_MODEL_c7a2694d833a4b14a6fa5aef929f6e27"
      }
     },
     "9c7dc3d78d854a8eae3eaadf77f11984": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
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     },
     "a3fbac2633da48d48e478413556d9015": {
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      "model_module_version": "1.5.0",
      "model_name": "RadioButtonsModel",
      "state": {
       "_options_labels": [
        "train",
        "test"
       ],
       "description": "Data:",
       "index": 0,
       "layout": "IPY_MODEL_7c68de4693154e46aa79380239c3729a",
       "style": "IPY_MODEL_dd329244bafa4644a38f7c1d87a6c565"
      }
     },
     "a629bf55a2e64bc8b92e524b34707d2e": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "a7a7b9c69a2b4bdea2af728cb6a2cfb9": {
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      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_57b4a45781dc4d61882f494d32ff2ac2",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
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     },
     "b60b797f2bac4ee29ede12ba820c4716": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "b6e56635765b4418932a8807faaf32bf": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_54d91f0f61ff420aad7dbb277df32252",
        "IPY_MODEL_35c9caf76fec41139ab8e7bf140cc27d",
        "IPY_MODEL_d7725669caf24a44a05d47d8c68e60c5"
       ],
       "layout": "IPY_MODEL_5ab24da9fcfc4a62b1c50e34fcd367e9"
      }
     },
     "b6f35f863202499a835ceca850031082": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_fa5014a930494bdda610e68b151047bc",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "b9aa896db6e94ad5bfda710219c3f059": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_58bda2dea56d4c698a916fc440081f28",
       "outputs": [
        {
         "data": {
          "image/png": 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ISDpRrBORTNGg451KaUXSRyqSzeXAgcaYpsYYAxwJzE/BdUVE0olinYhkigYb77R2UyS9pGLN5kzgNeAL4Jv4NcfX9LoiIulEsU5EMkVDj3dauymSPvypuIi19kbgxlRcS0QkXSnWiUimULwTkVRI1dYnIiIiIiJpQ6W0IvVPyaaIiIiINCpauymSHpRsioiIiEijo4RTpP4p2RQRERGRRkkJp0j9UrIpIiIiIo2WutOK1B8lmyIiIiIiIpJySjZFREREpNFTKa1I3VOyKSIiIiKNmtZuitQPJZsiIiIi0ugp4RSpe0o2RURERCQjKOEUqVtKNkWkWowxTxpj1hljvk3y/ghjzGZjzNz464a6HqOI1L6iIEyeDPfdDy+9BBs21veIUkuxrvFRd1qRRLUV6/ypHaaIZJAJwEPAMxWc84m19vi6GY6I1LUtW+CSS92fwSLwZ8Mbb8Ctt0Gf3vU9upSZgGKdiDR+E6iFWKeZTRGpFmvtdKCRzWGISFW88CJs3OgSTYBIGIqK4IEHwNr6HVuqKNY1XiqlFSlRW7FOM5siGWR7aHtd/5/rcGPMV8Aq4HJr7Xd1+eUiUrtmzIBoJPH4unVQUACtW9f9mECxTnYtb2QeBVMKyF+Rz7Auw+p7OCLV0hBinZJNkQzib+GvylqVdsaY2aV+Hm+tHV+Fr/sC6G6t3WaMORb4D9CrCp8XkTQXCCR5w0J2dp0OpQzFOqmM4oRTpKFqCLEuJWW0xpg8Y8xrxpgFxpj5xpjhqbiuiNSrn621Q0q9qhKQsNZusdZui/99EpBtjGlXKyOtI4p1ImUdMzox4fRlwd79oHnz+hlTNSjWeVC8E2l06iXWpWrN5oPAZGttX2AgMD9F1xWRBsoYs5sxxsT/PgwXbzbU76hqTLFOpJQTxsKg/V3CmZsLTZrAbrvBZZfV98jqTiONdaB4JyKlVDfW1biM1hjTEjgMOAvAWhsCQjW9roikN2PMi8AIXFnGCuBGIBvAWvsv4GTgz8aYCFAInGJtw20ZolgnksifBdddC8uXw6LF0KE97LMv+Ex9jyx1Mi3WQWbFu7yReeRP0bpNkdqKdalYs7knsB54yhgzEJgDXGyt3Z6Ca4tImrLW/m4X7z+Ea6HdWCjWiSTRrZt7NUYZGOsgw+KdEk6R2ot1qSij9QP7A49aawcB24Gry59kjBlnjJltjJm9edPmFHytiEidUqwTkUyxy3jX2GJd3sg8bYUiUgtSkWyuAFZYa2fGf34NF6DKsNaOL16Q2qp1qxR8rYhInVKsE5FMsct41xhjnRJOkdSrcbJprV0D/GSM6RM/dCQwr6bXFRFJJ4p1IpIpMjneKeEUSa1U7bN5EfC8MSYALAXOTtF1RUTSiWKdiGQKxTsRqbGUJJvW2rnAkFRcS0QkXSnWiUimULwTkVRI1T6bIiIiIiKNgkppRVJDyaaIiIiISFzeyDxACadIKijZFBEREREppT4Tzg0bYO6XsGZ1nX91tW3ZAnPmwJIlYG19j0bSSaoaBImIiIiINBp5I/MomFJA/op8hnUZVuvfF43CP/8Jn0yHQADCEei/L1x9DeTk1PrXV4u18MLz8OabkJ3tfocOHeHmm6Ft2/oenaQDzWyKiIiIiHgonuGsC2+8Dv/71CWZ23dAKATffAP/Hl9nQ6iymTPhrbcgFHZjLgrCihVw++31PTJJF0o2RURERETq2TvvQDBU9lgoDFOnuhnDdPT2Wy7BLC0Wg+XLYc2a+hmTpBclmyIiIiIiFaiLtZs7dngfj8YgEqn1r6+Wbdu8j2dlwfbtdTsWSU9KNkVEREREkqirZkH79gfjcbxrl/Rds3nAAZDt0QHGZ6B7t7ofj6QfJZsiIiIiIhWoi4TznD9A06bgjydvWT7IzYELLqi1r6yxsSdCm7auoRG4JDMnAOefD/7s+h2bpAd1oxURERER2YWadKfdvg1WroL27aF1a+9zOneBhx6Gt9+GhQuge3cYOxY6dU7B4GtJ8+bw4IPw/ntu65O27WDMGOjZs75HJulCyaaIiIiISCUUJ5yVZS08PQH++183YxmJwNChcOmlkB1IPL9tWzj77NSNty40bQon/tK9RMpTGa2IiIiISC2Y/K7rMhsKw45C9+esWfDYY/U9MpG6oWRTRERERKQKKrt28803vbczmTYNwmFYtRJmz4J1a1M/RpF0oDJaEREREZFKqsraza1bvY/HYnDzzbBggevmGg7D0GFw+WWQpbtzaUQ0sykiIiIiUgXF3Wl3pd8+3tuZ+LNhwXwIhWD7jpLy2pdeSu04Reqbkk0RERERkVpw9lmQ28RtYwIu8QwEIBJ2CWZpoRC8+27lrmstfPMNvPoKfPgBFBamctQiqZOyZNMYk2WM+dIY899UXVNEJN0o1olIJlCsq5xdrd3s0tVtDTLqKOjRHQ46CP52O0Sj3ucXBXf9nZEw3HA93HoLPP88jB8Pfzgbli6pxi8gUstSWRV+MTAfaJnCa4qIpBvFOhHJBIp1u1DZtZu77QYXXFD2WM+esLhccmiA/vvu+nvfnezWehY3HipOUO+8Ex4bD8arbleknqRkZtMY0wU4Dng8FdcTEUlHinUikgkU6yqveO1mZbvTFjv/fMjNBX+W+znb7/arPPfcXX/2gw8SO9wCbNoEq1dV/NlwGF54Hs46C077PTz8MGzZXKWhi1RJqspo/w5cCcRSdD0RkXSkWCcimUCxrgqqk3Du1Qse+iccexwMGABjx7rEr3OXSnzYJn9r61ZYsgS2b/N+/9Zb4I03YeNG2LIVPvoQLr0UgpUo3xWpjhqX0RpjjgfWWWvnGGNGVHDeOGAcQPtO7Wv6tSIidUqxTkQygWJd9RSX1FZFh46Vm8ks78hR8OyzrqFQacYH114L2dkQicDRv4A/nuuOAyxeBPPnl/1cJApbtsAn0926UpFUS8XM5sHACcaYH4GXgJHGmOfKn2StHW+tHWKtHdKqdasUfK2ISJ1SrBORTKBYV015I/OqXE5bHccdC337uDJcA+TmgN8PsSiEI7Cj0HW6/eB9eP2Nks8tXep9vaKgWwMqUhtqPLNprb0GuAYg/gTscmvtaTW9rohIOlGsE5FMoFiX/vzZcOtt8PXXbq/O1q3h8SegqKjsecGQW5/5yivunAMPBF9W4vUCgUqW7yZhrUt0s1LZdlQaDe2zKSIiIiKSInUxu2kMDBwIvz0FRo1KTDSLRaLuvdWr4Z133AxoVrm7f38WHHlk1cdgLUyaBGecASed5JoOTZ1a9etI45bSZNNaO81ae3wqrykikm4U60QkEyjWVV1lmwXt2OESs0mTdt1Bdld8WdCqEpXMoRCEQ9C/v0sw/Vmw5x5wx53Qshob3Lz7Ljz1JGze7HoWbdwIjzwMn3xS9WtJ46UJbxERERGRFNnV/pvffO3KYMGVn2Lg+OPgrLOr/53RSOXPvfBCl1xGo9CsefW+z1p48YXELViCIXjuOTj00OpdVxofldGKiIiIiKRQshnOcAj+9jdX2lpU5Br5hEJuhvPrr6r/faFw5c6LWTcLmtuk+okmuCR5yxbv99avr/51pfFRsikiIiIikmLFCWdpX3/jZgXLKwrChx9V7rqbNsLbb8FLL8HCBe56+/Tb9edyAvCLoyEnt3LfU5Esv2s65GX33Wt+fWk8VEYrIiIiIlIHKip3jVSiFHbWLLjrLsC6819/DQ46CHbbzft8407FAEOGwh/OqfqYkznzTHjkkbKltDkBd1ykmGY261lREOZ+5fY3ink86RIRaQzCYfdE/9vv3DohEZHGKGqjzFs/j6/WfkUo6rKw0qW0/Qd4x8DcHDj8sIqvHQzCPXe7sttQ2N03BkMwYwZ88KH3Z2ypP2fOhEnvgI1V/ffycsRI+MvFbibTnwVdu8KVV8GwxGWqksE0s1mPpkx1T4SysgALTZrCTTdBj+71PTIRkdSZ8wXcfXfJz1lZcO21sO8+9TcmEUml7UA+kNlZxsINC7n141sJx0oWUF584MX0+77fzmZBTZrARRfBP/4JsZib6czJgcFDdp2kffst+DymiYqCiduZeIlE4N+Pw4svwqmnwvFjqvgLejj0UDUDkoppZrOe/LjMtYcOBaFwBxQWwsYNcP3/6am/iDQeGzfBHXfE41z8tW0r3HIzbN9R36MTkVRoldss/rfa318yXQWjQW6ceiNbQlsojBTufN3/2f0EDwgCJTOchx0ODz8Mv/0NjB0L198AV14JZhd35aaC97zWgSazbTs8/TR8mGQ2VCSV6inZLH4ClrlB6b33vGvzQ2H4+uu6H4+I1AbFuk+mJ78JmvFZ3Y5FRGrPmD7F03L5ZGLcm7VyFpbEYBcjxpSlUxK603bsCL89xa2h7N8fTEWZZFz//nh8gyvB7d8fAoHKjzcYgpderPz5ItVVL8lmq9xmjOkzLB6YMisYFdu82ZVPlFdUBE9NgC++rPMhiUiKKdbBlq2u1X95RUF49VX49H9VeyIvIumrON6VTTwzw7bQNqKxxNK0SCzC5CWT+WDpB7Q4okWNviM7AFdf7Zrw5ATcOsmcABw+Am64EY4+yiWcXqW2XjZurNFwRCql3stoS27CMusp2AEHeLeetjH48QdXdvbqa3U/LhGpHYmxLjPi3aBBSdrsW1i9Gh58EB79V50PS0RqWaYlnAM6DvCc2QTYVLSJx+Y8xu3Tb6/x9wwaBE8+CeecC6edBnffAxdcANnZMO48ePkleP45OGHMrtdxdulS4+GI7FK9J5tQ/klYZgSlgw92jYACOd7vB4vcAu4tW+t2XCJSezLxqf8+/WC//ZLv6xYscuuGVq6q23GJSO3LpFjXqUUnju55NDlZ3jd2oWiIr9d+zfLNy8t0p62OFi1h9Gg46Vewxx5l38vyQ7PmcO4f4fEn4IorYOwJbha0vCOPrNEwRColLZLN0jLl6b8/C/72Nxg3zgUFL5Ew/OEP8Oyzahok0thkyvomY1zZ10UXQdt23udEwnDhhfDoo661v4g0HpkS6wDG7T+OKw++ki4tvKcMQ7EQNwRv4M0FbzL9x+mVuua2bfDsM3D+n+GKy+Hjjyu/9KBtW9cp9sQT8ewu9MKLrkGlSG1Ky61PSgITTFxYHJgaXjtta2HdOvBnQ9s2ie9nZ7v6+m+/gWkf47nqOxSEt96GLVtcmcTiJW7Gc9mP0K0bnHIK9O5d27+JiNSGxhLrANb/7GJe+3aJjS6yfHDYofDTcnj9de/maNEIfPgRrF3rtoBasdI1r1iwADp0dF0bBw6sk19FRFKsMcW6jYUbCUVDdGzWEVMu2BljGNppKJsKN/HvL/5NMJr49CxGjIltJ7L+q/Uc2v1QNuzYwMvzXmbu6rnk5eZx0t4nMbzrcMAlgpdc4nYrCMfj5rKHYPEiV0ZbWdOmeXeytRY+/xyOOKLy1xKpqrRMNksb02dYgwxM8xfAffdCQYHLIbt1g6uvct3Hyjv+ePhshkssvYSCbk/OAw6EO+90m/liYd16t0n69dfDwAG1+duISG1rqLFu+U9w912weo37uUN718K/fGkXwKij4M03k18rHHL7yM2e464ZDLl17OvWwfffu9nPEYfXzu8hInWjbKwrlv4xb/2O9dz96d0sKViCz/hoEWjBpcMvpX+H/gnnHtztYJ748omk14rYCAXBAmb8NIOHZz3MjvAOojbK2u1reWDGA6zcupKT+53Mhx9CwaaSRBNcc7VJk+CXv4Q2bSs39q1by16jWDTiZk5FalPaldF6aWg1/xs3wY03uBukUMjdQC1dCldf410O27s3/Ok8t6Yp2R5Lfj888UQ8IS2eAbXu58ceq63fRETqUkOLdcGgK5Fd/pOLc+EQrFwJ11wLOzz20OzYAa66Gpo1S94t0Z/tGlwUBV2iWSwUhH+Ph6hHF28RaVga2vr1mI1x7UfXsmjjIiKxCKFoiA2FG7jl41tYv2N9wvnNsptx84ibycvJI8t4LJYEYrEYkxZPojBcSNSW3BwWRYt46duXKAoX8eUX7qFbednZ8P2iyo9///0h12PdvPHBoP0qfx2R6mgQySY0rJr/Dz9MvCGyMdixHb6c6/2ZUaPguefiey15/KcSicDqJA00VvykrVJEGouGFOs++8wH1i5xAAAgAElEQVSttyy/BCAahU8+9f7M0CHw7HNuU/Msj9qacDjeLMhjWcHWrfDuuzUdtYikk4aQcH677lu2BLcQo+zNXdRGmbx4sudn+rbry4QTJ3Bi3xPJ9mW7gzvy4OtTYPo1LIwMYNm69URs4pRjKBriua+fo30H7wdzMQttWld+/P0HwID+bj/OYrk5cORI6NK18tcRqY4aJ5vGmK7GmKnGmPnGmO+MMRenYmBeGsqTsPXrvPeVi8Zgwwbvzyz8Hh56yHVmLB9YAjnwi6OhZcvk3/m3v7mSXRGpHYp1iTZshFA48XiwCH7+2fszy5a5RkBr1ySu7QwE3BP4dkkaCQFMeMrNpIpI7anLeAfpn3BuKNzgua1JJBZh7ba1np9Zs20Nj3/xOAvWL8BgYFMPeOdRmHcyrBhO9NuT+eLbP0NhnufnJy+ZTK8DF5Jd7qGcz+fWxvfqDevXw3/ehNdeheXLk4/fGLj2WteobchgOPAAuPwK+NOfK/svIFJ9qVizGQEus9Z+YYxpAcwxxnxgrZ2Xgmsnlc41//vs67qFFRUlvufVzGfye/D44yVrMbMD4Au42YEWzWHsWNfeun1715nWq7mGtTD9E7evkojUCsW6cvr0hkA2FJVbHpCbC337JJ4/axbcdbebDY3FXMms3+8mMXNz4Bej4fenwsyZcP8D8VnTciIReO89+GMVmmOISJXVebxL51jXu21vYrHEGv6crBwGdExsmrFww0L+b8r/EYlFiNoofuOHWedDuAk753kiAaIxP4s2/4JeTV5OuEYoGmLm1te44orrePAfruojFnXr4a++BqZOgUcedZVzsRi89LK7BzzjTO/fwZcFhx7mXiJ1qcbJprV2NbA6/vetxpj5QGegVm/AIH27mx18ELz6imuYUXyzFMhxT+z36FH23KJgPNEs1RwoHHIJ51lnwYljS46PPRFmzXbda8sLh2DrlhT/IiKyk2Jdon33hZ57waLv4w/LcLOT3brDoP3Lnhuz8M9/lo11kbC7ATr2WBj3x5LjhxwCM/Ph42mJ3xmLwWZVcYjUqvqKd+ka6zq36MzwrsOZsWIGoagLdn6fnzZN2nB4j8SuZQ/PerhMJ9pIJAYbepFQUBjzYdYO4vvDb6X3wsTZiIKiAoYdBs88AytWQNOmbuJhy2Z45JGylSXREEycCAceCL09HvaJ1JeUrtk0xvQABgEzPd4bZ4yZbYyZvX795lR+LZBe65yys+Gee1ynsN12d51ozzwTrroy8dzFSRZ4h0MwbWrZYz4D55zjEtfycnJhoBZ5i9QJxTrHGLjlZvjdqdC5M3TqDL/5Ddx+u4tXpa1ZA9s9mgbFovCpx/rOs850M5/l5eTC0Pq/9xTJGMniXSbFOoC/HvhX/rDfH+jeqjsdm3XkhN4ncN/R95GTVfamLBgNsqxgWdkPmxgY7w3TY9Essot2TzgeyAowvIvbAmX7NmjX1iWa4CYevNZyBkOuPPY3v4bxjyXf5UCkLqVs6xNjTHPgdeCv1tqEOTZr7XhgPMCQIb0quR1t1aTTE7GmTeH009yrIs2alcwIlLdxY+KxnnvCQcNhxuduXRS4m6/9BsI+/Wo2ZhHZNcW6srKz4VcnuVdFmjZ1ZWBedmxPPNa2LfzyRLfPcPENUyAHuneHgw+u2ZhFpHIqineZFuuyTBbH9jqWY3sdW+F5fp/HrbUP6PYJ/DiSxB0vDXutug7je4RoLIrFEsgK0LZJW/r6juOC80u2lurbBy67fOfHkioKwvvvw6pVcNPNlfwFRWpJSpJNY0w2Lhg9b619IxXXrKmGsmdd+/Z4dl0EKPRY8wnw10tg2Geu620sCkceCYccmthsQ0RSS7Gu+vJaJX8vFHIN1LLKPak//XTotw9Mfhd2FMKhh7h45/feSUBEUijd4l1DiXVZJotsXzahWLmZhD5vw7IRYMsFMAs/L+3GZXecweevfo4xhmGdhjG83TFcfGEOhYUlp86b77abuuced/9XkVAYvv3Old926ZKSX02kWmqcbBpjDPAEMN9ae3/Nh5Q6DSEw5eS6BhleTX+S3Zz5DBxysHuJSN1QrKu5Fs3d9iXl5eQmlt0WG7y/e4lI3UnXeNdQYt1uzXdj+ZZy7WGb/exKacsnm0BeHvRr349+5/ejYEoBw7oM4/XXIFru3jAWgy1b4Icf4MIL3S4G4KpGvOYt/FlKNqX+pWLN5sHA6cBIY8zc+KviGoM6lI7ttK2F9T/Dlq2Q7YcjjkhcmxTIgRNPrP715y9wJRTz5rufRaTGFOuqYcNGKIgv5zphbOKa80AAjj2m+pUZS39wsW7uV64JkYikRNrGu3SNdQXBAjYUuv3tfrX3rxLWcvqbFtJ6z2X4y03z5OSWXYaQNzKP/BX5rFrtvbVUJBJlzZooI46Ax8a7niD9B3hXfESi0FWJptSzVHSj/ZQKK8frXzq10/7mG3jg725PzFgMunaFCy6Abdtg9pySWc7Ro12HxqoqLIT/u97tt2Stu4Hr0gVuuw2aNU397yOSKRTrqmbpD3DvvbB2rYt1HdrDn8+HI0bAlKlurWcoBAcdBKedXvXrhyNuf+Fv4t25s3zQKg/uuAPatknpryKScdI93qVTrFuzbQ33fHYPPxT8ABZa5rbk3P3OZWyfsby54E38Pj+RWIT+Hftz4Y1d+Md98N08d78XjcCvf+3iYGl5I/No8nU+udOHUVSuyU84FuG5lbfRf8t5dGnbhTEnuHXs558P0cKSGc5AtusY3lnJptSzlDUISne1ucg8GnVP1MtvvFvemjVw8y1lu4Mt+xGuvBKOO851Dlv/s+vq2KJ59cbyxJOuvKL0/nTLlrntVS7+S/WuKSINR63GuphbJ5Tt0SW2tG3b4JproLBU99nVq+GG62H4QTB+PKxfB7vt5srHquPNN+Gbr8s2WAsG4YH73cM1EWncajPWxWyMSCxCICtQ4XnhWJirPryKTUWbdh7bWLiRu2fczd7t9mb88eNZX7ietk3a0r6payV7yy2wfj1s3ATdukKTJt7XPuD8PKZ/kk9owRBi0Xghoi8IHb5lW7OvuX367Txy3CMYY2jT1q3jfOwxt04zJwdGHelmPUXqW8Ykm6Wl6olYwWZXLz97NmBh735w0UXQKbGDNQCTJrnENIF1ZWC9e7mS2pr4+OPEjdAjYZg+XcmmSKZJVawrLIRH/wWffuISzj33hAsvgJ49vc+fOi1xrVGxWfmuq/ZvflPlYZTx3nuJnbxjMZg3z22xokoOkcyRqlgXjoZ5au5TvL/kfcKxMJ1adOLPQ/7MgI4DPM+fvWo2RRHvbo4LNyzkhW9f4KJhFyW81759yTYmO787vu9wcaO0nACc8wd48ukZbPp+b/CFYa/3oe+bWCw/7/iZlVtX0qWlm7rs2g1uu73Kv7JIrcvIZBNq/kQsGnP7Zq5dV9IRbN48uOIK+Pd41+a/vFWrk9+AhUPw3PPQqzd06Vz536M8r0ZD4L63uKxWRDJHKp7+33wLfP99SXxZshiuvRYefsTt/Vbe2rXJt3SKRNys5OAhLumsrmTbqBR/h4hkltKxDorjXdVi3YMzH+TzFZ/v7CS7cutKbpl+C/eMuoc9Wu+RcP7PO34mHPMORjEb46MfPuLIPY5k73Z7Y5LcgM1fAI884pY/+f0wciSce65LNps0gdaHvMqmfZYmfM4YQzhaQSAUSROpaBDU4FVnsfncL+PrLkvNVNqYu8GaPt37M/33hewKKjLWr4OLL4aHH65+U59B+4Ep95+q8cHA/ZRoimS66sS6H5fB4sWJFRPhMLzzjvdn9t7bNb1IZvt2t3zg1ttcA4vqOGg4ZHk8Lt19d2jVsnrXFJHGw8W7yse6gqICZqyYkbBlSTga5rX5r3l+plebXmSZ5HsxxWyM66dez5UfXklhpDDh/ZWr4IYb3JIqG3MTD1OmwN13lZyzR94enuW8gawA3Vt1r9wvJ1KPMiPZ/PlnuO8++N3v4Oyz4ZVXEh59V/UmbNVq75ukYBEs/8n7M0cdBS1aVHzdcAimToX/fVapYSQ470/uO4o7PgZyoHkz+NOfqnc9EWlAtm51j8h//3s4/QyYMMEtZCylyrFuFWR5dTmMuBskLwcc4NZjVtReJByCL7+E//63UsNIcOrv3axqcVKbHZ8FuOTS6l1PRBqQYNDFtzPOcPHukUc891WqSsK5dvtasn2JC9ItluWbl3t8Avq07UPfdn0xFQS7cCzM4o2LeearZxLe+8+bLhaWOT/kumuvXecaBQ3tNJQ2uW3IzXLBzu/zk5OVw2XDL8Pny4zbeGnYGn8Z7datcMkl7s9oDLZtd8nmDz/AVVeVOdWr5j8YHMazz8KHH7lZy0H7wR//CD26u7r68gUMubnJ1zE1bQp//zv88x8wK77O00soBJMnV28fzY4d3ALxKVNg6VLYcw84YqRLOEWkEQuH4fLLXeeJcPxh2sSJ8N13cPfdZUobvGJdNDqMV16F/050azT79IVxf4Tu3b3L/7MD0LuP91D8We7J/L8ecw/PksW6SBjemwwnjq36r9uyhVszP/0Tt4ShcycYNar6DYdEpIGwFq6/HpYsKdkb5IMPYO5cVxpWroNZSbwr/rhl4qK1vDH/DTYXbWaPvD04Z/9z6Naqm2dJrA8fvdr08hyKMYYbDruBZ75+hrcXvo1NEuyiNsq0H6dx3uDzyhxfttytNS8vOxvWrHb3dO1GteNsczaRWIS5q+fSrlk7Ru0xivbN2yd+UCQNNf5k8/333Z1TtNT/moMhyM93j+w7dSpzevma/99cn8+7k4ftfPI0ew4sWOCaZXTp4krMisvLfFnQvAUcckjy4SxZAhs2uJbUydY0QfL3ioKwdQu0aeM92wCuMcaY40t+DkdcY6Jk54tIIzBjBmzaVJJogrsRW7bMJZz77lvm9PKx7tx78nn99WE7u2V/9617HvePf8CgQW4WsjguGZ/rdnjMMcmH8+My14E7ECjbgbu8ZGsvQ2HYXOCSx2Tdb3Ny4KhR7gWu2iQS9d5vTkQaiXnz4Mcfy25CGYm6tU2ffQaHH57wkdLx7rL37ua7dZ+zsdDFysWbFnPjtBu548g7OLrn0Xyw9ANC0ZKbsIA/wMn9Tk46nFXbVrF883Jy/DlJmwUBnols716waJElGik7MxoOQ5euJT9nmSyGdx/Ood0PBSAaixKOhsnO2kVrcJE00PiTzXnzXHJZnt/vZjfLJZul/fADxOYPY7+BJU/EZs0aRjAIH34At98OzzwL06ZCLGo5oOd6/pD9LDl3bnc9p4cPL7OA8vOZcO89FSeZABgYMaLsoXDEbRcwZYqboMj2w5lnwehfJL/MipXuyf+C+W4Yw4a6PT1baj2TSOPz/fdQ6HGjE4m4ModyyWZpGzfCxhnDGDigbLnZnC+G8Z//wJVXwUsvuQ6wwSDs16OAP+S+QKv71sBhh8OIw8ssoFywwE08VJRkFjv00LI/xyw8/xy89bb72Wfg5JPdXnTJ1p1v2Ohi3Zdfup8H9IcLL3J7e4pII7N0qXcXsMIiWLTIM9ksFowEWbY5n0gswtBSt3+zVoV44ZsXuP6w6+nQrANvLXyLbcFt9G3SlXOWtqLT3Y/AgQfCqKPcU664VVtXccUHV1SYZBYb2mlowrEm+75P9N1DgFyKV7YFciyHHGwS9gvOX5HPPh324dHZj/LZ8s+IEaNXm15cOOxCuudp7aakr8Zf7N2tm/cGmLFYfFFRcsuXg88HHTcP2/kaOjSfUMjFsyZN4Lxx8OILlpeH3celSy4gb+7Hbi+Uv/8d7ru/TKefJx6vRKKJy3+Ln9Rv2w7z5sODD8LUKa6WPxR0DTYefxxmJlmKsG2ba8Axb577VaMRyJ/l9r6LVbP5kEh5xpjRxpiFxpjFxpirPd4/yxiz3hgzN/46tz7GmRE6d4bcnMTj/mzo2LHCj65a5WYgS8c6gMH757NosQuhp58Gzz0Lrx7/NNf9+Ed2nzsZvpwLj/3LZZal9nV6akLlEs2WreDkX7u/FwVdV8YJT7lEMxR0r6IiePU1t3WUl3DEdQH/8gvXsC0Wha+/dhXFXs8ZRapDsS6NdOzo4lp5OQHYPfkEAsCGwg34jI+Ozdn5AhjaCX4s+BGf8fHLvr9kwtgJvNbsbG575if2mPIFfPW1WyN62WWuOUfcS9++RDCy62AXyApw7v7uvxLhaJgFGxbw+rzXeXP5eDj6Mtj9S8gKQm4BPQ/5govK7ZaSN9KtD7j0vUv57KfPiNgIMRtj4YaFXP3h1Wwu2rzLMYhURm3EusY/s3nMMW7dUmnZfrch0Z4V993v1CmxK2zHzcMYPjyfg0uvp1yUB/kz3d1SsaIgzPwcFi0i1qs3TzzhtgNIxu93SeEhh7glpj6fmzV96y33XunN0YuFgvDyS3CAR2fvKVPjiW2p8UcjbjnXN9/AQO8to0QqzRiTBTwMHAWsAGYZY9621s4rd+rL1toL63yAmeaww9zNUGlZPmjRHIYMqfCju+2WWM7acfMw1rfOZ8SIUk+01veAt98uW75WFITFS9wGmgcO57XXYH75/waUUhzrBgyA6/7P3R++PRGeecaV+nvFumA84TzuuMT3ZuXD9m1l1z3FYlBUCJ/9r+Z7F4so1qWZwYOhaRMXGIqfnhtcvf2I5LOaAG1y2xCzZRdJdmwOa7fBqD1LlX3t2AFPPVV2hiAYgrVr3PrQ48fw0dKPmLZsWtLvyjJZxGyMnq17ctOIm2iZ05Lpy6bz8KyHAUq607ZaCUfcvPNzS7NysOZFyt+irxm4hp//9zORWNlZ3XAszHuL3+M3+9Zw82LJeLUV6xp3srlmLdxwvfu7z7ig5DPuxusvf9nlXiB77QU9erh1lsU3YoYY3bYM5Jr9fiKvz15u0fm6/5a9+SoWjsDcubzzfW/em5z8e/Ly4Pob3P6aTZq4Yx9+6O7pwqHETmWl/bzB+/hPy71nFmIWVq9SsikpMQxYbK1dCmCMeQkYC1SQakit2LwZbrwxvjjb59aoG2CffdzTq10s2G7XDoYNg1mzyjav7bp1EDcMXEKX3n2Y+P0sWPWWW5xevjVaURHk5/M5w3np5eTfE8iB2251692bx2cUvvzSJZq7mgndnOTB/arV3jOYRUVuWwGRFFCsSxeFhW4N09at8Xs462LdXnu5WNes4m6Iudm5HNvrWCYtmkSw1LrMbs18HGZ6QOxz8B0Ii753i7/Lx5ZgCGbMYOHw3jw6+9Gk3+M3fq4//Hr2aL0HeTluVvKHgh/4x8x/JGytUl7URimKFNE80HznsR9+hOlfRVjUeTs9fiq7DUooGmLZ5mUVXlOkkmol1jXeMlpr4eab3HRiMFTy9Cs72812Nm9e4cfBxbGbb3bl/9lZUXxE2Yd53B2+lLw7roZHH2VM76GuBe2Bif+U1u9n+ppePF5B+WwgAKeeCr32Kkk0wW16vssyNAO9e3u/1bOn9z53xkD3Hru4rkjldAZKb/SzIn6svF8ZY742xrxmjOnq8b7U1D33uEZAwVBJM7RAwAWvdu0qdYlLL4XRoyE3O4ohRk+WcGvkGro8dj3cfjtj9hrsYt0Qj9aJWT7m7Nibu+9JHrcCATjhBOjbt2z4/c9blSu57d4tyfHuruFaeU2auIeFIimgWJcuHhvv1geFwiWxLjvbzXZ2rdw/+Vn7ncXJ/U6mWVYOxkKXrXDttBjnvzwDnn4aIp9B+x9hkMe6UAPz2htumnZT0qTR7/NzULeDGLTboJ2JJsCkRZMSZiW9tAi0oFm2S5p37HCN2q64Aj54YW9CE+/h+3UnQazknjMnK4febZPcDIpUTa3EusY7s7lsmdtfs/wCxWDIldUOGlSpyzRtChefsYm/fHwusWiErOK61CCuW8/hhzNmzGlM/OhDGArMKvnsS9GTee3jgViPe7Nivz0FfuHR5Mdju6gEPp9rmuHl8BGuoUc47NYwgVvi0KMH9E2yXYFkgu1UYZPrdsaY2aV+Hm+tHV/qZ6/SgPIrgicCL1prg8aYPwFPAyMrOwCphM2b3c1X+Y1/gyG3ieXRR1fqMtnZcO7pQc5573Ri4WBJrCsCvvoKPvuMMcecwsSJExNi3UfmSB7JH+XZs6PYEUfAaaclHt+0addjMz74zW+939t/f+jQwa07Lf7+LD+0ynP7fUqmUqxrdKJRmP5x2Y7b4BLPyZPdfpuV4DM+Tun3G35777vENgXJ2nmPVsSYxeth4Vr45YlMfPNNOGATzCz57Bdd/Pxtt/mEyo+hlEEdB3HxsIsTjm8s3EiMCm4IAYPhpL1PwsQr7x551PUIcbEty71WDYYd66HHJ/iMj1x/LqP2HFWp310ao/SPdY032dy+3WVjXiqTyZU2ezYmy0dWuHziGoRPP4Vx4xjzlxuY+NBtcAhgIWizeT3/14TDySePW7eBk3/lXc07YAB88ikVJqrGwHPPwa23JL7XJNf1J3rqSddEyO+HkSPh9NN3WT0sjVir3GYJW15U4GdrbUWL/VYApZ9odQHKFC5aa0sXev8buKuyXy6VVFiYPNZt3161a82bh/GZkkSzWFEQpk6DQw9lzNV3MPHu/4ODXSltNBbjiTnjCIeSx7pAAM77k1vFUN7gwbBiRckWUl4MLtYNPzAxfmX54M674OkJJTHzoIPh7LO8e8NJZlCsa4RisTKNyMooLKzatX5agdm+o1SiGRcMuS0GTvolY665k4l3XAUHbwcMxCL8u1sOIZLHVR8+Lhl+ieeWJEM6DeGrtV+V2ValPIvl9Xmvc8xex+AjwGf/82i8G82B1UPI3vNzhnYeyjmDzqFZQJupZ6qGEOsabxntXnt575SbE4CDDqratfx+7wzNmJKOaPvtx5hHX2TMiLGM2QLrac+wQf+r8LLHjE6e+J12mptVzargZikacY04Vq/xfr91azebcORIOPZYOO5Y72aVItU0C+hljNnDGBMATgHeLn2CMWb3Uj+eAMyvw/Flhg4dvNcp+bPcQsyqSJa0Qknm1rMnYx55jjFjT2fMtiy2+VrSf+Ds5J8DDj4k+d6XvzwRWrbwbi5ZLBaDn9e7ztxemjWFEUe4B2qjR8OYMdriSVJKsS4dZGd718YbYMDAql3Ln5XYAbJY8Rr33XdnzINPM+b35zOmKEDM56NTl4of4O3dbu8yay1LG7nHSDo260jAF/B8v1gwGuTzFZ8TjXjfxgIsad6eQbsNolebXrRvpj2eJGVqJdalJNncVZvcepGTA+ed55LL4sfpOQF3YzZ6dNWuNXSo9//iy3c+W7HCtY8Nhjj5561EyWLoUO+pbX82HD8m+Vfuths89E+XJO65JzRv4X2eP9t1mC0vGnONOO66y20Z8PrrrifS1GnJv1OkKqy1EeBC4D1csHnFWvudMeYWY8wJ8dP+Yoz5zhjzFfAX4Kz6GW1qpGWs8/nc/7hzAm6aD9zfW7VKXnuazD77eCecuTlw1FElPxcUwLPPQmEhJ6/fBpA81vnhd6ck/8qWLeEf/4STToI9e0KbNsnPXbcu8Zi18MgjcNNNrmr4rbfgyivg9TeSX0ekKjIx1kGaxrsLLnSlW8VPr7L97mHbuedU7TqdOkHbtonHcwJl1zYFg/Dvf8PWbYxdHyE3Spn9OUvL9mVz+sDTk35lTlYO9x59L6f2P5W9Wu9Fx2beW1IFI0HWbV9HTg5089o+00SJdsznuRbP8fw3z3PLxx7lbSLVUFuxrsZFRlVok1v3Ro1y3SPeecftWn7AAe5YThWn95o3d3sr3Xefm4q01r1OOaXs9invvruz3qE9Gzhqcy7vtwqWuQmbNWso2b4o5xyymOaBPYHkT7jatoU/xnevmfA0vP1WYjlFOOy2Ei1vxgz45tuS7aBiUQhF4eGH3b7ETTyaB4lUlbV2EjCp3LEbSv39GuCauh5XbUjrWDd4MDzwgFuPvmaNq8MfPbpSjdDK8Pvdnpk33QxYV7JmjIubgweXnDdt2s4HcLmE+P3mrTzfqkVCrPP7oozt/yO7teoMNCGZli3gtN+716RJ8ORTiU2DYjHo6bFb1YKFMO3jUrHOuoZsL7zgdoNpX7n+SCIVyqRYB2kc73r3gn/+08W6ZcugTx+3J1Lr1lW7jjFw7XVw7TVuDWgk7B60DR5c9sHazJllJhsuXAZ/7+ESzlmligv91jCcruyd06XCr23ib8JJe5/ESXufxMyVM7lvxn0URYrKnBPwB+jZpicAF10E113r7v0iEdxenFlBGPQUAPN6zYNF8NaCtxjbd2zV/g1EPNRGrEvFipb0bgneqxf89a81v87w4fDkky7whMNutrN9udKFTZtKuqMBV3EXOZv/ymwGQZaP1c1n8usDXuXAmTPoNWMlzGvlEthK1HudcAK89x5Ed5Ss4wzEJxvyWiWeP316mX2Hd8rKgm+/ccMXkSpJ71jXtSucf37Nr9Ovn9uvc+bnbs3nfvu5vUpKKygo06RjHI8R2/wnpjICsrJY1XwWY4e9xbD8mfSfvxjG5cC997nN2HfhiCPcnpoFUbdUANyaz0GDvB+sfT6j7HYtxYyBObOrXsgiIkA6x7uOHeHcXe4jv2vdu7m9NPPz3f1bv36ulX9pW7aUecp/8jzYkQ3jO8Pw3Q0zV1q6bIUz5lqGrv8J88Yf4W9/c2UauzCk0xA6NuvIyq0rd3ap9fv8dGnZhYEdXVlwr73g4Udg0juQP28tKwMfEev5DuSW9B6Z32s+C35ewFiUbEp6SkWy6dUmt3H2AGzZsuwTr/KGDoW5c10zDaApRVzLnWzLzmNbxz1pv2Iuk1rFXCdHgKyQK0W74ALPy23b7nLbYNA9bPv7A+70L+e6CYuxJ8DoY7yHEqhgSUBFa6NEJKnMiXVNm7isL5n99nNPvwrdE61solzEw5wTeJYtPfen7cL/MblFuCTW+YKurOIW73KvoqCLddu2uqVXDzwAzz8Hn9M2Ls4AACAASURBVH/uHqqNHg2//KX3UPzZbkIiVq5viM+4lQ4iUi2ZEe8CATjkkOTv77tvmaUFPgtnzYXfLc7h5QGduXz5j2SHY9AJWBl2nXHvu9/FOw/hWJhZq2axccdG+rbry12j7uLlb19m2rJpGGM4oscR/Haf3+IzJd/Zvh2ceSZ0XPIlj3/xRkKDIZ/xke1TsJP0lYpkszJtcjHGjAPGAXTr1kgXM48Y4Uo7VpfaZTw3h+bHHkHzt98GYowptTH5xFYxKJoOJCabc76AO+5wN0yxGDzxBJx8Mlx+eeWGctRR8US13Oymz+dip4hUmWJdsUGDXNXIwoVlYl3TgwbT9NNPIRYuF+uAnK9cWYYpuyZ00SK4/gb3ViTq/pFHHAEXnJ/0OVwZI0bAW/9xywRKi8W09YlIDewy3mVErNtjD9dUcsaMnRMJ5ATI6dmHMxaugA2u1GxiK0q2hFqz2lV/5OWVudSqrau4+sOrCUaDRGIRjDEM7DCQaw+7lrMHnb3LoQzvMpzH5zyecDzLZNGvQz/yV+QzrEsVm8KJ1IFUNAjaZZtcAGvteGvtEGvtkPbtPeo+G4NAwG2uftppbjPLwfvDlVfCqad6nj5mM/EnZvESjldegb8/QOHE97nzDksoCEVFbv1ROOSa/Cz8vnJDGTjAdWTMDriZgSZNoElTtxxL2wGIVItiXTGfD26+2ZWy9dvbBZwLL4SLL/ZsMORinQFmwbZtLjt84H6ib77FrbfE2LHd7VwQDrl49/HH8PnMhMt46toFzjrbxbqcXMjNdTHv8iuqvmRVRHaqzBYIjT/WgVuKdeGFLs712xvGjXMdyfwlN1M7H64NBYbEIDDXPe2fPNmVpb3yCnd+fBsFwQIKI4WEY2FC0RBfrfuKSYsmeX1rglY5rbhk+CUEfAFy/bnkZOWQ7cvm3MHnsuexbkF7/opK77coUmdSkXbsbJMLrMS1yfXOrjJBbi6ceKJ7lda/P3z9dZk1nQSyGTN8NBNXrYJn74ZZFkJhvvgkhi9yKOUbaoTDMHUK9OlduaGccbprqvbVXLeNytChVe+NJCI7KdaV5ve7+tbyiyIPOwymTi278bo/izH7HMTEgk3w5DkwIwqhEIv86wlGjqZ8rAsWuSrd4QdWbijHHwcHHwRz5rjtooYOhebadk6kJhTvivl8cPjh7lXa0Ue7SYJ4dceYzbiO4L17MxELj50Dn4agKMj6Vn5W/iKScNcdioZ4b/F7jOldwfYEpRzc9WAGdhzIrJWziBFjcKfB5OW4GdS8kXkUTCnQDKeknRrPbCZrk1vT6zY4y5fDf/7jnmJt2ZL4/sUXu4ZCTZq41tq5Oa4M7ZRTGPPaB+5x/kC3xqnVfus993+yMZdwVkXHDi4eHnKIEk2RmlCs+//27jxMqupO4/j3VHXTDaLssisoCnFBZWmMGE1QFEkal8eJTuKI4pLMjFFjfAaXGTWaDWeMW8a4RbOMo3GNRuO44Ba3NKAiiwouqCSyRBYFpNczf/yq6OrqW9XV3bf29/M89VBddfveW93t6z3nnvM7MWvWwiOP2Dojn37a/v05c6yST89qy7qePWHYcPjOd6h9/BXY/gUc0ACToedBnwHBC8l1Nuv69bOiuV/7qhqaIt2lvMNWMXjsMVtP6W/tBrHYRPJ99rHruR6VlnX9+8OFF1L78nIrvLG/Db1tam7CpVjWs7Glc2HXu0dvvjb6axwx+ogdDc24vtPsa93hlEISyoDKoDK5JWX9eptY1L+/ldl2CVMZvIdf/ALmz7e7lg645RaYO9fWGIkbMABuvtkKCK1ZazX8x46Fzz+HTz6hNiFrtvV5nwMnv84rC6a2OY2qajj0K9n9qCKSWsln3aZN8NZbsPPOdhGVPCT2nnvsER+hcfvtcNbZ8PWZrdvstJNV+Fm2zJYmGDHCRnZEIrB4MbUJcysf6vNXJk5eyIsL2t4xqKqGaWnqE4lI9pV03m3ZAkuXWi/8/vu3GRILwNPzbbHzeNbdeaeNWDvttNZtKiut6NmKlbByBQza1aZPRaPw6qvUbmrZMZdzyALoWw/rkur4VEYq+dqocMMufodTpFBo9p73sGqVVZMYNcpCIq65Ga66yhqIztl7gwfba/GVxxcsgCefStgfVuXiZz+zi7LqhAUto9G2a9VB+4ADTtq8nXf6/B/UQIurpMXDm2/WcMghcOABYX1wESkr3sPHH9tE8NGj25Zq9R5uuMGGv8azbpddLOuGD7dtPvjAFq9M7J1vboFbboaDp7RdIN05q0SWXI2sogISKikev7mFD/r8gebJFfiKSpqbYMmSGsaNs8I/IiJd8sknsHmzZV3ysK7f/c6KYMSzrqoKLr8c9o7NUdq8GW64vn3WPfigLYM3dmzb/e29lz0SxfK1drMVD3KT4YotcNeeULe+ksaWRqorqhnaeyjHjUuadiVSYsq7sfnKK3DtdVaVIhq1huHcudbL1dwM3/8+fLCqdfumZrtYmzfPHmANyiDNLfDUU1alJ51eveyCLGk+52Xb3+LMGV/muV4zeWVDHbNn1zFyRE2bm6oiIhlZtszWftu61Rp80Sicey5MnWoNzSuvhIWLWrdvaob1f7ciQLfcYhdl990XUHsXe+2BB6xoRkcOP7zdfM4Ltn3IqYes4JndTufPa+v4x2/VscceNVZPSESkMz780HJrw4bWzvzT57SOvrjlFnj0sdbtm5ptzuXll8Nvf2uNxEceSZ11d99txYE6MmPGjvmcO4oHbYnQb8gIlhy6N2+uq2a/QfsxZcQUoi6adlddpbmbUijKt7H52J9sWGtcPHB++EO47XZYttRCK5nHhtRu3GiThDalGaqwbl1m5/L978PFF1s4em+P8eMZNns636qEb1HDH9+pAxLH4CtARCQDdXXwox+1XjzF7yxeey2MHGkN0NdfD/7eDRvg/fdtofOg+Zlx69dndi5nnGkjST76qPW13Xdn4L+czDd7wTeVdSLSVW+/bTcMWmJhF8+6O++wstW77gqPPx78vY2Ntoh5zeT0124bN2Z2Lscfb+fz5pvWWecc9O/PyedexU7rVnLwiPiGi8hGxqlYkBSS8mxsfvYZ3H5b8HvNzfD8c3YnoCXFbG6wOv39+tm8pudfCN6mJsP/wPv1g5tusvkD69bbfM7Ro9tsUju2dV+tF2MKEBFJo7HRlmMKirLGRitoVlHRtkp2Iu8t6wAOPBCWvxW83aRJmZ1Pr57wX/9l63OuXm3zOZPmwSdmHcTzTlknIml4byPOgq7b6hvgDw/DQQcGFl8E7Nrvi232fNIkeO754O0OODCz86mshMsus+kH770Puw6yUWyRCLX9cpNxanBKoQhjnc3is3gxKcejNjVbz1WPHqm/v7oahgyx56edBhUBQyAGD24/XymdSATGj4cjj2jX0EzWejGmamMiksbKlakvrlq83a2srCTlmFXvrWo2WHGMqoBc7L0THHFE5ufkHIwbZ6Vjx41LncUxlnfKOhFJY+06m2uZysYNlnXRFENWYyPKACvfv8vO7beprIBv/kPnzmv0aLuuGz8+cA1iyG7GxavTiuRTeTY2o9HUgeOwQkFHHRV8YQVwwQWtoTFwoN05GDbUvjcasWpk1/68w4uoHerrrZc/fgchA2pwikiHotH0ObTHHjaPsrIy+P0zz2wtrtGzpxUR2nMPy7qIg3Fj4cYbAwudBWpshL/+1YbudoIanCKSVkUHWTd6tBX3SdHgo7bWRpmB5eaNN8J++1rOOWDU7nD99dC7d2bn09xsy6UELYUXdHhlnJSw8hxGO2FC6lDywK9+ZZPIa2ttonhLi/V6RSJw/vnth4yNGWPbb/vCer5SXbi1O5aH//kfW8MpErHjHHMMnH566kBMUDtW85tEJI299rIiZNvrg99/4EGYNg1mz7bS/mA5BJZDM2e23X7YMLjuOqto61znFu99+GG46y573tQEhx0G//qvGedla94lUt6JCNbxP2KEDVsNGszxwgt2TXf++TZfHaxBCDDrWJhzetvt+/eHn/7UbgZ433ZlgY48/7xdEzY22jEOOshuUuyUfgHgbGachtJKPpVnY7O62gry/PjHNpY/2fbt8MwzdgF29AxY/IZdsE2enD5wevXs3Hk8/LA9Es/h8cctkE4+OaNdaH6TiKQUicC//7s9tgWMnGhqtAw680yrTLtokd2lnDw5fQ9+Zy68AF56yZYbSMy6F1+0Owjf+17Gu9HcdRFJae5cmHtRcOHGhgarJHvJJXDAAbZsXUsLTJwE/dIMNe1MhxrA8uV2VzQx615/3eaTXnllh9+ejYzT3E3Jt/IcRgvW0zRnjt2JTFbfYAUsAIYMhilTbMmTn/wE7rgD1q619xYuhHPOsapjZ50Fzz3XuXN44MH2jd36Brv46yINxRCRNvbaCy68MHhaQGMTrFhhz/v3h0MOgY2bbGrAL3/ZWjV2+XL4wQ/ghBNsnvof/5h6LmiQ2BIAbdQ3WGZu396VT6WpBCLS1rBhcOUPoUfAaAmPVdYG2Hln61xrbITrr4PrrocVK+29Vausc+6EE+Db37YGavwOaCYeDLiua2yyopOZVu2OCTPj4nM361YrLyX3yvPOZtzo0daLn7DmG2AXZaNG2fM1a2z4Q309NDTCkiVWwfHb327bU79mLfziF7bd0UdndvzPU4zl37LVetwyGEobRMPNRKSNkbsFNw6jEdh9d3u+ebMNMfv8c8u1aATmz4dTT7X15+JZ9+kG+M1vbPtTTsns+Bs2BL/uHGzZ0vk7pTGaSiAibQwenPq9EbH1RurrrfNszRrLtYiDF/9sI8ruva+1fkbj57aG8Jo1tkRdJlItm1JRYTk4aFDmn4VwM053OCVfSruxuX49/O//wmuv2ZCwY4+F6dNb52uOG2c9YR991NrgdFgoTJ9uX99xhxWziJfTbmq2x69/bf8mqm+w7YcO3VHiOq1Ro6wkdrKRI7rc0IzTcDORMvLZZ3DPPfDKK1ZJe8YMmDWrtRDakMFWsn/xG9ZpFldZaVVmAe67zxqQ8SxsbrF16u64o/3SKPUN1oO/114wcWLHBYK+9CV49dX2c6mqqlqLcnSRsk6kjGzfDvffD88+a19PmwYnntg63LVXLzhyOsx/uu0dxqoecNJJ9vzJJ1sbmmDXd/UNVkMjWX2DzfccP96q1HY0rHb8eBsJl3x92NxsnX5dEGbGxRucIrlUusNoN22yXvpnn4UNG+Gjj+HWW+H221u3cc4WO59ysFUyi0asATrvaujTx7Z5Y3Hwuk3JQRK37Qvb51lnWZilc9ZZFoDJtYpGjgyeX9VFbYdiJPeQiUhRq6+HC35gIy7+/in87RMrxDNvXtvt5v6bXZj1iC11MnqUzSEaPtzer6trP8oDUq/B2dhka2bOng3vvZf+HE85xe5eJi+xMnKk3UkNibJOpIS1tNicy4cesjXJ1623Tq9LLmktbAZw9llWDKhnLHOGDoGLLrJOL4CXXw6u19HcEpx3Tc02reCfTrWl89I5/nhr8EaTLq+HDEk9mq0TNH1AilHpNjYffdSGQiQGR32DXZAlTh7v3dsuwu6/33r2r74adk/ofaru5ORwgC+2w9//DlddlX67ffe1hmlyT9mCBXDJxW3Ds5tqx9bseBgFlUhJeO452LypbUOxvsFGdHz4UetrVVVW/fXeey3vbrih9eIL7AKps7bXw2efw+WXp5/XtNtucM01Nlcq0Tvv2HC2+hTVcrtAWSdSol5/3ZaJSxyd0dBodxITG4HRqHWC3XOPXdfdemvbVQQyXb4kUX2DXVP+6Efpl24aMMAqdu+6a9sbCR9/bFOy0q0FmiFlmxSb0m1sLlkS3EtfWWkTwJNFo8El+GfOTL3eZjot3goJrV6dfrtPP22/DEtjk63P1FEPWhcpqERKyLJlwUubOAfvrmz/eqqsq63tWuca2AXf0qXpt9m6tX2jsqnZhgD/+cWuHbcDyjqRErJyZXBBsfp6ey9ZJGLTCpJ9/etdu64Dy9W//CX9Ni0tdm2XOCiuxdu5/+lPXTtuku6M4ug7ra8KBUlOlW5jc9iw9sMYwNZ3Gzgw8/2ceCJMrgmuWtuRSLR1onkq771nd0KTNTTAB6s6f8wM6SJMpEQMGxacTy7SuWIU06bZXPWuZJ2j46x7//3gIkXb62Hlis4fM0PKOpESMXBQcDGxqqrOZd2BB9r8za5kXUtL8DVbolWrgjv0Ghrh7bc7f8wUujOKQw1OyaXSbWwee2z7ohWVFTBmTGtFskxUVMBXDk39fmUF7POl4FLb0YhVvA3S0GDzSd9/PzjwelRZUY8s0vwmkRIwfXr7rItGoG8fK1SWKeds6ZNUxckizgoCBd0RaGpKfaymJpsjtWRJ8NSAqh6t80azRFknUgIOnWqNuMTBYA577ZBDOrevmhqoqGxfMyNuxPDgrPMeJhwU/D0tLTZ94dVXg6cGVERtnnoWqMEphaxbjU3n3H865952zr3pnHvIOZdmZdwcGzUKLr4YBvS3wKisgAkTbP2kzqivh2uvDR6SWxG1QkIXXGCTv+ND0KIRO+b3vhdcpXHDBvjud23C+aLX2u87GoGdetnC6lmm+U0iHSvorBswwAr9DBtqnV6VFTYX86c/7VxV65YWm7MeVDgjGoGddoILvm8NznjWRZxl3Zw5wfOgtm2zQm3XXQcvvmQNz0TxC8Vp0zI/zy5S1olkpmDzrroafvYz2GMPy7nKCns+b17HVWKTXXutjcZIHmwRcVZY6IILrEEazzqHZd2sWbbiQLLGRviP/7Dze3p+8Bz2igr4Rm3nzrMT1OCUQtXdpU+eAi723jc55+YBFwNzu39aIZk4Ee6808bO9+xpF0udtWxZ6gu26mo48R+gb1/4+c/h+edh0SK7+DvmmNQ9WLfdbg3O5KpnDjvWfvvBeecFD8PIIq1ZJ5JSYWfduHFw882WKz16tC/Ek4mPPw6eDwU2z/OEE6B/fyuQ8fLL9ujd29YVHjMm+Pvuvdfmn8c71BIv7KIR2HNPy7quFOzoBmWdSFqFm3cjR1rnVbzQY98utIO3bLEl74I4B9/4hhX4ufBCWLgIXnjeGopHHpl6BMeTT1nBs3hnXXLWDR8B3zsnJyPWlG1SaLrV2PTeP5nw5avAid07nSxwrnNzNJNFo+17vuK2bIVf3wkPPmCVFo86yh4dWVAXXF47EoG777aGcZ5ozTqR9oom6wYM6Pr3R6OpK2A3NFplx4cesuVOvvIVe3TkhRdSFGqrgJtushEheaKsEwlWFHnXlUZmXLoRH80t8Mgj8Ohj8JMfQ81ke3TkmfnBo0J6VsNll3VuSkM3Kduk0IQ5Z3MO8HiI+ysM++4bXGgobnu93U343e8y32dy9dnE14Mmv+eJ5jmJBCrNrBs+PH1jtb7B7gjcdFPm+0yVddC1pVayRFknklLp5V2vXjB2bOpru/gyJ9dck/k+o9HU73VlVF1IMsk2DaWVbOuwsemce9o5tzTgcWzCNpcCTcBdafZztnNuoXNu4fr13V9nKGcqKmwcfs+e1kMVpKkZXnkl830eemj7okDRCEyZkv7iLA80z0nKRdlnnXNwyaWwy86pR1e0+NSFfoJMn96+yEbE2TyrXXbp3vmGTFkn5SSMvCvarAObk9m/f/qRZGvX2s2ETBx9dPDSUb17Ww2RPMok29TglGzqsLHpvT/Se79fwONhAOfcbOAbwLe9D6prv2M/t3rvJ3nvJw0a1Ce8T5AL++wDv/k1nHVW6p6waCdGJJ9xBgwdZo3XygoLu8GD4Z//OZTTzRZdhEkpU9YBu+9m89zPOzf1sgCRSOadYiec0FpQKJ51ffrYXKgCpqyTUhdG3hV11g0aBLfdBhf+wDrYUgkq8hjkq1+FSZNaC1L2rIbeO8GllxbUTQQ1OCUfujVn0zk3A5s0frj3fls4p1Sgeva0XvqXXoI33mg757JHJRx5ROb76t0bbrzB9vPRRzZ8bcKE9MMwCkTbyeeaAyDloayyrkcPmDrV8mn+/LZzLiuitsRAphdPPXrAT34Cy5fDu+/a/PmampwXP+sKZZ2Uq7LJu2jU8ui44+D3v2875zIasY6yTEdgRKMwd67l3LJl1ql28MEFNTUqLl229Z3Wl7pn6qgZocyT8HS3Gu0vgCrgKWcXH69677/b7bMqZOedBxddBBs3QUuzXXSNGQMnn9y5/UQi1sCcMCE755lFqnYmZaj8su700+G992D1ahs2G4lYhcbvfKdz+3HO5r7vu292zjOLlHVSpsor7447zhqIS5fa15Go3ZXsygiMMWNSV+cuIMo2yaXuVqMt/P+iwtavn62PuXgxrFljc4/23rughknkgqqdSTkpy6zr1csKZCxfDh9+CCNGwP77K+uUdVLiyi7vKivhiivsruTKlTbE9qCDimK0WXco2yRXwqxGWz4iEQuiY46ximZldvGVTPObREpU/K7kzJkwfryyTlknUrrGjLHrukmTSr6hmSw52+pW12n+poRGjU0JhZYOEJFyoKwTkVIUz7a+01bQd9oKYKUanBKK7s7ZFNlBQzJEpBwkZh3E805ZJyLFrc11HHVsemYldatRwSDpFt3ZlKxQ77+IlAvLuzqUdyJSKmrH1tB3mkd3OKW7dGczWzZugoULwEWgZnLBLWCeC+r9FykDW7bAggXQ2AgTJ8KAAfk+o7zQyA6REldfD3V1sHWrzWEfNizfZ5R1tWNrdIdTuk2NzWx48km45RYrJATwy5vg3HPh8MPze1551lpqW2ElUhLqFsDV8yzrWlrAezjlFDj++HyfWV5pjU6REvP221axtsXbsnfeWzGhM84o+cJpanBKd2kYbdjWrLWGZkMjbK+3R0Mj3HgjbNyY77PLu9bhZiJS1LZutYZmfQN8sd3+bWiEu+6CDz7I99nlnSrXipSI5ma46irYug2++KI16554Al57Ld9nlxMaUivdocZm2F560Xq8grz8cm7PpUBpfpNICViwwBY/T9bUBM8+l/PTKUSauy5SApYvh8am9q9vr7eRbGVCDU7pKg2jDVtjow0nS9bSYu8JoPlNIkWvqQl8qqxryP35FChlnUiRa2qCVCNly+y6LnlIbZyG1ko6urMZtilToCKgDe8c1Og/xiDq/RcpQhMmBHesVVXB1Km5P58ioKwTKUL77BOcddVVZVmLI36H09bj7AugO52SlhqbYRs9GmZ+Hap6WE9YxNnzE08si8plXVU7tmbHwyi4RApa//5w2mmWb9GI5V11FRx2GOy7b77PrmAp60SKTFUVnH++ZV1l7GZCz2rLuUMPze+55UlifvWdtgINrZV0NIw2G+acDodOhRdfBBwcfhjsuWe+z6poqJKjSJGorYXxB8Dzz9myAIccYncBSrw6Y1jaZl2cMk+k4Eydatdxzzxjyz1NnAgHHdS66kAZajNFQNVqJQ01NrNl773tIV2iBqdIkdh9Nzj11HyfRdHSnE6RIjFkCHzrW/k+i4Kk5VEknfLtkpGCp/lNIlJONLRWRIqVqtVKKmpsSkHT/CYRKSfKOhEpVmpwShA1NqVo6E6niJQDZZ2IFCs1OCVZKI1N59yFzjnvnBsYxv5EUtGdTsk35Z3kgrJO8k1ZJ12lBqck6nZj0zk3EpgOfNT90xHJnC7CJNeUd5IPyjrJNWWddJcanBIXxp3Na4F/A3wI+xLpFA03kxxT3kletN7lVNZJTijrpNvU4BTo5tInzrlZwF+994tdB+uqOefOBs4G2G23Qd05rEgbWjpAciHTvFPWSTbF805ZJ9mirJMwJS+LEqflUcpHh41N59zTwJCAty4FLgGOyuRA3vtbgVsBJk3aSz1lkhVan1O6I4y8U9ZJLrTNujhlnmRGWSe5FG9wwgoANj3jtB5nGemwsem9PzLodefc/sBoIN7zNQJ4zTlX471fE+pZinSCGpzSVco7KSYa1SFdpayTXGuTVwl3OtXgLH1dnrPpvV/ivd/Vez/Kez8KWA1MUBhJIdBcTgmT8k4KnYoISRiUdZILmstZXrTOppQsLR0gIuVEWScixUINzvIRWmMz1gv297D2JxIm3emUMCnvpFAp6yRMyjrJJjU4y0O3qtGKFBPNbxKRcpCYdRDPO2WdiBSe5Gq1msNZejSMVsqSev9FpFxofU4RKWS6w1nadGdTypZ6/0WkXLQf2aGsE5HCoTucpUt3NkViWnv/RURKV/s7nco9Ecm/5Duc8YcUNzU2RRKowSki5UDVukWkEMUbnH2nraDvtBVoaG3xU2NTJInmN4lIOVGDU0QKSWJnmOZyFj81NkUCtO31V8CJSGlLnsMuIlII1OAsfnkpELRo0btbnJv1Tj6ODQwE8rVmlI5dHsfN1bF3z/L+O+ScmwFcD0SB2733P0t6vwr4LTAR+BQ4yXu/KtfnmS/KOh27DI6trENZp6zTsXXsUJRk1uWrGu073vtJ+Tiwc26hjl0exy7Hz5xLzrko8N/AdGA1sMA594j3fnnCZmcAG733Y5xzJwPzgJNyf7Z5o6zTsUv62Mq6HZR1Zfa3r2Pr2KUmW1mnYbQi0lU1wLve+/e99w3APcCxSdscC/wm9vx+4AjnnMvhOYqIdJeyTkTKQVayTutsipSRRYvefcK5WQMz3LzaObcw4etbvfe3Jnw9HPg44evVwJSkfezYxnvf5JzbDAwgf0NgRKQMKOtEpBwUQ9blq7F5a8eb6Ng6dtEeN9/HTsl7PyPE3QX1ZPkubFPKyvVvUMcun2Mr6zLfppSV49++jq1j510xZJ3zvpyyUETC4pz7MnCF9/7o2NcXA3jvf5qwzROxbV5xzlUAa4BBXsEjIkVCWSci5SBbWac5myLSVQuAvZxzo51zPYCTgUeStnkEmB17fiLwjC6+RKTIKOtEpBxkJety0th0zl3hnPurc+6N2GNmiu1mOOfecc6965y7KKRj/6dz7m3n3JvOf2VrNgAABZdJREFUuYecc31TbLfKObckdn4Lg7bJ8HhpP4Nzrso59/vY+39xzo3q6rGS9jvSOfesc+4t59wy59x5Adt81Tm3OeH3cFkYx47tO+3Pz5kbYp/7TefchJCOOzbh87zhnPvMOXd+0jahfW7n3B3OuXXOuaUJr/V3zj3lnFsZ+7dfiu+dHdtmpXNudtA2xcR73wScAzwBvAXc671f5py70jk3K7bZr4ABzrl3gQuAUP67LlTllHWxfeU87/KddbH95zzvlHX5o6xrT1nX7n1d2xVp1sX2p7wji1nnvc/6A7gCuLCDbaLAe8AeQA9gMbBPCMc+CqiIPZ8HzEux3SpgYDeP1eFnAP4FuDn2/GTg9yH9jIcCE2LPdwZWBBz7q8CjWfodp/35ATOBx7Gx3gcDf8nCOUSx2/m7Z+tzA4cBE4ClCa9dDVwUe35R0N8Y0B94P/Zvv9jzftn4XeiRv0e5ZF2mnyMbeZfvrMvkZ5jtvFPW6ZHvh7JO13ax94s+62L7U95l8VFIw2gzKbfbad77J7211AFeBUZ0d59p5K08uvf+E+/9a7Hnn2M9EsO7u98QHQv81ptXgb7OuaEhH+MI4D3v/Ych73cH7/0LwIaklxN/p78Bjgv41qOBp7z3G7z3G4GngDAndUvxKIWsgzzlXRFkHWQ/75R1UgyUdd1UBHlX9FkHyrtsy2Vj85zYLfY7UtyKDiq3G/Z/UHOwHpggHnjSObfIOXd2F/efyWdoUzIYiJcMDk1s+MZBwF8C3v6yc26xc+5x59y+IR62o59fLn6/JwN3p3gvW58bYLD3/hOw/zEAuwZsk4vPL4WhHLIOCiDv8pR1kP+8U9ZJIVDWBWyja7uSyDpQ3oUmtKVPnHNPA0MC3roU+CVwFfZHexVwDRYQbXYR8L0ZTa5Pd2zv/cOxbS4FmoC7Uuxmqvf+b865XYGnnHNvx3o6OiPv5dGdc72BB4DzvfefJb39GjYUYUtsfsUfgL1COnRHP79sf+4ewCzg4oC3s/m5M1XuZfFLhrKu9XQCXstZ3uUx6yCPeaesk1xR1rWeTsBruraLnVrA95RL1oHyLiOhNTa990dmsp1z7jbg0YC3VgMjE74eAfwtjGPHJux+AzjCex/4R+C9/1vs33XOuYewYROdDaVMPkN8m9XOSgb3of2t+y5xzlViYXSX9/7B5PcTA8p7/yfn3E3OuYHe+24vOp3Bz6/Lv98MHQO85r1fG3BuWfvcMWudc0O995/Eho+sC9hmNTbHIG4E8FxIx5ccUtbtkLe8y2fWxfaZz7xT1klOKOt20LVd+WUdKO9Ck6tqtInjt48HlgZslkm53a4cewYwF5jlvd+WYpudnHM7x59jk8+DzrEjeSuPHpsb8CvgLe/9z1NsMyQ+h8A5V4P9/j8N4diZ/PweAU515mBgc3x4Qkj+kRRDLbL1uRMk/k5nAw8HbPMEcJRzrl9suNFRsdekhJRR1kGe8i6fWRfbX77zTlkneaes07VdTKlmHSjvwuNzUIUI+B2wBHgT++UNjb0+DPhTwnYzsUpb72FDJcI49rvYeOo3Yo+bk4+NVRhbHHss686xgz4DcCUWigDVwH2x86oD9gjpcx6K3bp/M+GzzgS+C3w3ts05sc+3GJtUf0hIxw78+SUd2wH/Hfu5LAEmhfj31QsLmT4Jr2Xlc2PB9wnQiPVonYHNy5gPrIz92z+27STg9oTvnRP7vb8LnB7W59ejcB7llHWpPke28y6fWZfuZ5iLvFPW6VEoD2Wdru1iz4s+62L7U95l8eFiPygRERERERGR0BTS0iciIiIiIiJSItTYFBERERERkdCpsSkiIiIiIiKhU2NTREREREREQqfGpoiIiIiIiIROjU0REREREREJnRqbIiIiIiIiEjo1NkVERERERCR0/w/jRHF8lOLlGAAAAABJRU5ErkJggg==\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "bad36c44719d419f83c835c6f373307c": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "c0f66cf1159d40ecb667d08f2a4a21c1": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_3c2688631fb84562b4e035ee8feecf6a",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 1296x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "c0fd899fd2204716a32db2981bb65d73": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "c28b5e44f3404a58b5b9af7a9a399213": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "c2c0c3e04391477c801662d6526368b7": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "IntTextModel",
      "state": {
       "description": "Index:",
       "layout": "IPY_MODEL_128fdd0d83a64197a9d269c29bb7bf6a",
       "step": 1,
       "style": "IPY_MODEL_2256d9b068964bdb94efe3008f11e47f",
       "value": 7
      }
     },
     "c4e0d5a703b448a6b893aec858281fff": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 4,
       "layout": "IPY_MODEL_6651be2c98e14f4ca10fd84758df32d0",
       "style": "IPY_MODEL_92dd9905a5d542498707b95e1a40ce6b"
      }
     },
     "c590453e492c4b22a1187c4c9b50127b": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "c6ed83722e2f4396aa04e8fb40828266": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_905cf1eee78e448aad5bd7e66d17c55e",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "c75a77d26e4b4576a4b824f24ea3000a": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "c79d0f053173432c913cfc08ba5397e3": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {
       "height": "30px",
       "width": "270px"
      }
     },
     "c7a2694d833a4b14a6fa5aef929f6e27": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": "initial"
      }
     },
     "c807ffecfb4645be82fc342b156202d1": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "cebe583b636649e3a37a0747f8d0afda": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 2,
       "layout": "IPY_MODEL_685ed2f5cf7746d8828f2ab178e70390",
       "style": "IPY_MODEL_92d51825631e43bfb0bccc549dcb71a1"
      }
     },
     "cff2d964a6af4894a6bfd775bb9c451a": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_17a9553850174fa0b79151089a1f4706",
       "outputs": [
        {
         "data": {
          "image/png": 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ISDpRrBORTNGg451KaUXSRyqSzeXAgcaYpsYYAxwJzE/BdUVE0olinYhkigYb77R2UyS9pGLN5kzgNeAL4Jv4NcfX9LoiIulEsU5EMkVDj3dauymSPvypuIi19kbgxlRcS0QkXSnWiUimULwTkVRI1dYnIiIiIiJpQ6W0IvVPyaaIiIiINCpauymSHpRsioiIiEijo4RTpP4p2RQRERGRRkkJp0j9UrIpIiIiIo2WutOK1B8lmyIiIiIiIpJySjZFREREpNFTKa1I3VOyKSIiIiKNmtZuitQPJZsiIiIi0ugp4RSpe0o2RURERCQjKOEUqVtKNkWkWowxTxpj1hljvk3y/ghjzGZjzNz464a6HqOI1L6iIEyeDPfdDy+9BBs21veIUkuxrvFRd1qRRLUV6/ypHaaIZJAJwEPAMxWc84m19vi6GY6I1LUtW+CSS92fwSLwZ8Mbb8Ctt0Gf3vU9upSZgGKdiDR+E6iFWKeZTRGpFmvtdKCRzWGISFW88CJs3OgSTYBIGIqK4IEHwNr6HVuqKNY1XiqlFSlRW7FOM5siGWR7aHtd/5/rcGPMV8Aq4HJr7Xd1+eUiUrtmzIBoJPH4unVQUACtW9f9mECxTnYtb2QeBVMKyF+Rz7Auw+p7OCLV0hBinZJNkQzib+GvylqVdsaY2aV+Hm+tHV+Fr/sC6G6t3WaMORb4D9CrCp8XkTQXCCR5w0J2dp0OpQzFOqmM4oRTpKFqCLEuJWW0xpg8Y8xrxpgFxpj5xpjhqbiuiNSrn621Q0q9qhKQsNZusdZui/99EpBtjGlXKyOtI4p1ImUdMzox4fRlwd79oHnz+hlTNSjWeVC8E2l06iXWpWrN5oPAZGttX2AgMD9F1xWRBsoYs5sxxsT/PgwXbzbU76hqTLFOpJQTxsKg/V3CmZsLTZrAbrvBZZfV98jqTiONdaB4JyKlVDfW1biM1hjTEjgMOAvAWhsCQjW9roikN2PMi8AIXFnGCuBGIBvAWvsv4GTgz8aYCFAInGJtw20ZolgnksifBdddC8uXw6LF0KE97LMv+Ex9jyx1Mi3WQWbFu7yReeRP0bpNkdqKdalYs7knsB54yhgzEJgDXGyt3Z6Ca4tImrLW/m4X7z+Ea6HdWCjWiSTRrZt7NUYZGOsgw+KdEk6R2ot1qSij9QP7A49aawcB24Gry59kjBlnjJltjJm9edPmFHytiEidUqwTkUyxy3jX2GJd3sg8bYUiUgtSkWyuAFZYa2fGf34NF6DKsNaOL16Q2qp1qxR8rYhInVKsE5FMsct41xhjnRJOkdSrcbJprV0D/GSM6RM/dCQwr6bXFRFJJ4p1IpIpMjneKeEUSa1U7bN5EfC8MSYALAXOTtF1RUTSiWKdiGQKxTsRqbGUJJvW2rnAkFRcS0QkXSnWiUimULwTkVRI1T6bIiIiIiKNgkppRVJDyaaIiIiISFzeyDxACadIKijZFBEREREppT4Tzg0bYO6XsGZ1nX91tW3ZAnPmwJIlYG19j0bSSaoaBImIiIiINBp5I/MomFJA/op8hnUZVuvfF43CP/8Jn0yHQADCEei/L1x9DeTk1PrXV4u18MLz8OabkJ3tfocOHeHmm6Ft2/oenaQDzWyKiIiIiHgonuGsC2+8Dv/71CWZ23dAKATffAP/Hl9nQ6iymTPhrbcgFHZjLgrCihVw++31PTJJF0o2RURERETq2TvvQDBU9lgoDFOnuhnDdPT2Wy7BLC0Wg+XLYc2a+hmTpBclmyIiIiIiFaiLtZs7dngfj8YgEqn1r6+Wbdu8j2dlwfbtdTsWSU9KNkVEREREkqirZkH79gfjcbxrl/Rds3nAAZDt0QHGZ6B7t7ofj6QfJZsiIiIiIhWoi4TznD9A06bgjydvWT7IzYELLqi1r6yxsSdCm7auoRG4JDMnAOefD/7s+h2bpAd1oxURERER2YWadKfdvg1WroL27aF1a+9zOneBhx6Gt9+GhQuge3cYOxY6dU7B4GtJ8+bw4IPw/ntu65O27WDMGOjZs75HJulCyaaIiIiISCUUJ5yVZS08PQH++183YxmJwNChcOmlkB1IPL9tWzj77NSNty40bQon/tK9RMpTGa2IiIiISC2Y/K7rMhsKw45C9+esWfDYY/U9MpG6oWRTRERERKQKKrt28803vbczmTYNwmFYtRJmz4J1a1M/RpF0oDJaEREREZFKqsraza1bvY/HYnDzzbBggevmGg7D0GFw+WWQpbtzaUQ0sykiIiIiUgXF3Wl3pd8+3tuZ+LNhwXwIhWD7jpLy2pdeSu04Reqbkk0RERERkVpw9lmQ28RtYwIu8QwEIBJ2CWZpoRC8+27lrmstfPMNvPoKfPgBFBamctQiqZOyZNMYk2WM+dIY899UXVNEJN0o1olIJlCsq5xdrd3s0tVtDTLqKOjRHQ46CP52O0Sj3ucXBXf9nZEw3HA93HoLPP88jB8Pfzgbli6pxi8gUstSWRV+MTAfaJnCa4qIpBvFOhHJBIp1u1DZtZu77QYXXFD2WM+esLhccmiA/vvu+nvfnezWehY3HipOUO+8Ex4bD8arbleknqRkZtMY0wU4Dng8FdcTEUlHinUikgkU6yqveO1mZbvTFjv/fMjNBX+W+znb7/arPPfcXX/2gw8SO9wCbNoEq1dV/NlwGF54Hs46C077PTz8MGzZXKWhi1RJqspo/w5cCcRSdD0RkXSkWCcimUCxrgqqk3Du1Qse+iccexwMGABjx7rEr3OXSnzYJn9r61ZYsgS2b/N+/9Zb4I03YeNG2LIVPvoQLr0UgpUo3xWpjhqX0RpjjgfWWWvnGGNGVHDeOGAcQPtO7Wv6tSIidUqxTkQygWJd9RSX1FZFh46Vm8ks78hR8OyzrqFQacYH114L2dkQicDRv4A/nuuOAyxeBPPnl/1cJApbtsAn0926UpFUS8XM5sHACcaYH4GXgJHGmOfKn2StHW+tHWKtHdKqdasUfK2ISJ1SrBORTKBYV015I/OqXE5bHccdC337uDJcA+TmgN8PsSiEI7Cj0HW6/eB9eP2Nks8tXep9vaKgWwMqUhtqPLNprb0GuAYg/gTscmvtaTW9rohIOlGsE5FMoFiX/vzZcOtt8PXXbq/O1q3h8SegqKjsecGQW5/5yivunAMPBF9W4vUCgUqW7yZhrUt0s1LZdlQaDe2zKSIiIiKSInUxu2kMDBwIvz0FRo1KTDSLRaLuvdWr4Z133AxoVrm7f38WHHlk1cdgLUyaBGecASed5JoOTZ1a9etI45bSZNNaO81ae3wqrykikm4U60QkEyjWVV1lmwXt2OESs0mTdt1Bdld8WdCqEpXMoRCEQ9C/v0sw/Vmw5x5wx53Qshob3Lz7Ljz1JGze7HoWbdwIjzwMn3xS9WtJ46UJbxERERGRFNnV/pvffO3KYMGVn2Lg+OPgrLOr/53RSOXPvfBCl1xGo9CsefW+z1p48YXELViCIXjuOTj00OpdVxofldGKiIiIiKRQshnOcAj+9jdX2lpU5Br5hEJuhvPrr6r/faFw5c6LWTcLmtuk+okmuCR5yxbv99avr/51pfFRsikiIiIikmLFCWdpX3/jZgXLKwrChx9V7rqbNsLbb8FLL8HCBe56+/Tb9edyAvCLoyEnt3LfU5Esv2s65GX33Wt+fWk8VEYrIiIiIlIHKip3jVSiFHbWLLjrLsC6819/DQ46CHbbzft8407FAEOGwh/OqfqYkznzTHjkkbKltDkBd1ykmGY261lREOZ+5fY3ink86RIRaQzCYfdE/9vv3DohEZHGKGqjzFs/j6/WfkUo6rKw0qW0/Qd4x8DcHDj8sIqvHQzCPXe7sttQ2N03BkMwYwZ88KH3Z2ypP2fOhEnvgI1V/ffycsRI+MvFbibTnwVdu8KVV8GwxGWqksE0s1mPpkx1T4SysgALTZrCTTdBj+71PTIRkdSZ8wXcfXfJz1lZcO21sO8+9TcmEUml7UA+kNlZxsINC7n141sJx0oWUF584MX0+77fzmZBTZrARRfBP/4JsZib6czJgcFDdp2kffst+DymiYqCiduZeIlE4N+Pw4svwqmnwvFjqvgLejj0UDUDkoppZrOe/LjMtYcOBaFwBxQWwsYNcP3/6am/iDQeGzfBHXfE41z8tW0r3HIzbN9R36MTkVRoldss/rfa318yXQWjQW6ceiNbQlsojBTufN3/2f0EDwgCJTOchx0ODz8Mv/0NjB0L198AV14JZhd35aaC97zWgSazbTs8/TR8mGQ2VCSV6inZLH4ClrlB6b33vGvzQ2H4+uu6H4+I1AbFuk+mJ78JmvFZ3Y5FRGrPmD7F03L5ZGLcm7VyFpbEYBcjxpSlUxK603bsCL89xa2h7N8fTEWZZFz//nh8gyvB7d8fAoHKjzcYgpderPz5ItVVL8lmq9xmjOkzLB6YMisYFdu82ZVPlFdUBE9NgC++rPMhiUiKKdbBlq2u1X95RUF49VX49H9VeyIvIumrON6VTTwzw7bQNqKxxNK0SCzC5CWT+WDpB7Q4okWNviM7AFdf7Zrw5ATcOsmcABw+Am64EY4+yiWcXqW2XjZurNFwRCql3stoS27CMusp2AEHeLeetjH48QdXdvbqa3U/LhGpHYmxLjPi3aBBSdrsW1i9Gh58EB79V50PS0RqWaYlnAM6DvCc2QTYVLSJx+Y8xu3Tb6/x9wwaBE8+CeecC6edBnffAxdcANnZMO48ePkleP45OGHMrtdxdulS4+GI7FK9J5tQ/klYZgSlgw92jYACOd7vB4vcAu4tW+t2XCJSezLxqf8+/WC//ZLv6xYscuuGVq6q23GJSO3LpFjXqUUnju55NDlZ3jd2oWiIr9d+zfLNy8t0p62OFi1h9Gg46Vewxx5l38vyQ7PmcO4f4fEn4IorYOwJbha0vCOPrNEwRColLZLN0jLl6b8/C/72Nxg3zgUFL5Ew/OEP8Oyzahok0thkyvomY1zZ10UXQdt23udEwnDhhfDoo661v4g0HpkS6wDG7T+OKw++ki4tvKcMQ7EQNwRv4M0FbzL9x+mVuua2bfDsM3D+n+GKy+Hjjyu/9KBtW9cp9sQT8ewu9MKLrkGlSG1Ky61PSgITTFxYHJgaXjtta2HdOvBnQ9s2ie9nZ7v6+m+/gWkf47nqOxSEt96GLVtcmcTiJW7Gc9mP0K0bnHIK9O5d27+JiNSGxhLrANb/7GJe+3aJjS6yfHDYofDTcnj9de/maNEIfPgRrF3rtoBasdI1r1iwADp0dF0bBw6sk19FRFKsMcW6jYUbCUVDdGzWEVMu2BljGNppKJsKN/HvL/5NMJr49CxGjIltJ7L+q/Uc2v1QNuzYwMvzXmbu6rnk5eZx0t4nMbzrcMAlgpdc4nYrCMfj5rKHYPEiV0ZbWdOmeXeytRY+/xyOOKLy1xKpqrRMNksb02dYgwxM8xfAffdCQYHLIbt1g6uvct3Hyjv+ePhshkssvYSCbk/OAw6EO+90m/liYd16t0n69dfDwAG1+duISG1rqLFu+U9w912weo37uUN718K/fGkXwKij4M03k18rHHL7yM2e464ZDLl17OvWwfffu9nPEYfXzu8hInWjbKwrlv4xb/2O9dz96d0sKViCz/hoEWjBpcMvpX+H/gnnHtztYJ748omk14rYCAXBAmb8NIOHZz3MjvAOojbK2u1reWDGA6zcupKT+53Mhx9CwaaSRBNcc7VJk+CXv4Q2bSs39q1by16jWDTiZk5FalPaldF6aWg1/xs3wY03uBukUMjdQC1dCldf410O27s3/Ok8t6Yp2R5Lfj888UQ8IS2eAbXu58ceq63fRETqUkOLdcGgK5Fd/pOLc+EQrFwJ11wLOzz20OzYAa66Gpo1S94t0Z/tGlwUBV2iWSwUhH+Ph6hHF28RaVga2vr1mI1x7UfXsmjjIiKxCKFoiA2FG7jl41tYv2N9wvnNsptx84ibycvJI8t4LJYEYrEYkxZPojBcSNSW3BwWRYt46duXKAoX8eUX7qFbednZ8P2iyo9///0h12PdvPHBoP0qfx2R6mgQySY0rJr/Dz9MvCGyMdixHb6c6/2ZUaPguefiey15/KcSicDqJA00VvykrVJEGouGFOs++8wH1i5xAAAgAElEQVSttyy/BCAahU8+9f7M0CHw7HNuU/Msj9qacDjeLMhjWcHWrfDuuzUdtYikk4aQcH677lu2BLcQo+zNXdRGmbx4sudn+rbry4QTJ3Bi3xPJ9mW7gzvy4OtTYPo1LIwMYNm69URs4pRjKBriua+fo30H7wdzMQttWld+/P0HwID+bj/OYrk5cORI6NK18tcRqY4aJ5vGmK7GmKnGmPnGmO+MMRenYmBeGsqTsPXrvPeVi8Zgwwbvzyz8Hh56yHVmLB9YAjnwi6OhZcvk3/m3v7mSXRGpHYp1iTZshFA48XiwCH7+2fszy5a5RkBr1ySu7QwE3BP4dkkaCQFMeMrNpIpI7anLeAfpn3BuKNzgua1JJBZh7ba1np9Zs20Nj3/xOAvWL8BgYFMPeOdRmHcyrBhO9NuT+eLbP0NhnufnJy+ZTK8DF5Jd7qGcz+fWxvfqDevXw3/ehNdeheXLk4/fGLj2WteobchgOPAAuPwK+NOfK/svIFJ9qVizGQEus9Z+YYxpAcwxxnxgrZ2Xgmsnlc41//vs67qFFRUlvufVzGfye/D44yVrMbMD4Au42YEWzWHsWNfeun1715nWq7mGtTD9E7evkojUCsW6cvr0hkA2FJVbHpCbC337JJ4/axbcdbebDY3FXMms3+8mMXNz4Bej4fenwsyZcP8D8VnTciIReO89+GMVmmOISJXVebxL51jXu21vYrHEGv6crBwGdExsmrFww0L+b8r/EYlFiNoofuOHWedDuAk753kiAaIxP4s2/4JeTV5OuEYoGmLm1te44orrePAfruojFnXr4a++BqZOgUcedZVzsRi89LK7BzzjTO/fwZcFhx7mXiJ1qcbJprV2NbA6/vetxpj5QGegVm/AIH27mx18ELz6imuYUXyzFMhxT+z36FH23KJgPNEs1RwoHHIJ51lnwYljS46PPRFmzXbda8sLh2DrlhT/IiKyk2Jdon33hZ57waLv4w/LcLOT3brDoP3Lnhuz8M9/lo11kbC7ATr2WBj3x5LjhxwCM/Ph42mJ3xmLwWZVcYjUqvqKd+ka6zq36MzwrsOZsWIGoagLdn6fnzZN2nB4j8SuZQ/PerhMJ9pIJAYbepFQUBjzYdYO4vvDb6X3wsTZiIKiAoYdBs88AytWQNOmbuJhy2Z45JGylSXREEycCAceCL09HvaJ1JeUrtk0xvQABgEzPd4bZ4yZbYyZvX795lR+LZBe65yys+Gee1ynsN12d51ozzwTrroy8dzFSRZ4h0MwbWrZYz4D55zjEtfycnJhoBZ5i9QJxTrHGLjlZvjdqdC5M3TqDL/5Ddx+u4tXpa1ZA9s9mgbFovCpx/rOs850M5/l5eTC0Pq/9xTJGMniXSbFOoC/HvhX/rDfH+jeqjsdm3XkhN4ncN/R95GTVfamLBgNsqxgWdkPmxgY7w3TY9Essot2TzgeyAowvIvbAmX7NmjX1iWa4CYevNZyBkOuPPY3v4bxjyXf5UCkLqVs6xNjTHPgdeCv1tqEOTZr7XhgPMCQIb0quR1t1aTTE7GmTeH009yrIs2alcwIlLdxY+KxnnvCQcNhxuduXRS4m6/9BsI+/Wo2ZhHZNcW6srKz4VcnuVdFmjZ1ZWBedmxPPNa2LfzyRLfPcPENUyAHuneHgw+u2ZhFpHIqineZFuuyTBbH9jqWY3sdW+F5fp/HrbUP6PYJ/DiSxB0vDXutug7je4RoLIrFEsgK0LZJW/r6juOC80u2lurbBy67fOfHkioKwvvvw6pVcNPNlfwFRWpJSpJNY0w2Lhg9b619IxXXrKmGsmdd+/Z4dl0EKPRY8wnw10tg2Geu620sCkceCYccmthsQ0RSS7Gu+vJaJX8vFHIN1LLKPak//XTotw9Mfhd2FMKhh7h45/feSUBEUijd4l1DiXVZJotsXzahWLmZhD5vw7IRYMsFMAs/L+3GZXecweevfo4xhmGdhjG83TFcfGEOhYUlp86b77abuuced/9XkVAYvv3Old926ZKSX02kWmqcbBpjDPAEMN9ae3/Nh5Q6DSEw5eS6BhleTX+S3Zz5DBxysHuJSN1QrKu5Fs3d9iXl5eQmlt0WG7y/e4lI3UnXeNdQYt1uzXdj+ZZy7WGb/exKacsnm0BeHvRr349+5/ejYEoBw7oM4/XXIFru3jAWgy1b4Icf4MIL3S4G4KpGvOYt/FlKNqX+pWLN5sHA6cBIY8zc+KviGoM6lI7ttK2F9T/Dlq2Q7YcjjkhcmxTIgRNPrP715y9wJRTz5rufRaTGFOuqYcNGKIgv5zphbOKa80AAjj2m+pUZS39wsW7uV64JkYikRNrGu3SNdQXBAjYUuv3tfrX3rxLWcvqbFtJ6z2X4y03z5OSWXYaQNzKP/BX5rFrtvbVUJBJlzZooI46Ax8a7niD9B3hXfESi0FWJptSzVHSj/ZQKK8frXzq10/7mG3jg725PzFgMunaFCy6Abdtg9pySWc7Ro12HxqoqLIT/u97tt2Stu4Hr0gVuuw2aNU397yOSKRTrqmbpD3DvvbB2rYt1HdrDn8+HI0bAlKlurWcoBAcdBKedXvXrhyNuf+Fv4t25s3zQKg/uuAPatknpryKScdI93qVTrFuzbQ33fHYPPxT8ABZa5rbk3P3OZWyfsby54E38Pj+RWIT+Hftz4Y1d+Md98N08d78XjcCvf+3iYGl5I/No8nU+udOHUVSuyU84FuG5lbfRf8t5dGnbhTEnuHXs558P0cKSGc5AtusY3lnJptSzlDUISne1ucg8GnVP1MtvvFvemjVw8y1lu4Mt+xGuvBKOO851Dlv/s+vq2KJ59cbyxJOuvKL0/nTLlrntVS7+S/WuKSINR63GuphbJ5Tt0SW2tG3b4JproLBU99nVq+GG62H4QTB+PKxfB7vt5srHquPNN+Gbr8s2WAsG4YH73cM1EWncajPWxWyMSCxCICtQ4XnhWJirPryKTUWbdh7bWLiRu2fczd7t9mb88eNZX7ietk3a0r6payV7yy2wfj1s3ATdukKTJt7XPuD8PKZ/kk9owRBi0Xghoi8IHb5lW7OvuX367Txy3CMYY2jT1q3jfOwxt04zJwdGHelmPUXqW8Ykm6Wl6olYwWZXLz97NmBh735w0UXQKbGDNQCTJrnENIF1ZWC9e7mS2pr4+OPEjdAjYZg+XcmmSKZJVawrLIRH/wWffuISzj33hAsvgJ49vc+fOi1xrVGxWfmuq/ZvflPlYZTx3nuJnbxjMZg3z22xokoOkcyRqlgXjoZ5au5TvL/kfcKxMJ1adOLPQ/7MgI4DPM+fvWo2RRHvbo4LNyzkhW9f4KJhFyW81759yTYmO787vu9wcaO0nACc8wd48ukZbPp+b/CFYa/3oe+bWCw/7/iZlVtX0qWlm7rs2g1uu73Kv7JIrcvIZBNq/kQsGnP7Zq5dV9IRbN48uOIK+Pd41+a/vFWrk9+AhUPw3PPQqzd06Vz536M8r0ZD4L63uKxWRDJHKp7+33wLfP99SXxZshiuvRYefsTt/Vbe2rXJt3SKRNys5OAhLumsrmTbqBR/h4hkltKxDorjXdVi3YMzH+TzFZ/v7CS7cutKbpl+C/eMuoc9Wu+RcP7PO34mHPMORjEb46MfPuLIPY5k73Z7Y5LcgM1fAI884pY/+f0wciSce65LNps0gdaHvMqmfZYmfM4YQzhaQSAUSROpaBDU4FVnsfncL+PrLkvNVNqYu8GaPt37M/33hewKKjLWr4OLL4aHH65+U59B+4Ep95+q8cHA/ZRoimS66sS6H5fB4sWJFRPhMLzzjvdn9t7bNb1IZvt2t3zg1ttcA4vqOGg4ZHk8Lt19d2jVsnrXFJHGw8W7yse6gqICZqyYkbBlSTga5rX5r3l+plebXmSZ5HsxxWyM66dez5UfXklhpDDh/ZWr4IYb3JIqG3MTD1OmwN13lZyzR94enuW8gawA3Vt1r9wvJ1KPMiPZ/PlnuO8++N3v4Oyz4ZVXEh59V/UmbNVq75ukYBEs/8n7M0cdBS1aVHzdcAimToX/fVapYSQ470/uO4o7PgZyoHkz+NOfqnc9EWlAtm51j8h//3s4/QyYMMEtZCylyrFuFWR5dTmMuBskLwcc4NZjVtReJByCL7+E//63UsNIcOrv3axqcVKbHZ8FuOTS6l1PRBqQYNDFtzPOcPHukUc891WqSsK5dvtasn2JC9ItluWbl3t8Avq07UPfdn0xFQS7cCzM4o2LeearZxLe+8+bLhaWOT/kumuvXecaBQ3tNJQ2uW3IzXLBzu/zk5OVw2XDL8Pny4zbeGnYGn8Z7datcMkl7s9oDLZtd8nmDz/AVVeVOdWr5j8YHMazz8KHH7lZy0H7wR//CD26u7r68gUMubnJ1zE1bQp//zv88x8wK77O00soBJMnV28fzY4d3ALxKVNg6VLYcw84YqRLOEWkEQuH4fLLXeeJcPxh2sSJ8N13cPfdZUobvGJdNDqMV16F/050azT79IVxf4Tu3b3L/7MD0LuP91D8We7J/L8ecw/PksW6SBjemwwnjq36r9uyhVszP/0Tt4ShcycYNar6DYdEpIGwFq6/HpYsKdkb5IMPYO5cVxpWroNZSbwr/rhl4qK1vDH/DTYXbWaPvD04Z/9z6Naqm2dJrA8fvdr08hyKMYYbDruBZ75+hrcXvo1NEuyiNsq0H6dx3uDzyhxfttytNS8vOxvWrHb3dO1GteNsczaRWIS5q+fSrlk7Ru0xivbN2yd+UCQNNf5k8/333Z1TtNT/moMhyM93j+w7dSpzevma/99cn8+7k4ftfPI0ew4sWOCaZXTp4krMisvLfFnQvAUcckjy4SxZAhs2uJbUydY0QfL3ioKwdQu0aeM92wCuMcaY40t+DkdcY6Jk54tIIzBjBmzaVJJogrsRW7bMJZz77lvm9PKx7tx78nn99WE7u2V/9617HvePf8CgQW4WsjguGZ/rdnjMMcmH8+My14E7ECjbgbu8ZGsvQ2HYXOCSx2Tdb3Ny4KhR7gWu2iQS9d5vTkQaiXnz4Mcfy25CGYm6tU2ffQaHH57wkdLx7rL37ua7dZ+zsdDFysWbFnPjtBu548g7OLrn0Xyw9ANC0ZKbsIA/wMn9Tk46nFXbVrF883Jy/DlJmwUBnols716waJElGik7MxoOQ5euJT9nmSyGdx/Ood0PBSAaixKOhsnO2kVrcJE00PiTzXnzXHJZnt/vZjfLJZul/fADxOYPY7+BJU/EZs0aRjAIH34At98OzzwL06ZCLGo5oOd6/pD9LDl3bnc9p4cPL7OA8vOZcO89FSeZABgYMaLsoXDEbRcwZYqboMj2w5lnwehfJL/MipXuyf+C+W4Yw4a6PT1baj2TSOPz/fdQ6HGjE4m4ModyyWZpGzfCxhnDGDigbLnZnC+G8Z//wJVXwUsvuQ6wwSDs16OAP+S+QKv71sBhh8OIw8ssoFywwE08VJRkFjv00LI/xyw8/xy89bb72Wfg5JPdXnTJ1p1v2Ohi3Zdfup8H9IcLL3J7e4pII7N0qXcXsMIiWLTIM9ksFowEWbY5n0gswtBSt3+zVoV44ZsXuP6w6+nQrANvLXyLbcFt9G3SlXOWtqLT3Y/AgQfCqKPcU664VVtXccUHV1SYZBYb2mlowrEm+75P9N1DgFyKV7YFciyHHGwS9gvOX5HPPh324dHZj/LZ8s+IEaNXm15cOOxCuudp7aakr8Zf7N2tm/cGmLFYfFFRcsuXg88HHTcP2/kaOjSfUMjFsyZN4Lxx8OILlpeH3celSy4gb+7Hbi+Uv/8d7ru/TKefJx6vRKKJy3+Ln9Rv2w7z5sODD8LUKa6WPxR0DTYefxxmJlmKsG2ba8Axb577VaMRyJ/l9r6LVbP5kEh5xpjRxpiFxpjFxpirPd4/yxiz3hgzN/46tz7GmRE6d4bcnMTj/mzo2LHCj65a5WYgS8c6gMH757NosQuhp58Gzz0Lrx7/NNf9+Ed2nzsZvpwLj/3LZZal9nV6akLlEs2WreDkX7u/FwVdV8YJT7lEMxR0r6IiePU1t3WUl3DEdQH/8gvXsC0Wha+/dhXFXs8ZRapDsS6NdOzo4lp5OQHYPfkEAsCGwg34jI+Ozdn5AhjaCX4s+BGf8fHLvr9kwtgJvNbsbG575if2mPIFfPW1WyN62WWuOUfcS9++RDCy62AXyApw7v7uvxLhaJgFGxbw+rzXeXP5eDj6Mtj9S8gKQm4BPQ/5govK7ZaSN9KtD7j0vUv57KfPiNgIMRtj4YaFXP3h1Wwu2rzLMYhURm3EusY/s3nMMW7dUmnZfrch0Z4V993v1CmxK2zHzcMYPjyfg0uvp1yUB/kz3d1SsaIgzPwcFi0i1qs3TzzhtgNIxu93SeEhh7glpj6fmzV96y33XunN0YuFgvDyS3CAR2fvKVPjiW2p8UcjbjnXN9/AQO8to0QqzRiTBTwMHAWsAGYZY9621s4rd+rL1toL63yAmeaww9zNUGlZPmjRHIYMqfCju+2WWM7acfMw1rfOZ8SIUk+01veAt98uW75WFITFS9wGmgcO57XXYH75/waUUhzrBgyA6/7P3R++PRGeecaV+nvFumA84TzuuMT3ZuXD9m1l1z3FYlBUCJ/9r+Z7F4so1qWZwYOhaRMXGIqfnhtcvf2I5LOaAG1y2xCzZRdJdmwOa7fBqD1LlX3t2AFPPVV2hiAYgrVr3PrQ48fw0dKPmLZsWtLvyjJZxGyMnq17ctOIm2iZ05Lpy6bz8KyHAUq607ZaCUfcvPNzS7NysOZFyt+irxm4hp//9zORWNlZ3XAszHuL3+M3+9Zw82LJeLUV6xp3srlmLdxwvfu7z7ig5DPuxusvf9nlXiB77QU9erh1lsU3YoYY3bYM5Jr9fiKvz15u0fm6/5a9+SoWjsDcubzzfW/em5z8e/Ly4Pob3P6aTZq4Yx9+6O7pwqHETmWl/bzB+/hPy71nFmIWVq9SsikpMQxYbK1dCmCMeQkYC1SQakit2LwZbrwxvjjb59aoG2CffdzTq10s2G7XDoYNg1mzyjav7bp1EDcMXEKX3n2Y+P0sWPWWW5xevjVaURHk5/M5w3np5eTfE8iB2251692bx2cUvvzSJZq7mgndnOTB/arV3jOYRUVuWwGRFFCsSxeFhW4N09at8Xs462LdXnu5WNes4m6Iudm5HNvrWCYtmkSw1LrMbs18HGZ6QOxz8B0Ii753i7/Lx5ZgCGbMYOHw3jw6+9Gk3+M3fq4//Hr2aL0HeTluVvKHgh/4x8x/JGytUl7URimKFNE80HznsR9+hOlfRVjUeTs9fiq7DUooGmLZ5mUVXlOkkmol1jXeMlpr4eab3HRiMFTy9Cs72812Nm9e4cfBxbGbb3bl/9lZUXxE2Yd53B2+lLw7roZHH2VM76GuBe2Bif+U1u9n+ppePF5B+WwgAKeeCr32Kkk0wW16vssyNAO9e3u/1bOn9z53xkD3Hru4rkjldAZKb/SzIn6svF8ZY742xrxmjOnq8b7U1D33uEZAwVBJM7RAwAWvdu0qdYlLL4XRoyE3O4ohRk+WcGvkGro8dj3cfjtj9hrsYt0Qj9aJWT7m7Nibu+9JHrcCATjhBOjbt2z4/c9blSu57d4tyfHuruFaeU2auIeFIimgWJcuHhvv1geFwiWxLjvbzXZ2rdw/+Vn7ncXJ/U6mWVYOxkKXrXDttBjnvzwDnn4aIp9B+x9hkMe6UAPz2htumnZT0qTR7/NzULeDGLTboJ2JJsCkRZMSZiW9tAi0oFm2S5p37HCN2q64Aj54YW9CE+/h+3UnQazknjMnK4febZPcDIpUTa3EusY7s7lsmdtfs/wCxWDIldUOGlSpyzRtChefsYm/fHwusWiErOK61CCuW8/hhzNmzGlM/OhDGArMKvnsS9GTee3jgViPe7Nivz0FfuHR5Mdju6gEPp9rmuHl8BGuoUc47NYwgVvi0KMH9E2yXYFkgu1UYZPrdsaY2aV+Hm+tHV/qZ6/SgPIrgicCL1prg8aYPwFPAyMrOwCphM2b3c1X+Y1/gyG3ieXRR1fqMtnZcO7pQc5573Ri4WBJrCsCvvoKPvuMMcecwsSJExNi3UfmSB7JH+XZs6PYEUfAaaclHt+0addjMz74zW+939t/f+jQwa07Lf7+LD+0ynP7fUqmUqxrdKJRmP5x2Y7b4BLPyZPdfpuV4DM+Tun3G35777vENgXJ2nmPVsSYxeth4Vr45YlMfPNNOGATzCz57Bdd/Pxtt/mEyo+hlEEdB3HxsIsTjm8s3EiMCm4IAYPhpL1PwsQr7x551PUIcbEty71WDYYd66HHJ/iMj1x/LqP2HFWp310ao/SPdY032dy+3WVjXiqTyZU2ezYmy0dWuHziGoRPP4Vx4xjzlxuY+NBtcAhgIWizeT3/14TDySePW7eBk3/lXc07YAB88ikVJqrGwHPPwa23JL7XJNf1J3rqSddEyO+HkSPh9NN3WT0sjVir3GYJW15U4GdrbUWL/VYApZ9odQHKFC5aa0sXev8buKuyXy6VVFiYPNZt3161a82bh/GZkkSzWFEQpk6DQw9lzNV3MPHu/4ODXSltNBbjiTnjCIeSx7pAAM77k1vFUN7gwbBiRckWUl4MLtYNPzAxfmX54M674OkJJTHzoIPh7LO8e8NJZlCsa4RisTKNyMooLKzatX5agdm+o1SiGRcMuS0GTvolY665k4l3XAUHbwcMxCL8u1sOIZLHVR8+Lhl+ieeWJEM6DeGrtV+V2ValPIvl9Xmvc8xex+AjwGf/82i8G82B1UPI3vNzhnYeyjmDzqFZQJupZ6qGEOsabxntXnt575SbE4CDDqratfx+7wzNmJKOaPvtx5hHX2TMiLGM2QLrac+wQf+r8LLHjE6e+J12mptVzargZikacY04Vq/xfr91azebcORIOPZYOO5Y72aVItU0C+hljNnDGBMATgHeLn2CMWb3Uj+eAMyvw/Flhg4dvNcp+bPcQsyqSJa0Qknm1rMnYx55jjFjT2fMtiy2+VrSf+Ds5J8DDj4k+d6XvzwRWrbwbi5ZLBaDn9e7ztxemjWFEUe4B2qjR8OYMdriSVJKsS4dZGd718YbYMDAql3Ln5XYAbJY8Rr33XdnzINPM+b35zOmKEDM56NTl4of4O3dbu8yay1LG7nHSDo260jAF/B8v1gwGuTzFZ8TjXjfxgIsad6eQbsNolebXrRvpj2eJGVqJdalJNncVZvcepGTA+ed55LL4sfpOQF3YzZ6dNWuNXSo9//iy3c+W7HCtY8Nhjj5561EyWLoUO+pbX82HD8m+Vfuths89E+XJO65JzRv4X2eP9t1mC0vGnONOO66y20Z8PrrrifS1GnJv1OkKqy1EeBC4D1csHnFWvudMeYWY8wJ8dP+Yoz5zhjzFfAX4Kz6GW1qpGWs8/nc/7hzAm6aD9zfW7VKXnuazD77eCecuTlw1FElPxcUwLPPQmEhJ6/fBpA81vnhd6ck/8qWLeEf/4STToI9e0KbNsnPXbcu8Zi18MgjcNNNrmr4rbfgyivg9TeSX0ekKjIx1kGaxrsLLnSlW8VPr7L97mHbuedU7TqdOkHbtonHcwJl1zYFg/Dvf8PWbYxdHyE3Spn9OUvL9mVz+sDTk35lTlYO9x59L6f2P5W9Wu9Fx2beW1IFI0HWbV9HTg5089o+00SJdsznuRbP8fw3z3PLxx7lbSLVUFuxrsZFRlVok1v3Ro1y3SPeecftWn7AAe5YThWn95o3d3sr3Xefm4q01r1OOaXs9invvruz3qE9Gzhqcy7vtwqWuQmbNWso2b4o5xyymOaBPYHkT7jatoU/xnevmfA0vP1WYjlFOOy2Ei1vxgz45tuS7aBiUQhF4eGH3b7ETTyaB4lUlbV2EjCp3LEbSv39GuCauh5XbUjrWDd4MDzwgFuPvmaNq8MfPbpSjdDK8Pvdnpk33QxYV7JmjIubgweXnDdt2s4HcLmE+P3mrTzfqkVCrPP7oozt/yO7teoMNCGZli3gtN+716RJ8ORTiU2DYjHo6bFb1YKFMO3jUrHOuoZsL7zgdoNpX7n+SCIVyqRYB2kc73r3gn/+08W6ZcugTx+3J1Lr1lW7jjFw7XVw7TVuDWgk7B60DR5c9sHazJllJhsuXAZ/7+ESzlmligv91jCcruyd06XCr23ib8JJe5/ESXufxMyVM7lvxn0URYrKnBPwB+jZpicAF10E113r7v0iEdxenFlBGPQUAPN6zYNF8NaCtxjbd2zV/g1EPNRGrEvFipb0bgneqxf89a81v87w4fDkky7whMNutrN9udKFTZtKuqMBV3EXOZv/ymwGQZaP1c1n8usDXuXAmTPoNWMlzGvlEthK1HudcAK89x5Ed5Ss4wzEJxvyWiWeP316mX2Hd8rKgm+/ccMXkSpJ71jXtSucf37Nr9Ovn9uvc+bnbs3nfvu5vUpKKygo06RjHI8R2/wnpjICsrJY1XwWY4e9xbD8mfSfvxjG5cC997nN2HfhiCPcnpoFUbdUANyaz0GDvB+sfT6j7HYtxYyBObOrXsgiIkA6x7uOHeHcXe4jv2vdu7m9NPPz3f1bv36ulX9pW7aUecp/8jzYkQ3jO8Pw3Q0zV1q6bIUz5lqGrv8J88Yf4W9/c2UauzCk0xA6NuvIyq0rd3ap9fv8dGnZhYEdXVlwr73g4Udg0juQP28tKwMfEev5DuSW9B6Z32s+C35ewFiUbEp6SkWy6dUmt3H2AGzZsuwTr/KGDoW5c10zDaApRVzLnWzLzmNbxz1pv2Iuk1rFXCdHgKyQK0W74ALPy23b7nLbYNA9bPv7A+70L+e6CYuxJ8DoY7yHEqhgSUBFa6NEJKnMiXVNm7isL5n99nNPvwrdE61solzEw5wTeJYtPfen7cL/MblFuCTW+YKurOIW73KvoqCLddu2uqVXDzwAzz8Hn9M2Ls4AACAASURBVH/uHqqNHg2//KX3UPzZbkIiVq5viM+4lQ4iUi2ZEe8CATjkkOTv77tvmaUFPgtnzYXfLc7h5QGduXz5j2SHY9AJWBl2nXHvu9/FOw/hWJhZq2axccdG+rbry12j7uLlb19m2rJpGGM4oscR/Haf3+IzJd/Zvh2ceSZ0XPIlj3/xRkKDIZ/xke1TsJP0lYpkszJtcjHGjAPGAXTr1kgXM48Y4Uo7VpfaZTw3h+bHHkHzt98GYowptTH5xFYxKJoOJCabc76AO+5wN0yxGDzxBJx8Mlx+eeWGctRR8US13Oymz+dip4hUmWJdsUGDXNXIwoVlYl3TgwbT9NNPIRYuF+uAnK9cWYYpuyZ00SK4/gb3ViTq/pFHHAEXnJ/0OVwZI0bAW/9xywRKi8W09YlIDewy3mVErNtjD9dUcsaMnRMJ5ATI6dmHMxaugA2u1GxiK0q2hFqz2lV/5OWVudSqrau4+sOrCUaDRGIRjDEM7DCQaw+7lrMHnb3LoQzvMpzH5zyecDzLZNGvQz/yV+QzrEsVm8KJ1IFUNAjaZZtcAGvteGvtEGvtkPbtPeo+G4NAwG2uftppbjPLwfvDlVfCqad6nj5mM/EnZvESjldegb8/QOHE97nzDksoCEVFbv1ROOSa/Cz8vnJDGTjAdWTMDriZgSZNoElTtxxL2wGIVItiXTGfD26+2ZWy9dvbBZwLL4SLL/ZsMORinQFmwbZtLjt84H6ib77FrbfE2LHd7VwQDrl49/HH8PnMhMt46toFzjrbxbqcXMjNdTHv8iuqvmRVRHaqzBYIjT/WgVuKdeGFLs712xvGjXMdyfwlN1M7H64NBYbEIDDXPe2fPNmVpb3yCnd+fBsFwQIKI4WEY2FC0RBfrfuKSYsmeX1rglY5rbhk+CUEfAFy/bnkZOWQ7cvm3MHnsuexbkF7/opK77coUmdSkXbsbJMLrMS1yfXOrjJBbi6ceKJ7lda/P3z9dZk1nQSyGTN8NBNXrYJn74ZZFkJhvvgkhi9yKOUbaoTDMHUK9OlduaGccbprqvbVXLeNytChVe+NJCI7KdaV5ve7+tbyiyIPOwymTi278bo/izH7HMTEgk3w5DkwIwqhEIv86wlGjqZ8rAsWuSrd4QdWbijHHwcHHwRz5rjtooYOhebadk6kJhTvivl8cPjh7lXa0Ue7SYJ4dceYzbiO4L17MxELj50Dn4agKMj6Vn5W/iKScNcdioZ4b/F7jOldwfYEpRzc9WAGdhzIrJWziBFjcKfB5OW4GdS8kXkUTCnQDKeknRrPbCZrk1vT6zY4y5fDf/7jnmJt2ZL4/sUXu4ZCTZq41tq5Oa4M7ZRTGPPaB+5x/kC3xqnVfus993+yMZdwVkXHDi4eHnKIEk2RmlCs+//27jxMqupO4/j3VHXTDaLssisoCnFBZWmMGE1QFEkal8eJTuKI4pLMjFFjfAaXGTWaDWeMW8a4RbOMo3GNRuO44Ba3NKAiiwouqCSyRBYFpNczf/yq6OrqW9XV3bf29/M89VBddfveW93t6z3nnvM7MWvWwiOP2Dojn37a/v05c6yST89qy7qePWHYcPjOd6h9/BXY/gUc0ACToedBnwHBC8l1Nuv69bOiuV/7qhqaIt2lvMNWMXjsMVtP6W/tBrHYRPJ99rHruR6VlnX9+8OFF1L78nIrvLG/Db1tam7CpVjWs7Glc2HXu0dvvjb6axwx+ogdDc24vtPsa93hlEISyoDKoDK5JWX9eptY1L+/ldl2CVMZvIdf/ALmz7e7lg645RaYO9fWGIkbMABuvtkKCK1ZazX8x46Fzz+HTz6hNiFrtvV5nwMnv84rC6a2OY2qajj0K9n9qCKSWsln3aZN8NZbsPPOdhGVPCT2nnvsER+hcfvtcNbZ8PWZrdvstJNV+Fm2zJYmGDHCRnZEIrB4MbUJcysf6vNXJk5eyIsL2t4xqKqGaWnqE4lI9pV03m3ZAkuXWi/8/vu3GRILwNPzbbHzeNbdeaeNWDvttNZtKiut6NmKlbByBQza1aZPRaPw6qvUbmrZMZdzyALoWw/rkur4VEYq+dqocMMufodTpFBo9p73sGqVVZMYNcpCIq65Ga66yhqIztl7gwfba/GVxxcsgCefStgfVuXiZz+zi7LqhAUto9G2a9VB+4ADTtq8nXf6/B/UQIurpMXDm2/WcMghcOABYX1wESkr3sPHH9tE8NGj25Zq9R5uuMGGv8azbpddLOuGD7dtPvjAFq9M7J1vboFbboaDp7RdIN05q0SWXI2sogISKikev7mFD/r8gebJFfiKSpqbYMmSGsaNs8I/IiJd8sknsHmzZV3ysK7f/c6KYMSzrqoKLr8c9o7NUdq8GW64vn3WPfigLYM3dmzb/e29lz0SxfK1drMVD3KT4YotcNeeULe+ksaWRqorqhnaeyjHjUuadiVSYsq7sfnKK3DtdVaVIhq1huHcudbL1dwM3/8+fLCqdfumZrtYmzfPHmANyiDNLfDUU1alJ51eveyCLGk+52Xb3+LMGV/muV4zeWVDHbNn1zFyRE2bm6oiIhlZtszWftu61Rp80Sicey5MnWoNzSuvhIWLWrdvaob1f7ciQLfcYhdl990XUHsXe+2BB6xoRkcOP7zdfM4Ltn3IqYes4JndTufPa+v4x2/VscceNVZPSESkMz780HJrw4bWzvzT57SOvrjlFnj0sdbtm5ptzuXll8Nvf2uNxEceSZ11d99txYE6MmPGjvmcO4oHbYnQb8gIlhy6N2+uq2a/QfsxZcQUoi6adlddpbmbUijKt7H52J9sWGtcPHB++EO47XZYttRCK5nHhtRu3GiThDalGaqwbl1m5/L978PFF1s4em+P8eMZNns636qEb1HDH9+pAxLH4CtARCQDdXXwox+1XjzF7yxeey2MHGkN0NdfD/7eDRvg/fdtofOg+Zlx69dndi5nnGkjST76qPW13Xdn4L+czDd7wTeVdSLSVW+/bTcMWmJhF8+6O++wstW77gqPPx78vY2Ntoh5zeT0124bN2Z2Lscfb+fz5pvWWecc9O/PyedexU7rVnLwiPiGi8hGxqlYkBSS8mxsfvYZ3H5b8HvNzfD8c3YnoCXFbG6wOv39+tm8pudfCN6mJsP/wPv1g5tusvkD69bbfM7Ro9tsUju2dV+tF2MKEBFJo7HRlmMKirLGRitoVlHRtkp2Iu8t6wAOPBCWvxW83aRJmZ1Pr57wX/9l63OuXm3zOZPmwSdmHcTzTlknIml4byPOgq7b6hvgDw/DQQcGFl8E7Nrvi232fNIkeO754O0OODCz86mshMsus+kH770Puw6yUWyRCLX9cpNxanBKoQhjnc3is3gxKcejNjVbz1WPHqm/v7oahgyx56edBhUBQyAGD24/XymdSATGj4cjj2jX0EzWejGmamMiksbKlakvrlq83a2srCTlmFXvrWo2WHGMqoBc7L0THHFE5ufkHIwbZ6Vjx41LncUxlnfKOhFJY+06m2uZysYNlnXRFENWYyPKACvfv8vO7beprIBv/kPnzmv0aLuuGz8+cA1iyG7GxavTiuRTeTY2o9HUgeOwQkFHHRV8YQVwwQWtoTFwoN05GDbUvjcasWpk1/68w4uoHerrrZc/fgchA2pwikiHotH0ObTHHjaPsrIy+P0zz2wtrtGzpxUR2nMPy7qIg3Fj4cYbAwudBWpshL/+1YbudoIanCKSVkUHWTd6tBX3SdHgo7bWRpmB5eaNN8J++1rOOWDU7nD99dC7d2bn09xsy6UELYUXdHhlnJSw8hxGO2FC6lDywK9+ZZPIa2ttonhLi/V6RSJw/vnth4yNGWPbb/vCer5SXbi1O5aH//kfW8MpErHjHHMMnH566kBMUDtW85tEJI299rIiZNvrg99/4EGYNg1mz7bS/mA5BJZDM2e23X7YMLjuOqto61znFu99+GG46y573tQEhx0G//qvGedla94lUt6JCNbxP2KEDVsNGszxwgt2TXf++TZfHaxBCDDrWJhzetvt+/eHn/7UbgZ433ZlgY48/7xdEzY22jEOOshuUuyUfgHgbGachtJKPpVnY7O62gry/PjHNpY/2fbt8MwzdgF29AxY/IZdsE2enD5wevXs3Hk8/LA9Es/h8cctkE4+OaNdaH6TiKQUicC//7s9tgWMnGhqtAw680yrTLtokd2lnDw5fQ9+Zy68AF56yZYbSMy6F1+0Owjf+17Gu9HcdRFJae5cmHtRcOHGhgarJHvJJXDAAbZsXUsLTJwE/dIMNe1MhxrA8uV2VzQx615/3eaTXnllh9+ejYzT3E3Jt/IcRgvW0zRnjt2JTFbfYAUsAIYMhilTbMmTn/wE7rgD1q619xYuhHPOsapjZ50Fzz3XuXN44MH2jd36Brv46yINxRCRNvbaCy68MHhaQGMTrFhhz/v3h0MOgY2bbGrAL3/ZWjV2+XL4wQ/ghBNsnvof/5h6LmiQ2BIAbdQ3WGZu396VT6WpBCLS1rBhcOUPoUfAaAmPVdYG2Hln61xrbITrr4PrrocVK+29Vausc+6EE+Db37YGavwOaCYeDLiua2yyopOZVu2OCTPj4nM361YrLyX3yvPOZtzo0daLn7DmG2AXZaNG2fM1a2z4Q309NDTCkiVWwfHb327bU79mLfziF7bd0UdndvzPU4zl37LVetwyGEobRMPNRKSNkbsFNw6jEdh9d3u+ebMNMfv8c8u1aATmz4dTT7X15+JZ9+kG+M1vbPtTTsns+Bs2BL/uHGzZ0vk7pTGaSiAibQwenPq9EbH1RurrrfNszRrLtYiDF/9sI8ruva+1fkbj57aG8Jo1tkRdJlItm1JRYTk4aFDmn4VwM053OCVfSruxuX49/O//wmuv2ZCwY4+F6dNb52uOG2c9YR991NrgdFgoTJ9uX99xhxWziJfTbmq2x69/bf8mqm+w7YcO3VHiOq1Ro6wkdrKRI7rc0IzTcDORMvLZZ3DPPfDKK1ZJe8YMmDWrtRDakMFWsn/xG9ZpFldZaVVmAe67zxqQ8SxsbrF16u64o/3SKPUN1oO/114wcWLHBYK+9CV49dX2c6mqqlqLcnSRsk6kjGzfDvffD88+a19PmwYnntg63LVXLzhyOsx/uu0dxqoecNJJ9vzJJ1sbmmDXd/UNVkMjWX2DzfccP96q1HY0rHb8eBsJl3x92NxsnX5dEGbGxRucIrlUusNoN22yXvpnn4UNG+Gjj+HWW+H221u3cc4WO59ysFUyi0asATrvaujTx7Z5Y3Hwuk3JQRK37Qvb51lnWZilc9ZZFoDJtYpGjgyeX9VFbYdiJPeQiUhRq6+HC35gIy7+/in87RMrxDNvXtvt5v6bXZj1iC11MnqUzSEaPtzer6trP8oDUq/B2dhka2bOng3vvZf+HE85xe5eJi+xMnKk3UkNibJOpIS1tNicy4cesjXJ1623Tq9LLmktbAZw9llWDKhnLHOGDoGLLrJOL4CXXw6u19HcEpx3Tc02reCfTrWl89I5/nhr8EaTLq+HDEk9mq0TNH1AilHpNjYffdSGQiQGR32DXZAlTh7v3dsuwu6/33r2r74adk/ofaru5ORwgC+2w9//DlddlX67ffe1hmlyT9mCBXDJxW3Ds5tqx9bseBgFlUhJeO452LypbUOxvsFGdHz4UetrVVVW/fXeey3vbrih9eIL7AKps7bXw2efw+WXp5/XtNtucM01Nlcq0Tvv2HC2+hTVcrtAWSdSol5/3ZaJSxyd0dBodxITG4HRqHWC3XOPXdfdemvbVQQyXb4kUX2DXVP+6Efpl24aMMAqdu+6a9sbCR9/bFOy0q0FmiFlmxSb0m1sLlkS3EtfWWkTwJNFo8El+GfOTL3eZjot3goJrV6dfrtPP22/DEtjk63P1FEPWhcpqERKyLJlwUubOAfvrmz/eqqsq63tWuca2AXf0qXpt9m6tX2jsqnZhgD/+cWuHbcDyjqRErJyZXBBsfp6ey9ZJGLTCpJ9/etdu64Dy9W//CX9Ni0tdm2XOCiuxdu5/+lPXTtuku6M4ug7ra8KBUlOlW5jc9iw9sMYwNZ3Gzgw8/2ceCJMrgmuWtuRSLR1onkq771nd0KTNTTAB6s6f8wM6SJMpEQMGxacTy7SuWIU06bZXPWuZJ2j46x7//3gIkXb62Hlis4fM0PKOpESMXBQcDGxqqrOZd2BB9r8za5kXUtL8DVbolWrgjv0Ghrh7bc7f8wUujOKQw1OyaXSbWwee2z7ohWVFTBmTGtFskxUVMBXDk39fmUF7POl4FLb0YhVvA3S0GDzSd9/PzjwelRZUY8s0vwmkRIwfXr7rItGoG8fK1SWKeds6ZNUxckizgoCBd0RaGpKfaymJpsjtWRJ8NSAqh6t80azRFknUgIOnWqNuMTBYA577ZBDOrevmhqoqGxfMyNuxPDgrPMeJhwU/D0tLTZ94dVXg6cGVERtnnoWqMEphaxbjU3n3H865952zr3pnHvIOZdmZdwcGzUKLr4YBvS3wKisgAkTbP2kzqivh2uvDR6SWxG1QkIXXGCTv+ND0KIRO+b3vhdcpXHDBvjud23C+aLX2u87GoGdetnC6lmm+U0iHSvorBswwAr9DBtqnV6VFTYX86c/7VxV65YWm7MeVDgjGoGddoILvm8NznjWRZxl3Zw5wfOgtm2zQm3XXQcvvmQNz0TxC8Vp0zI/zy5S1olkpmDzrroafvYz2GMPy7nKCns+b17HVWKTXXutjcZIHmwRcVZY6IILrEEazzqHZd2sWbbiQLLGRviP/7Dze3p+8Bz2igr4Rm3nzrMT1OCUQtXdpU+eAi723jc55+YBFwNzu39aIZk4Ee6808bO9+xpF0udtWxZ6gu26mo48R+gb1/4+c/h+edh0SK7+DvmmNQ9WLfdbg3O5KpnDjvWfvvBeecFD8PIIq1ZJ5JSYWfduHFw882WKz16tC/Ek4mPPw6eDwU2z/OEE6B/fyuQ8fLL9ujd29YVHjMm+Pvuvdfmn8c71BIv7KIR2HNPy7quFOzoBmWdSFqFm3cjR1rnVbzQY98utIO3bLEl74I4B9/4hhX4ufBCWLgIXnjeGopHHpl6BMeTT1nBs3hnXXLWDR8B3zsnJyPWlG1SaLrV2PTeP5nw5avAid07nSxwrnNzNJNFo+17vuK2bIVf3wkPPmCVFo86yh4dWVAXXF47EoG777aGcZ5ozTqR9oom6wYM6Pr3R6OpK2A3NFplx4cesuVOvvIVe3TkhRdSFGqrgJtushEheaKsEwlWFHnXlUZmXLoRH80t8Mgj8Ohj8JMfQ81ke3TkmfnBo0J6VsNll3VuSkM3Kduk0IQ5Z3MO8HiI+ysM++4bXGgobnu93U343e8y32dy9dnE14Mmv+eJ5jmJBCrNrBs+PH1jtb7B7gjcdFPm+0yVddC1pVayRFknklLp5V2vXjB2bOpru/gyJ9dck/k+o9HU73VlVF1IMsk2DaWVbOuwsemce9o5tzTgcWzCNpcCTcBdafZztnNuoXNu4fr13V9nKGcqKmwcfs+e1kMVpKkZXnkl830eemj7okDRCEyZkv7iLA80z0nKRdlnnXNwyaWwy86pR1e0+NSFfoJMn96+yEbE2TyrXXbp3vmGTFkn5SSMvCvarAObk9m/f/qRZGvX2s2ETBx9dPDSUb17Ww2RPMok29TglGzqsLHpvT/Se79fwONhAOfcbOAbwLe9D6prv2M/t3rvJ3nvJw0a1Ce8T5AL++wDv/k1nHVW6p6waCdGJJ9xBgwdZo3XygoLu8GD4Z//OZTTzRZdhEkpU9YBu+9m89zPOzf1sgCRSOadYiec0FpQKJ51ffrYXKgCpqyTUhdG3hV11g0aBLfdBhf+wDrYUgkq8hjkq1+FSZNaC1L2rIbeO8GllxbUTQQ1OCUfujVn0zk3A5s0frj3fls4p1Sgeva0XvqXXoI33mg757JHJRx5ROb76t0bbrzB9vPRRzZ8bcKE9MMwCkTbyeeaAyDloayyrkcPmDrV8mn+/LZzLiuitsRAphdPPXrAT34Cy5fDu+/a/PmampwXP+sKZZ2Uq7LJu2jU8ui44+D3v2875zIasY6yTEdgRKMwd67l3LJl1ql28MEFNTUqLl229Z3Wl7pn6qgZocyT8HS3Gu0vgCrgKWcXH69677/b7bMqZOedBxddBBs3QUuzXXSNGQMnn9y5/UQi1sCcMCE755lFqnYmZaj8su700+G992D1ahs2G4lYhcbvfKdz+3HO5r7vu292zjOLlHVSpsor7447zhqIS5fa15Go3ZXsygiMMWNSV+cuIMo2yaXuVqMt/P+iwtavn62PuXgxrFljc4/23rughknkgqqdSTkpy6zr1csKZCxfDh9+CCNGwP77K+uUdVLiyi7vKivhiivsruTKlTbE9qCDimK0WXco2yRXwqxGWz4iEQuiY46ximZldvGVTPObREpU/K7kzJkwfryyTlknUrrGjLHrukmTSr6hmSw52+pW12n+poRGjU0JhZYOEJFyoKwTkVIUz7a+01bQd9oKYKUanBKK7s7ZFNlBQzJEpBwkZh3E805ZJyLFrc11HHVsemYldatRwSDpFt3ZlKxQ77+IlAvLuzqUdyJSKmrH1tB3mkd3OKW7dGczWzZugoULwEWgZnLBLWCeC+r9FykDW7bAggXQ2AgTJ8KAAfk+o7zQyA6REldfD3V1sHWrzWEfNizfZ5R1tWNrdIdTuk2NzWx48km45RYrJATwy5vg3HPh8MPze1551lpqW2ElUhLqFsDV8yzrWlrAezjlFDj++HyfWV5pjU6REvP221axtsXbsnfeWzGhM84o+cJpanBKd2kYbdjWrLWGZkMjbK+3R0Mj3HgjbNyY77PLu9bhZiJS1LZutYZmfQN8sd3+bWiEu+6CDz7I99nlnSrXipSI5ma46irYug2++KI16554Al57Ld9nlxMaUivdocZm2F560Xq8grz8cm7PpUBpfpNICViwwBY/T9bUBM8+l/PTKUSauy5SApYvh8am9q9vr7eRbGVCDU7pKg2jDVtjow0nS9bSYu8JoPlNIkWvqQl8qqxryP35FChlnUiRa2qCVCNly+y6LnlIbZyG1ko6urMZtilToCKgDe8c1Og/xiDq/RcpQhMmBHesVVXB1Km5P58ioKwTKUL77BOcddVVZVmLI36H09bj7AugO52SlhqbYRs9GmZ+Hap6WE9YxNnzE08si8plXVU7tmbHwyi4RApa//5w2mmWb9GI5V11FRx2GOy7b77PrmAp60SKTFUVnH++ZV1l7GZCz2rLuUMPze+55UlifvWdtgINrZV0NIw2G+acDodOhRdfBBwcfhjsuWe+z6poqJKjSJGorYXxB8Dzz9myAIccYncBSrw6Y1jaZl2cMk+k4Eydatdxzzxjyz1NnAgHHdS66kAZajNFQNVqJQ01NrNl773tIV2iBqdIkdh9Nzj11HyfRdHSnE6RIjFkCHzrW/k+i4Kk5VEknfLtkpGCp/lNIlJONLRWRIqVqtVKKmpsSkHT/CYRKSfKOhEpVmpwShA1NqVo6E6niJQDZZ2IFCs1OCVZKI1N59yFzjnvnBsYxv5EUtGdTsk35Z3kgrJO8k1ZJ12lBqck6nZj0zk3EpgOfNT90xHJnC7CJNeUd5IPyjrJNWWddJcanBIXxp3Na4F/A3wI+xLpFA03kxxT3kletN7lVNZJTijrpNvU4BTo5tInzrlZwF+994tdB+uqOefOBs4G2G23Qd05rEgbWjpAciHTvFPWSTbF805ZJ9mirJMwJS+LEqflUcpHh41N59zTwJCAty4FLgGOyuRA3vtbgVsBJk3aSz1lkhVan1O6I4y8U9ZJLrTNujhlnmRGWSe5FG9wwgoANj3jtB5nGemwsem9PzLodefc/sBoIN7zNQJ4zTlX471fE+pZinSCGpzSVco7KSYa1SFdpayTXGuTVwl3OtXgLH1dnrPpvV/ivd/Vez/Kez8KWA1MUBhJIdBcTgmT8k4KnYoISRiUdZILmstZXrTOppQsLR0gIuVEWScixUINzvIRWmMz1gv297D2JxIm3emUMCnvpFAp6yRMyjrJJjU4y0O3qtGKFBPNbxKRcpCYdRDPO2WdiBSe5Gq1msNZejSMVsqSev9FpFxofU4RKWS6w1nadGdTypZ6/0WkXLQf2aGsE5HCoTucpUt3NkViWnv/RURKV/s7nco9Ecm/5Duc8YcUNzU2RRKowSki5UDVukWkEMUbnH2nraDvtBVoaG3xU2NTJInmN4lIOVGDU0QKSWJnmOZyFj81NkUCtO31V8CJSGlLnsMuIlII1OAsfnkpELRo0btbnJv1Tj6ODQwE8rVmlI5dHsfN1bF3z/L+O+ScmwFcD0SB2733P0t6vwr4LTAR+BQ4yXu/KtfnmS/KOh27DI6trENZp6zTsXXsUJRk1uWrGu073vtJ+Tiwc26hjl0exy7Hz5xLzrko8N/AdGA1sMA594j3fnnCZmcAG733Y5xzJwPzgJNyf7Z5o6zTsUv62Mq6HZR1Zfa3r2Pr2KUmW1mnYbQi0lU1wLve+/e99w3APcCxSdscC/wm9vx+4AjnnMvhOYqIdJeyTkTKQVayTutsipSRRYvefcK5WQMz3LzaObcw4etbvfe3Jnw9HPg44evVwJSkfezYxnvf5JzbDAwgf0NgRKQMKOtEpBwUQ9blq7F5a8eb6Ng6dtEeN9/HTsl7PyPE3QX1ZPkubFPKyvVvUMcun2Mr6zLfppSV49++jq1j510xZJ3zvpyyUETC4pz7MnCF9/7o2NcXA3jvf5qwzROxbV5xzlUAa4BBXsEjIkVCWSci5SBbWac5myLSVQuAvZxzo51zPYCTgUeStnkEmB17fiLwjC6+RKTIKOtEpBxkJety0th0zl3hnPurc+6N2GNmiu1mOOfecc6965y7KKRj/6dz7m3n3JvOf2VrNgAABZdJREFUuYecc31TbLfKObckdn4Lg7bJ8HhpP4Nzrso59/vY+39xzo3q6rGS9jvSOfesc+4t59wy59x5Adt81Tm3OeH3cFkYx47tO+3Pz5kbYp/7TefchJCOOzbh87zhnPvMOXd+0jahfW7n3B3OuXXOuaUJr/V3zj3lnFsZ+7dfiu+dHdtmpXNudtA2xcR73wScAzwBvAXc671f5py70jk3K7bZr4ABzrl3gQuAUP67LlTllHWxfeU87/KddbH95zzvlHX5o6xrT1nX7n1d2xVp1sX2p7wji1nnvc/6A7gCuLCDbaLAe8AeQA9gMbBPCMc+CqiIPZ8HzEux3SpgYDeP1eFnAP4FuDn2/GTg9yH9jIcCE2LPdwZWBBz7q8CjWfodp/35ATOBx7Gx3gcDf8nCOUSx2/m7Z+tzA4cBE4ClCa9dDVwUe35R0N8Y0B94P/Zvv9jzftn4XeiRv0e5ZF2mnyMbeZfvrMvkZ5jtvFPW6ZHvh7JO13ax94s+62L7U95l8VFIw2gzKbfbad77J7211AFeBUZ0d59p5K08uvf+E+/9a7Hnn2M9EsO7u98QHQv81ptXgb7OuaEhH+MI4D3v/Ych73cH7/0LwIaklxN/p78Bjgv41qOBp7z3G7z3G4GngDAndUvxKIWsgzzlXRFkHWQ/75R1UgyUdd1UBHlX9FkHyrtsy2Vj85zYLfY7UtyKDiq3G/Z/UHOwHpggHnjSObfIOXd2F/efyWdoUzIYiJcMDk1s+MZBwF8C3v6yc26xc+5x59y+IR62o59fLn6/JwN3p3gvW58bYLD3/hOw/zEAuwZsk4vPL4WhHLIOCiDv8pR1kP+8U9ZJIVDWBWyja7uSyDpQ3oUmtKVPnHNPA0MC3roU+CVwFfZHexVwDRYQbXYR8L0ZTa5Pd2zv/cOxbS4FmoC7Uuxmqvf+b865XYGnnHNvx3o6OiPv5dGdc72BB4DzvfefJb39GjYUYUtsfsUfgL1COnRHP79sf+4ewCzg4oC3s/m5M1XuZfFLhrKu9XQCXstZ3uUx6yCPeaesk1xR1rWeTsBruraLnVrA95RL1oHyLiOhNTa990dmsp1z7jbg0YC3VgMjE74eAfwtjGPHJux+AzjCex/4R+C9/1vs33XOuYewYROdDaVMPkN8m9XOSgb3of2t+y5xzlViYXSX9/7B5PcTA8p7/yfn3E3OuYHe+24vOp3Bz6/Lv98MHQO85r1fG3BuWfvcMWudc0O995/Eho+sC9hmNTbHIG4E8FxIx5ccUtbtkLe8y2fWxfaZz7xT1klOKOt20LVd+WUdKO9Ck6tqtInjt48HlgZslkm53a4cewYwF5jlvd+WYpudnHM7x59jk8+DzrEjeSuPHpsb8CvgLe/9z1NsMyQ+h8A5V4P9/j8N4diZ/PweAU515mBgc3x4Qkj+kRRDLbL1uRMk/k5nAw8HbPMEcJRzrl9suNFRsdekhJRR1kGe8i6fWRfbX77zTlkneaes07VdTKlmHSjvwuNzUIUI+B2wBHgT++UNjb0+DPhTwnYzsUpb72FDJcI49rvYeOo3Yo+bk4+NVRhbHHss686xgz4DcCUWigDVwH2x86oD9gjpcx6K3bp/M+GzzgS+C3w3ts05sc+3GJtUf0hIxw78+SUd2wH/Hfu5LAEmhfj31QsLmT4Jr2Xlc2PB9wnQiPVonYHNy5gPrIz92z+27STg9oTvnRP7vb8LnB7W59ejcB7llHWpPke28y6fWZfuZ5iLvFPW6VEoD2Wdru1iz4s+62L7U95l8eFiPygRERERERGR0BTS0iciIiIiIiJSItTYFBERERERkdCpsSkiIiIiIiKhU2NTREREREREQqfGpoiIiIiIiIROjU0REREREREJnRqbIiIiIiIiEjo1NkVERERERCR0/w/jRHF8lOLlGAAAAABJRU5ErkJggg==\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "d20927d137ec4648a1d0e88994a1c035": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "d3566a2a1b9043db9e259fbfdb52cc38": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "d5cf8033fd92451cbbf5ef4da80c0bc7": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "d618bcf1c24d4ed9ba20c7d266705fab": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_565249dc181546668563163c2767351b",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "d6ce7c10d396497e9467c717e273fcdc": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_d5cf8033fd92451cbbf5ef4da80c0bc7",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "d7725669caf24a44a05d47d8c68e60c5": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_0f53532b68474cd6ae0f17c39c3f76cc",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
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      }
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        "IPY_MODEL_ea1dfdb4a7384ba38bd218221db5b0f8"
       ],
       "layout": "IPY_MODEL_a629bf55a2e64bc8b92e524b34707d2e"
      }
     },
     "daf014586b404fe69ae87893242ca3b3": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": "initial"
      }
     },
     "db2d17263dc44efe8653a0a33a24e71f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "dd329244bafa4644a38f7c1d87a6c565": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "description_width": ""
      }
     },
     "e0cfe38baaeb48449c99a2c79544531e": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_9c7dc3d78d854a8eae3eaadf77f11984",
       "outputs": [
        {
         "ename": "KeyError",
         "evalue": "'LogisticRegression'",
         "output_type": "error",
         "traceback": [
          "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
          "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
          "\u001b[1;32m~\\AppData\\Local\\Continuum\\anaconda3\\envs\\bzan\\lib\\site-packages\\ipywidgets\\widgets\\interaction.py\u001b[0m in \u001b[0;36mupdate\u001b[1;34m(self, *args)\u001b[0m\n\u001b[0;32m    249\u001b[0m                     \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mwidget\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_interact_value\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    250\u001b[0m                     \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mwidget\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_kwarg\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 251\u001b[1;33m                 \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    252\u001b[0m                 \u001b[0mshow_inline_matplotlib_plots\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    253\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mauto_display\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mresult\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
          "\u001b[1;32m<ipython-input-11-62da58c78f31>\u001b[0m in \u001b[0;36mclassify\u001b[1;34m(method)\u001b[0m\n\u001b[0;32m     21\u001b[0m         \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m         \u001b[0mx_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mt_train\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 23\u001b[1;33m         \u001b[0mt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mglobals\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mfuncs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mmethod\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mt_train\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_test\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     24\u001b[0m         \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_train\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx_train\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mc\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mt_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcmap\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mmatplotlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcolors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mListedColormap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'red'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'green'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'blue'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     25\u001b[0m         plt.contourf(x1_test, x2_test, t.reshape(100, 100), alpha=0.3, levels=np.array([0., 0.5, 1.5, 2.]),\n",
          "\u001b[1;31mKeyError\u001b[0m: 'LogisticRegression'"
         ]
        }
       ]
      }
     },
     "e1682900ee7743908a81dae07815dbef": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_3ad7634ea51a46d78308615f57322e72",
       "outputs": [
        {
         "data": {
          "image/png": 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\n",
          "text/plain": "<Figure size 1152x288 with 6 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "e2752df1babb4ab8b4f7e847f148ccf9": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "e36f3b3f8b9f45ff89157ec8227159f7": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_9a42e6ff96ec48ff834108b49f28ff78",
        "IPY_MODEL_d618bcf1c24d4ed9ba20c7d266705fab"
       ],
       "layout": "IPY_MODEL_837d9362f68a45c4ad5abf299c7a2989"
      }
     },
     "e4dc3bd2ebd843088faf13eadd0a6897": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "e5cce49e0a304a0d9f534eec13b55b0e": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.2.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "ea1dfdb4a7384ba38bd218221db5b0f8": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_40c053fc5899440587b0b7d65f859fed",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "ebba467e624948489969c5305de8df80": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_7dc1822ecefc4a45937704b3b86cd728",
        "IPY_MODEL_4e28cc41091344a987ae9ae665cd5084"
       ],
       "layout": "IPY_MODEL_8f86ac7fc24c4f55947716c91ba1678d"
      }
     },
     "ebc6bf9b70af4286a71dea674f4b15bd": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_99bf2925deeb4b969e9c82ceb28ec716",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<Figure size 1440x288 with 5 Axes>"
         },
         "metadata": {
          "needs_background": "light"
         },
         "output_type": "display_data"
        }
       ]
      }
     },
     "ed3bf85fb2b647f9a4507f4859b000ec": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DropdownModel",
      "state": {
       "_options_labels": [
        "User Logistic",
        "Logistic Regression",
        "Linear Discriminant Analysis",
        "Quadratic Discriminant Analysis",
        "Bayesian Ridge"
       ],
       "description": "Methods:",
       "index": 0,
       "layout": "IPY_MODEL_694ec7b2b65f40628c52e249f903f29f",
       "style": "IPY_MODEL_92c43cadf302459293ec47ccc087a18d"
      }
     },
     "ed68b78803094750b9edf2ee60be36f3": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "IntTextModel",
      "state": {
       "description": "Index:",
       "layout": "IPY_MODEL_39739275238947a3ad2811f7ce817a24",
       "step": 1,
       "style": "IPY_MODEL_3b57245722804607beb23a835a5c2dac",
       "value": 7
      }
     },
     "f0bab0563ff643b0b0acd526466cea7e": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
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