TeoriaInformacao.ipynb

{
    "cells": [
        {
            "cell_type": "code",
            "execution_count": 1,
            "source": [
                "import numpy as np\r\n",
                "import matplotlib.pyplot as plt"
            ],
            "outputs": [],
            "metadata": {}
        },
        {
            "cell_type": "markdown",
            "source": [
                "**DEFINIÇÂO:** A entropia H(x) de uma variável aleatória discreta X é definida da seguinte maneira\r\n",
                "\r\n",
                "$$\r\n",
                "H(X) = - \\sum_{x \\in X}{p(x)}log_{2}p(x)\r\n",
                "$$\r\n",
                "\r\n",
                "A entropia H(x) é dado por um número real maior ou igual à zero. Esse número é aproximadamente a esperança da quantidade de perguntas binárias para decobrir o valor de x do resultado mais provável até o menos provável. \r\n",
                "\r\n",
                "Ex:\r\n",
                "    P(x = 0) = 0.05\r\n",
                "    P(x = 1) = 0.5\r\n",
                "    P(x = 2) = 0.3\r\n",
                "    P(x = 3) = 0.15\r\n",
                "\r\n",
                "A esperança do número de perguntas é cotado por baixo pela entropia H(x) e por cima pela entropia H(x) + 1."
            ],
            "metadata": {}
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "source": [
                "rep = 1000\r\n",
                "conjunto = 4\r\n",
                "prob = [0.05, 0.5, 0.3, 0.15]\r\n",
                "\r\n",
                "escolha = np.random.choice(conjunto, rep, prob)\r\n",
                "\r\n",
                "perguntas = np.zeros(rep)\r\n",
                "\r\n",
                "for i in range(rep):\r\n",
                "    if escolha[i] == 1:\r\n",
                "        perguntas[i] = 1\r\n",
                "    elif escolha[i] == 2:\r\n",
                "        perguntas[i] = 2\r\n",
                "    else:\r\n",
                "        perguntas[i] = 3\r\n",
                "\r\n",
                "\r\n",
                "print(\"H =\",sum(prob*(-np.log2(prob))), \" < Perguntas =\", np.mean(perguntas), \"< H + 1 =\",sum(prob*(-np.log2(prob)))+1)"
            ],
            "outputs": [
                {
                    "output_type": "stream",
                    "name": "stdout",
                    "text": [
                        "H aq1= 1.647730922119161  < Perguntas = 2.248 < H + 1 = 2.6477309221191607\n"
                    ]
                }
            ],
            "metadata": {}
        },
        {
            "cell_type": "markdown",
            "source": [
                "A entropia H(x) é convexa em P e atinge valor máximo no caso da distribuição uniforme."
            ],
            "metadata": {}
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "source": [
                "prob = np.arange(1, 100)/100\r\n",
                "prob2 = np.ones(99) - prob\r\n",
                "\r\n",
                "H = - (prob * np.log2(prob) + prob2 * np.log2(prob2))\r\n",
                "\r\n",
                "plt.plot(prob, H)"
            ],
            "outputs": [
                {
                    "output_type": "execute_result",
                    "data": {
                        "text/plain": [
                            "[<matplotlib.lines.Line2D at 0x189bbb084c8>]"
                        ]
                    },
                    "metadata": {},
                    "execution_count": 3
                },
                {
                    "output_type": "display_data",
                    "data": {
                        "text/plain": [
                            "<Figure size 432x288 with 1 Axes>"
                        ],
                        "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<svg height=\"248.518125pt\" version=\"1.1\" viewBox=\"0 0 372.103125 248.518125\" width=\"372.103125pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-08-25T15:04:40.407195</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.4.2, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n </defs>\r\n <g id=\"figure_1\">\r\n  <g id=\"patch_1\">\r\n   <path d=\"M 0 248.518125 \r\nL 372.103125 248.518125 \r\nL 372.103125 0 \r\nL 0 0 \r\nz\r\n\" style=\"fill:none;\"/>\r\n  </g>\r\n  <g id=\"axes_1\">\r\n   <g id=\"patch_2\">\r\n    <path d=\"M 30.103125 224.64 \r\nL 364.903125 224.64 \r\nL 364.903125 7.2 \r\nL 30.103125 7.2 \r\nz\r\n\" style=\"fill:#ffffff;\"/>\r\n   </g>\r\n   <g id=\"matplotlib.axis_1\">\r\n    <g id=\"xtick_1\">\r\n     <g id=\"line2d_1\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL 0 3.5 \r\n\" id=\"m2e66667aaa\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.215555\" xlink:href=\"#m2e66667aaa\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_1\">\r\n      <!-- 0.0 -->\r\n      <g transform=\"translate(34.263993 239.238438)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2034 4250 \r\nQ 1547 4250 1301 3770 \r\nQ 1056 3291 1056 2328 \r\nQ 1056 1369 1301 889 \r\nQ 1547 409 2034 409 \r\nQ 2525 409 2770 889 \r\nQ 3016 1369 3016 2328 \r\nQ 3016 3291 2770 3770 \r\nQ 2525 4250 2034 4250 \r\nz\r\nM 2034 4750 \r\nQ 2819 4750 3233 4129 \r\nQ 3647 3509 3647 2328 \r\nQ 3647 1150 3233 529 \r\nQ 2819 -91 2034 -91 \r\nQ 1250 -91 836 529 \r\nQ 422 1150 422 2328 \r\nQ 422 3509 836 4129 \r\nQ 1250 4750 2034 4750 \r\nz\r\n\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\r\n        <path d=\"M 684 794 \r\nL 1344 794 \r\nL 1344 0 \r\nL 684 0 \r\nL 684 794 \r\nz\r\n\" id=\"DejaVuSans-2e\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_2\">\r\n     <g id=\"line2d_2\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"104.330583\" xlink:href=\"#m2e66667aaa\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_2\">\r\n      <!-- 0.2 -->\r\n      <g transform=\"translate(96.379021 239.238438)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 1228 531 \r\nL 3431 531 \r\nL 3431 0 \r\nL 469 0 \r\nL 469 531 \r\nQ 828 903 1448 1529 \r\nQ 2069 2156 2228 2338 \r\nQ 2531 2678 2651 2914 \r\nQ 2772 3150 2772 3378 \r\nQ 2772 3750 2511 3984 \r\nQ 2250 4219 1831 4219 \r\nQ 1534 4219 1204 4116 \r\nQ 875 4013 500 3803 \r\nL 500 4441 \r\nQ 881 4594 1212 4672 \r\nQ 1544 4750 1819 4750 \r\nQ 2544 4750 2975 4387 \r\nQ 3406 4025 3406 3419 \r\nQ 3406 3131 3298 2873 \r\nQ 3191 2616 2906 2266 \r\nQ 2828 2175 2409 1742 \r\nQ 1991 1309 1228 531 \r\nz\r\n\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-32\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_3\">\r\n     <g id=\"line2d_3\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"166.445611\" xlink:href=\"#m2e66667aaa\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_3\">\r\n      <!-- 0.4 -->\r\n      <g transform=\"translate(158.494049 239.238438)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2419 4116 \r\nL 825 1625 \r\nL 2419 1625 \r\nL 2419 4116 \r\nz\r\nM 2253 4666 \r\nL 3047 4666 \r\nL 3047 1625 \r\nL 3713 1625 \r\nL 3713 1100 \r\nL 3047 1100 \r\nL 3047 0 \r\nL 2419 0 \r\nL 2419 1100 \r\nL 313 1100 \r\nL 313 1709 \r\nL 2253 4666 \r\nz\r\n\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-34\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_4\">\r\n     <g id=\"line2d_4\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"228.560639\" xlink:href=\"#m2e66667aaa\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_4\">\r\n      <!-- 0.6 -->\r\n      <g transform=\"translate(220.609076 239.238438)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2113 2584 \r\nQ 1688 2584 1439 2293 \r\nQ 1191 2003 1191 1497 \r\nQ 1191 994 1439 701 \r\nQ 1688 409 2113 409 \r\nQ 2538 409 2786 701 \r\nQ 3034 994 3034 1497 \r\nQ 3034 2003 2786 2293 \r\nQ 2538 2584 2113 2584 \r\nz\r\nM 3366 4563 \r\nL 3366 3988 \r\nQ 3128 4100 2886 4159 \r\nQ 2644 4219 2406 4219 \r\nQ 1781 4219 1451 3797 \r\nQ 1122 3375 1075 2522 \r\nQ 1259 2794 1537 2939 \r\nQ 1816 3084 2150 3084 \r\nQ 2853 3084 3261 2657 \r\nQ 3669 2231 3669 1497 \r\nQ 3669 778 3244 343 \r\nQ 2819 -91 2113 -91 \r\nQ 1303 -91 875 529 \r\nQ 447 1150 447 2328 \r\nQ 447 3434 972 4092 \r\nQ 1497 4750 2381 4750 \r\nQ 2619 4750 2861 4703 \r\nQ 3103 4656 3366 4563 \r\nz\r\n\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-36\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_5\">\r\n     <g id=\"line2d_5\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"290.675667\" xlink:href=\"#m2e66667aaa\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_5\">\r\n      <!-- 0.8 -->\r\n      <g transform=\"translate(282.724104 239.238438)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2034 2216 \r\nQ 1584 2216 1326 1975 \r\nQ 1069 1734 1069 1313 \r\nQ 1069 891 1326 650 \r\nQ 1584 409 2034 409 \r\nQ 2484 409 2743 651 \r\nQ 3003 894 3003 1313 \r\nQ 3003 1734 2745 1975 \r\nQ 2488 2216 2034 2216 \r\nz\r\nM 1403 2484 \r\nQ 997 2584 770 2862 \r\nQ 544 3141 544 3541 \r\nQ 544 4100 942 4425 \r\nQ 1341 4750 2034 4750 \r\nQ 2731 4750 3128 4425 \r\nQ 3525 4100 3525 3541 \r\nQ 3525 3141 3298 2862 \r\nQ 3072 2584 2669 2484 \r\nQ 3125 2378 3379 2068 \r\nQ 3634 1759 3634 1313 \r\nQ 3634 634 3220 271 \r\nQ 2806 -91 2034 -91 \r\nQ 1263 -91 848 271 \r\nQ 434 634 434 1313 \r\nQ 434 1759 690 2068 \r\nQ 947 2378 1403 2484 \r\nz\r\nM 1172 3481 \r\nQ 1172 3119 1398 2916 \r\nQ 1625 2713 2034 2713 \r\nQ 2441 2713 2670 2916 \r\nQ 2900 3119 2900 3481 \r\nQ 2900 3844 2670 4047 \r\nQ 2441 4250 2034 4250 \r\nQ 1625 4250 1398 4047 \r\nQ 1172 3844 1172 3481 \r\nz\r\n\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-38\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_6\">\r\n     <g id=\"line2d_6\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"352.790695\" xlink:href=\"#m2e66667aaa\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_6\">\r\n      <!-- 1.0 -->\r\n      <g transform=\"translate(344.839132 239.238438)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 794 531 \r\nL 1825 531 \r\nL 1825 4091 \r\nL 703 3866 \r\nL 703 4441 \r\nL 1819 4666 \r\nL 2450 4666 \r\nL 2450 531 \r\nL 3481 531 \r\nL 3481 0 \r\nL 794 0 \r\nL 794 531 \r\nz\r\n\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-31\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"matplotlib.axis_2\">\r\n    <g id=\"ytick_1\">\r\n     <g id=\"line2d_7\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL -3.5 0 \r\n\" id=\"m3c7ddba502\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m3c7ddba502\" y=\"189.121279\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_7\">\r\n      <!-- 0.2 -->\r\n      <g transform=\"translate(7.2 192.920498)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-32\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_2\">\r\n     <g id=\"line2d_8\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m3c7ddba502\" y=\"146.111868\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_8\">\r\n      <!-- 0.4 -->\r\n      <g transform=\"translate(7.2 149.911087)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-34\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_3\">\r\n     <g id=\"line2d_9\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m3c7ddba502\" y=\"103.102458\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_9\">\r\n      <!-- 0.6 -->\r\n      <g transform=\"translate(7.2 106.901676)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-36\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_4\">\r\n     <g id=\"line2d_10\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m3c7ddba502\" y=\"60.093047\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_10\">\r\n      <!-- 0.8 -->\r\n      <g transform=\"translate(7.2 63.892266)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-38\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_5\">\r\n     <g id=\"line2d_11\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m3c7ddba502\" y=\"17.083636\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_11\">\r\n      <!-- 1.0 -->\r\n      <g transform=\"translate(7.2 20.882855)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-31\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_12\">\r\n    <path clip-path=\"url(#p1b21a41545)\" d=\"M 45.321307 214.756364 \r\nL 48.427058 201.714318 \r\nL 51.53281 190.327293 \r\nL 54.638561 180.026468 \r\nL 57.744312 170.541868 \r\nL 60.850064 161.714625 \r\nL 63.955815 153.439887 \r\nL 67.061567 145.64324 \r\nL 70.167318 138.269142 \r\nL 73.273069 131.274569 \r\nL 76.378821 124.625236 \r\nL 79.484572 118.293195 \r\nL 82.590324 112.25525 \r\nL 85.696075 106.491855 \r\nL 88.801826 100.986329 \r\nL 91.907578 95.724289 \r\nL 95.013329 90.693215 \r\nL 98.11908 85.882125 \r\nL 101.224832 81.281319 \r\nL 104.330583 76.88218 \r\nL 107.436335 72.677011 \r\nL 110.542086 68.658908 \r\nL 113.647837 64.821651 \r\nL 116.753589 61.15962 \r\nL 119.85934 57.66772 \r\nL 122.965092 54.341318 \r\nL 126.070843 51.176199 \r\nL 129.176594 48.168514 \r\nL 132.282346 45.314745 \r\nL 135.388097 42.611679 \r\nL 138.493849 40.056369 \r\nL 141.5996 37.646122 \r\nL 144.705351 35.378469 \r\nL 147.811103 33.251152 \r\nL 150.916854 31.262107 \r\nL 154.022606 29.409448 \r\nL 157.128357 27.691457 \r\nL 160.234108 26.106576 \r\nL 163.33986 24.65339 \r\nL 166.445611 23.330625 \r\nL 169.551362 22.137141 \r\nL 172.657114 21.071922 \r\nL 175.762865 20.134071 \r\nL 178.868617 19.322809 \r\nL 181.974368 18.637469 \r\nL 185.080119 18.077489 \r\nL 188.185871 17.642417 \r\nL 191.291622 17.3319 \r\nL 194.397374 17.14569 \r\nL 197.503125 17.083636 \r\nL 200.608876 17.14569 \r\nL 203.714628 17.3319 \r\nL 206.820379 17.642417 \r\nL 209.926131 18.077489 \r\nL 213.031882 18.637469 \r\nL 216.137633 19.322809 \r\nL 219.243385 20.134071 \r\nL 222.349136 21.071922 \r\nL 225.454888 22.137141 \r\nL 228.560639 23.330625 \r\nL 231.66639 24.65339 \r\nL 234.772142 26.106576 \r\nL 237.877893 27.691457 \r\nL 240.983644 29.409448 \r\nL 244.089396 31.262107 \r\nL 247.195147 33.251152 \r\nL 250.300899 35.378469 \r\nL 253.40665 37.646122 \r\nL 256.512401 40.056369 \r\nL 259.618153 42.611679 \r\nL 262.723904 45.314745 \r\nL 265.829656 48.168514 \r\nL 268.935407 51.176199 \r\nL 272.041158 54.341318 \r\nL 275.14691 57.66772 \r\nL 278.252661 61.15962 \r\nL 281.358413 64.821651 \r\nL 284.464164 68.658908 \r\nL 287.569915 72.677011 \r\nL 290.675667 76.88218 \r\nL 293.781418 81.281319 \r\nL 296.88717 85.882125 \r\nL 299.992921 90.693215 \r\nL 303.098672 95.724289 \r\nL 306.204424 100.986329 \r\nL 309.310175 106.491855 \r\nL 312.415926 112.25525 \r\nL 315.521678 118.293195 \r\nL 318.627429 124.625236 \r\nL 321.733181 131.274569 \r\nL 324.838932 138.269142 \r\nL 327.944683 145.64324 \r\nL 331.050435 153.439887 \r\nL 334.156186 161.714625 \r\nL 337.261938 170.541868 \r\nL 340.367689 180.026468 \r\nL 343.47344 190.327293 \r\nL 346.579192 201.714318 \r\nL 349.684943 214.756364 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"patch_3\">\r\n    <path d=\"M 30.103125 224.64 \r\nL 30.103125 7.2 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_4\">\r\n    <path d=\"M 364.903125 224.64 \r\nL 364.903125 7.2 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_5\">\r\n    <path d=\"M 30.103125 224.64 \r\nL 364.903125 224.64 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_6\">\r\n    <path d=\"M 30.103125 7.2 \r\nL 364.903125 7.2 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n  </g>\r\n </g>\r\n <defs>\r\n  <clipPath id=\"p1b21a41545\">\r\n   <rect height=\"217.44\" width=\"334.8\" x=\"30.103125\" y=\"7.2\"/>\r\n  </clipPath>\r\n </defs>\r\n</svg>\r\n",
                        "image/png": "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"
                    },
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ],
            "metadata": {}
        },
        {
            "cell_type": "markdown",
            "source": [
                "**DEFINIÇÂO:** A entropia relativa D(p||q) é dado por\r\n",
                "\r\n",
                "$$\r\n",
                "D(p||q) = - \\sum_{x \\in \\Chi}{p(x)}log_{2} \\frac{p(x)}{q(x)}\r\n",
                "$$\r\n",
                "\r\n",
                "D(p||q) é o aumento da entropia que acontece quando é considerado uma distribuição de probabilidade errada.\r\n",
                "\r\n",
                "Ex:\r\n",
                "    P(x = 0) = 0.7\r\n",
                "    P(x = 1) = 0.3\r\n",
                "\r\n",
                "Na figura abaixo podemos ver que D(p||q) é minimizado quado consideramos a probabilidade correta."
            ],
            "metadata": {}
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "source": [
                "p = 0.7\r\n",
                "prob_real = [p, 1 - p]\r\n",
                "\r\n",
                "prob = np.arange(1, 100)/100\r\n",
                "prob2 = np.ones(99) - prob\r\n",
                "\r\n",
                "\r\n",
                "D = prob_real[0] * np.log2(prob_real[0]/prob) + prob_real[1] * np.log2(prob_real[1]/prob2)\r\n",
                "\r\n",
                "plt.plot(prob, D)"
            ],
            "outputs": [
                {
                    "output_type": "execute_result",
                    "data": {
                        "text/plain": [
                            "[<matplotlib.lines.Line2D at 0x189c6ffc388>]"
                        ]
                    },
                    "metadata": {},
                    "execution_count": 4
                },
                {
                    "output_type": "display_data",
                    "data": {
                        "text/plain": [
                            "<Figure size 432x288 with 1 Axes>"
                        ],
                        "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<svg height=\"248.518125pt\" version=\"1.1\" viewBox=\"0 0 372.103125 248.518125\" width=\"372.103125pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-08-25T15:04:44.582848</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.4.2, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style>\r\n </defs>\r\n <g id=\"figure_1\">\r\n  <g id=\"patch_1\">\r\n   <path d=\"M 0 248.518125 \r\nL 372.103125 248.518125 \r\nL 372.103125 0 \r\nL 0 0 \r\nz\r\n\" style=\"fill:none;\"/>\r\n  </g>\r\n  <g id=\"axes_1\">\r\n   <g id=\"patch_2\">\r\n    <path d=\"M 30.103125 224.64 \r\nL 364.903125 224.64 \r\nL 364.903125 7.2 \r\nL 30.103125 7.2 \r\nz\r\n\" style=\"fill:#ffffff;\"/>\r\n   </g>\r\n   <g id=\"matplotlib.axis_1\">\r\n    <g id=\"xtick_1\">\r\n     <g id=\"line2d_1\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL 0 3.5 \r\n\" id=\"m50929b34f7\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.215555\" xlink:href=\"#m50929b34f7\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_1\">\r\n      <!-- 0.0 -->\r\n      <g transform=\"translate(34.263993 239.238437)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2034 4250 \r\nQ 1547 4250 1301 3770 \r\nQ 1056 3291 1056 2328 \r\nQ 1056 1369 1301 889 \r\nQ 1547 409 2034 409 \r\nQ 2525 409 2770 889 \r\nQ 3016 1369 3016 2328 \r\nQ 3016 3291 2770 3770 \r\nQ 2525 4250 2034 4250 \r\nz\r\nM 2034 4750 \r\nQ 2819 4750 3233 4129 \r\nQ 3647 3509 3647 2328 \r\nQ 3647 1150 3233 529 \r\nQ 2819 -91 2034 -91 \r\nQ 1250 -91 836 529 \r\nQ 422 1150 422 2328 \r\nQ 422 3509 836 4129 \r\nQ 1250 4750 2034 4750 \r\nz\r\n\" id=\"DejaVuSans-30\" transform=\"scale(0.015625)\"/>\r\n        <path d=\"M 684 794 \r\nL 1344 794 \r\nL 1344 0 \r\nL 684 0 \r\nL 684 794 \r\nz\r\n\" id=\"DejaVuSans-2e\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_2\">\r\n     <g id=\"line2d_2\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"104.330583\" xlink:href=\"#m50929b34f7\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_2\">\r\n      <!-- 0.2 -->\r\n      <g transform=\"translate(96.379021 239.238437)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 1228 531 \r\nL 3431 531 \r\nL 3431 0 \r\nL 469 0 \r\nL 469 531 \r\nQ 828 903 1448 1529 \r\nQ 2069 2156 2228 2338 \r\nQ 2531 2678 2651 2914 \r\nQ 2772 3150 2772 3378 \r\nQ 2772 3750 2511 3984 \r\nQ 2250 4219 1831 4219 \r\nQ 1534 4219 1204 4116 \r\nQ 875 4013 500 3803 \r\nL 500 4441 \r\nQ 881 4594 1212 4672 \r\nQ 1544 4750 1819 4750 \r\nQ 2544 4750 2975 4387 \r\nQ 3406 4025 3406 3419 \r\nQ 3406 3131 3298 2873 \r\nQ 3191 2616 2906 2266 \r\nQ 2828 2175 2409 1742 \r\nQ 1991 1309 1228 531 \r\nz\r\n\" id=\"DejaVuSans-32\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-32\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_3\">\r\n     <g id=\"line2d_3\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"166.445611\" xlink:href=\"#m50929b34f7\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_3\">\r\n      <!-- 0.4 -->\r\n      <g transform=\"translate(158.494049 239.238437)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2419 4116 \r\nL 825 1625 \r\nL 2419 1625 \r\nL 2419 4116 \r\nz\r\nM 2253 4666 \r\nL 3047 4666 \r\nL 3047 1625 \r\nL 3713 1625 \r\nL 3713 1100 \r\nL 3047 1100 \r\nL 3047 0 \r\nL 2419 0 \r\nL 2419 1100 \r\nL 313 1100 \r\nL 313 1709 \r\nL 2253 4666 \r\nz\r\n\" id=\"DejaVuSans-34\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-34\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_4\">\r\n     <g id=\"line2d_4\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"228.560639\" xlink:href=\"#m50929b34f7\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_4\">\r\n      <!-- 0.6 -->\r\n      <g transform=\"translate(220.609076 239.238437)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2113 2584 \r\nQ 1688 2584 1439 2293 \r\nQ 1191 2003 1191 1497 \r\nQ 1191 994 1439 701 \r\nQ 1688 409 2113 409 \r\nQ 2538 409 2786 701 \r\nQ 3034 994 3034 1497 \r\nQ 3034 2003 2786 2293 \r\nQ 2538 2584 2113 2584 \r\nz\r\nM 3366 4563 \r\nL 3366 3988 \r\nQ 3128 4100 2886 4159 \r\nQ 2644 4219 2406 4219 \r\nQ 1781 4219 1451 3797 \r\nQ 1122 3375 1075 2522 \r\nQ 1259 2794 1537 2939 \r\nQ 1816 3084 2150 3084 \r\nQ 2853 3084 3261 2657 \r\nQ 3669 2231 3669 1497 \r\nQ 3669 778 3244 343 \r\nQ 2819 -91 2113 -91 \r\nQ 1303 -91 875 529 \r\nQ 447 1150 447 2328 \r\nQ 447 3434 972 4092 \r\nQ 1497 4750 2381 4750 \r\nQ 2619 4750 2861 4703 \r\nQ 3103 4656 3366 4563 \r\nz\r\n\" id=\"DejaVuSans-36\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-36\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_5\">\r\n     <g id=\"line2d_5\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"290.675667\" xlink:href=\"#m50929b34f7\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_5\">\r\n      <!-- 0.8 -->\r\n      <g transform=\"translate(282.724104 239.238437)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2034 2216 \r\nQ 1584 2216 1326 1975 \r\nQ 1069 1734 1069 1313 \r\nQ 1069 891 1326 650 \r\nQ 1584 409 2034 409 \r\nQ 2484 409 2743 651 \r\nQ 3003 894 3003 1313 \r\nQ 3003 1734 2745 1975 \r\nQ 2488 2216 2034 2216 \r\nz\r\nM 1403 2484 \r\nQ 997 2584 770 2862 \r\nQ 544 3141 544 3541 \r\nQ 544 4100 942 4425 \r\nQ 1341 4750 2034 4750 \r\nQ 2731 4750 3128 4425 \r\nQ 3525 4100 3525 3541 \r\nQ 3525 3141 3298 2862 \r\nQ 3072 2584 2669 2484 \r\nQ 3125 2378 3379 2068 \r\nQ 3634 1759 3634 1313 \r\nQ 3634 634 3220 271 \r\nQ 2806 -91 2034 -91 \r\nQ 1263 -91 848 271 \r\nQ 434 634 434 1313 \r\nQ 434 1759 690 2068 \r\nQ 947 2378 1403 2484 \r\nz\r\nM 1172 3481 \r\nQ 1172 3119 1398 2916 \r\nQ 1625 2713 2034 2713 \r\nQ 2441 2713 2670 2916 \r\nQ 2900 3119 2900 3481 \r\nQ 2900 3844 2670 4047 \r\nQ 2441 4250 2034 4250 \r\nQ 1625 4250 1398 4047 \r\nQ 1172 3844 1172 3481 \r\nz\r\n\" id=\"DejaVuSans-38\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-38\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"xtick_6\">\r\n     <g id=\"line2d_6\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"352.790695\" xlink:href=\"#m50929b34f7\" y=\"224.64\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_6\">\r\n      <!-- 1.0 -->\r\n      <g transform=\"translate(344.839132 239.238437)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 794 531 \r\nL 1825 531 \r\nL 1825 4091 \r\nL 703 3866 \r\nL 703 4441 \r\nL 1819 4666 \r\nL 2450 4666 \r\nL 2450 531 \r\nL 3481 531 \r\nL 3481 0 \r\nL 794 0 \r\nL 794 531 \r\nz\r\n\" id=\"DejaVuSans-31\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-31\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"matplotlib.axis_2\">\r\n    <g id=\"ytick_1\">\r\n     <g id=\"line2d_7\">\r\n      <defs>\r\n       <path d=\"M 0 0 \r\nL -3.5 0 \r\n\" id=\"m60a044ec88\" style=\"stroke:#000000;stroke-width:0.8;\"/>\r\n      </defs>\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"214.756364\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_7\">\r\n      <!-- 0.0 -->\r\n      <g transform=\"translate(7.2 218.555582)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_2\">\r\n     <g id=\"line2d_8\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"188.565931\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_8\">\r\n      <!-- 0.5 -->\r\n      <g transform=\"translate(7.2 192.365149)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 691 4666 \r\nL 3169 4666 \r\nL 3169 4134 \r\nL 1269 4134 \r\nL 1269 2991 \r\nQ 1406 3038 1543 3061 \r\nQ 1681 3084 1819 3084 \r\nQ 2600 3084 3056 2656 \r\nQ 3513 2228 3513 1497 \r\nQ 3513 744 3044 326 \r\nQ 2575 -91 1722 -91 \r\nQ 1428 -91 1123 -41 \r\nQ 819 9 494 109 \r\nL 494 744 \r\nQ 775 591 1075 516 \r\nQ 1375 441 1709 441 \r\nQ 2250 441 2565 725 \r\nQ 2881 1009 2881 1497 \r\nQ 2881 1984 2565 2268 \r\nQ 2250 2553 1709 2553 \r\nQ 1456 2553 1204 2497 \r\nQ 953 2441 691 2322 \r\nL 691 4666 \r\nz\r\n\" id=\"DejaVuSans-35\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-30\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_3\">\r\n     <g id=\"line2d_9\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"162.375498\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_9\">\r\n      <!-- 1.0 -->\r\n      <g transform=\"translate(7.2 166.174717)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-31\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_4\">\r\n     <g id=\"line2d_10\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"136.185065\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_10\">\r\n      <!-- 1.5 -->\r\n      <g transform=\"translate(7.2 139.984284)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-31\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_5\">\r\n     <g id=\"line2d_11\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"109.994632\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_11\">\r\n      <!-- 2.0 -->\r\n      <g transform=\"translate(7.2 113.793851)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-32\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_6\">\r\n     <g id=\"line2d_12\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"83.804199\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_12\">\r\n      <!-- 2.5 -->\r\n      <g transform=\"translate(7.2 87.603418)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-32\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_7\">\r\n     <g id=\"line2d_13\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"57.613766\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_13\">\r\n      <!-- 3.0 -->\r\n      <g transform=\"translate(7.2 61.412985)scale(0.1 -0.1)\">\r\n       <defs>\r\n        <path d=\"M 2597 2516 \r\nQ 3050 2419 3304 2112 \r\nQ 3559 1806 3559 1356 \r\nQ 3559 666 3084 287 \r\nQ 2609 -91 1734 -91 \r\nQ 1441 -91 1130 -33 \r\nQ 819 25 488 141 \r\nL 488 750 \r\nQ 750 597 1062 519 \r\nQ 1375 441 1716 441 \r\nQ 2309 441 2620 675 \r\nQ 2931 909 2931 1356 \r\nQ 2931 1769 2642 2001 \r\nQ 2353 2234 1838 2234 \r\nL 1294 2234 \r\nL 1294 2753 \r\nL 1863 2753 \r\nQ 2328 2753 2575 2939 \r\nQ 2822 3125 2822 3475 \r\nQ 2822 3834 2567 4026 \r\nQ 2313 4219 1838 4219 \r\nQ 1578 4219 1281 4162 \r\nQ 984 4106 628 3988 \r\nL 628 4550 \r\nQ 988 4650 1302 4700 \r\nQ 1616 4750 1894 4750 \r\nQ 2613 4750 3031 4423 \r\nQ 3450 4097 3450 3541 \r\nQ 3450 3153 3228 2886 \r\nQ 3006 2619 2597 2516 \r\nz\r\n\" id=\"DejaVuSans-33\" transform=\"scale(0.015625)\"/>\r\n       </defs>\r\n       <use xlink:href=\"#DejaVuSans-33\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-30\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n    <g id=\"ytick_8\">\r\n     <g id=\"line2d_14\">\r\n      <g>\r\n       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"30.103125\" xlink:href=\"#m60a044ec88\" y=\"31.423333\"/>\r\n      </g>\r\n     </g>\r\n     <g id=\"text_14\">\r\n      <!-- 3.5 -->\r\n      <g transform=\"translate(7.2 35.222552)scale(0.1 -0.1)\">\r\n       <use xlink:href=\"#DejaVuSans-33\"/>\r\n       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-2e\"/>\r\n       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-35\"/>\r\n      </g>\r\n     </g>\r\n    </g>\r\n   </g>\r\n   <g id=\"line2d_15\">\r\n    <path clip-path=\"url(#pf42a93ac6a)\" d=\"M 45.321307 17.083636 \r\nL 48.427058 53.520079 \r\nL 51.53281 74.736145 \r\nL 54.638561 89.719228 \r\nL 57.744312 101.285845 \r\nL 60.850064 110.690518 \r\nL 63.955815 118.602422 \r\nL 67.061567 125.42097 \r\nL 70.167318 131.403771 \r\nL 73.273069 136.726699 \r\nL 76.378821 141.515178 \r\nL 79.484572 145.861798 \r\nL 82.590324 149.836857 \r\nL 85.696075 153.494981 \r\nL 88.801826 156.879457 \r\nL 91.907578 160.025165 \r\nL 95.013329 162.96062 \r\nL 98.11908 165.709425 \r\nL 101.224832 168.291339 \r\nL 104.330583 170.72306 \r\nL 107.436335 173.018825 \r\nL 110.542086 175.19087 \r\nL 113.647837 177.24978 \r\nL 116.753589 179.204774 \r\nL 119.85934 181.063925 \r\nL 122.965092 182.834339 \r\nL 126.070843 184.522302 \r\nL 129.176594 186.133398 \r\nL 132.282346 187.672603 \r\nL 135.388097 189.144374 \r\nL 138.493849 190.552709 \r\nL 141.5996 191.901207 \r\nL 144.705351 193.193118 \r\nL 147.811103 194.43138 \r\nL 150.916854 195.618656 \r\nL 154.022606 196.757366 \r\nL 157.128357 197.849708 \r\nL 160.234108 198.897683 \r\nL 163.33986 199.903112 \r\nL 166.445611 200.867659 \r\nL 169.551362 201.792834 \r\nL 172.657114 202.680018 \r\nL 175.762865 203.530465 \r\nL 178.868617 204.345317 \r\nL 181.974368 205.125607 \r\nL 185.080119 205.872272 \r\nL 188.185871 206.586156 \r\nL 191.291622 207.268015 \r\nL 194.397374 207.918524 \r\nL 197.503125 208.538278 \r\nL 200.608876 209.127799 \r\nL 203.714628 209.687533 \r\nL 206.820379 210.217859 \r\nL 209.926131 210.719085 \r\nL 213.031882 211.19145 \r\nL 216.137633 211.635126 \r\nL 219.243385 212.050219 \r\nL 222.349136 212.436763 \r\nL 225.454888 212.794724 \r\nL 228.560639 213.123995 \r\nL 231.66639 213.424397 \r\nL 234.772142 213.695671 \r\nL 237.877893 213.937476 \r\nL 240.983644 214.149385 \r\nL 244.089396 214.330878 \r\nL 247.195147 214.481335 \r\nL 250.300899 214.600027 \r\nL 253.40665 214.686105 \r\nL 256.512401 214.738592 \r\nL 259.618153 214.756364 \r\nL 262.723904 214.738135 \r\nL 265.829656 214.682438 \r\nL 268.935407 214.5876 \r\nL 272.041158 214.451716 \r\nL 275.14691 214.272608 \r\nL 278.252661 214.047793 \r\nL 281.358413 213.774425 \r\nL 284.464164 213.449238 \r\nL 287.569915 213.068467 \r\nL 290.675667 212.627752 \r\nL 293.781418 212.122023 \r\nL 296.88717 211.545344 \r\nL 299.992921 210.890717 \r\nL 303.098672 210.149828 \r\nL 306.204424 209.312711 \r\nL 309.310175 208.367287 \r\nL 312.415926 207.298746 \r\nL 315.521678 206.088671 \r\nL 318.627429 204.713778 \r\nL 321.733181 203.144065 \r\nL 324.838932 201.339972 \r\nL 327.944683 199.24786 \r\nL 331.050435 196.792469 \r\nL 334.156186 193.863504 \r\nL 337.261938 190.289893 \r\nL 340.367689 185.78495 \r\nL 343.47344 179.811121 \r\nL 346.579192 171.161424 \r\nL 349.684943 155.984212 \r\n\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\r\n   </g>\r\n   <g id=\"patch_3\">\r\n    <path d=\"M 30.103125 224.64 \r\nL 30.103125 7.2 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_4\">\r\n    <path d=\"M 364.903125 224.64 \r\nL 364.903125 7.2 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_5\">\r\n    <path d=\"M 30.103125 224.64 \r\nL 364.903125 224.64 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n   <g id=\"patch_6\">\r\n    <path d=\"M 30.103125 7.2 \r\nL 364.903125 7.2 \r\n\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\r\n   </g>\r\n  </g>\r\n </g>\r\n <defs>\r\n  <clipPath id=\"pf42a93ac6a\">\r\n   <rect height=\"217.44\" width=\"334.8\" x=\"30.103125\" y=\"7.2\"/>\r\n  </clipPath>\r\n </defs>\r\n</svg>\r\n",
                        "image/png": "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"
                    },
                    "metadata": {
                        "needs_background": "light"
                    }
                }
            ],
            "metadata": {}
        },
        {
            "cell_type": "markdown",
            "source": [
                "**DEFINIÇÂO:** A informação mútua de entre duas variáveis aleatórias X e Y é definida como\r\n",
                "\r\n",
                "$$\r\n",
                "I(X;Y) = - \\sum_{x \\in X}\\sum_{y \\in Y}{p(x)}log_{2} \\frac{p(x,y)}{p(x)p(y)}\r\n",
                "$$\r\n",
                "\r\n",
                "I(X;Y) é o aumento na entropia que acontece quando consideramos que duas variáveis aleatórias são independentes.\r\n",
                "\r\n",
                "Obs: em epslon1 e epslon2 devemos colocar números que mantenham a probabilidade estritamente positiva."
            ],
            "metadata": {}
        },
        {
            "cell_type": "code",
            "execution_count": 31,
            "source": [
                "p = 0.5\r\n",
                "q = 0.5\r\n",
                "epslon1 = 0.49\r\n",
                "epslon2 = 0.49\r\n",
                "\r\n",
                "prob_inde = [p*q, p*(1-q), (1-p)*q, (1-q)*(1-p)]\r\n",
                "\r\n",
                "prob_depe = [p*(q - epslon1), p*(1-q + epslon1), (1-p)*(q +epslon2), (1-p)*(1 - q - epslon2)]\r\n",
                "\r\n",
                "sum(prob_depe * np.log2(prob_depe) - prob_depe * np.log2(prob_inde))"
            ],
            "outputs": [
                {
                    "output_type": "execute_result",
                    "data": {
                        "text/plain": [
                            "0.9192068641040888"
                        ]
                    },
                    "metadata": {},
                    "execution_count": 31
                }
            ],
            "metadata": {}
        }
    ],
    "metadata": {
        "orig_nbformat": 4,
        "language_info": {
            "name": "python",
            "version": "3.7.6",
            "mimetype": "text/x-python",
            "codemirror_mode": {
                "name": "ipython",
                "version": 3
            },
            "pygments_lexer": "ipython3",
            "nbconvert_exporter": "python",
            "file_extension": ".py"
        },
        "kernelspec": {
            "name": "python3",
            "display_name": "Python 3.7.6 64-bit ('myvenv': venv)"
        },
        "interpreter": {
            "hash": "6868c2c58928b2df756f83b0ee3c61f987925f733633c14067b8c2ee5ae10991"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}