06-regressao_classificacao.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Capítulo 6: Regressão e Classificação"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 1\n",
    "\n",
    "## Exercício 1\n",
    "**Objetivo: Visualizar pontos medidos e comparar com uma teoria**\n",
    "\n",
    "Quando observamos a realidade, somos capazes de *medir* coisas. Por exemplo, podemos tentar medir a velocidade do som da seguinte forma: uma pessoa dá um grito ao mesmo tempo em que aciona um cronômetro, e outra pessoa, a alguns metros de distância, pára esse mesmo cronômetro no momento em que ouve o grito. Repetimos o experimento para várias distâncias diferentes e conseguimos, então, uma série de medidas pareadas de tempo e distância.\n",
    "\n",
    "Se fôssemos capazes de acionar o cronômetro exatamente no tempo em que o grito é emitido, e pudéssemos parar o cronômetro exatamente no instante em que o grito é ouvido, então teríamos a seguinte situação:\n",
    "\n",
    "Sabemos que o som se propaga em uma determinada velocidade, que é constante, e portanto o som obedece a um movimento uniforme. Vamos chamar essa velocidade de $c$. Para cada distância $\\Delta s$ teríamos um tempo de propagação igual a $t = \\frac{1}{c} \\Delta s$.\n",
    "\n",
    "Essa ideia de que um fenômeno obedece a uma equação (ou a um modelo, ou a uma \"regra\", ou uma lei) chama-se *teoria*. Então, poderíamos ter resultados *teóricos* que poderiam se parecer com:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "c = 300 # velocidade do som, em metros por segundo - esse valor foi absolutamente inventado para fins de exemplo\n",
    "delta_s = np.linspace(60,100,20) # medimos 20 distâncias, indo de 60 a 100 metros\n",
    "t = (1/c) * delta_s\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(delta_s, t)\n",
    "plt.xlabel('Distância (m)')\n",
    "plt.ylabel('Tempo de propagação (s)')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Porém, na realidade, nossa medição é bastante imperfeita. A primeira fonte dessas imperfeições é que, ao medirmos o tempo de propagação do som, usamos um cronômetro acionado manualmente - então, não somos capazes de acionar o cronômetro *exatamente* no instante em que o som é gerado ou recebido. Outra fonte de erro é que a velocidade do som não é *exatamente* uma constante, porque alterações como ventos e diferenças de temperatura do ar podem afetar a propagação sonora. Também, há fontes de erro que não somos exatamente capazes de prever.\n",
    "\n",
    "Cada um desses erros gera um desvio, e cada um desses desvios tem uma distribuição diferente. Quando somamos todos esses desvios com distribuições diferentes, temos um desvio total com uma distribuição Gaussiana (lembre-se que a Normal, ou Gaussiana, é a distribuição que aparece quando somamos várias contribuições aleatórias de diferentes fontes!) com média zero e desvio padrão que não conhecemos ainda. Então, poderíamos encontrar, de fato, a seguinte situação:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "c = 300 # velocidade do som, em metros por segundo - esse valor foi absolutamente inventado para fins de exemplo\n",
    "delta_s = np.linspace(60,100,20) # medimos 20 distâncias, indo de 60 a 100 metros\n",
    "t = (1/c) * delta_s\n",
    "\n",
    "desvio_padrao_da_medicao = 0.01 # Desvio padrão, em segundos - esse número também é inventado!\n",
    "t_medido = t + np.random.randn(20) * desvio_padrao_da_medicao\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(delta_s, t, label='Teoria')\n",
    "plt.scatter(delta_s, t_medido, label='Medição')\n",
    "\n",
    "plt.xlabel('Distância (m)')\n",
    "plt.ylabel('Tempo de propagação (s)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O problema disso tudo é que, geralmente, não conseguimos saber quais são os parâmetros \"reais\" do fenômeno - na verdade, não sabemos nem ao certo que ele obedece a alguma equação. Por isso, precisamos trabalhar com essa suposição sobre como o fenômeno se comporta, e por isso essa suposição é chamada de *teoria*, e não de *realidade*.\n",
    "\n",
    "A palavra *teoria* pode ser entendida como: \"uma ideia que existe dentro na nossa cabeça e que pode ou não corresponder à realidade\". Claro que gostaríamos que nossa teoria se aproximasse mais da nossa realidade - realidade essa que só pode ser acessada à partir das medições. Então, vamos elaborar *hipóteses* sobre o fenômeno e usá-las para encontrar nosso modelo teórico.\n",
    "\n",
    "Usando o código abaixo, discuta:\n",
    "\n",
    "a) Apenas olhando a figura, é possível decidir qual das hipóteses é a que melhor explica os pontos que foram medidos? O que significa \"explicar melhor\"?\n",
    "\n",
    "b) Quando aumentamos o `desvio_padrao_da_medicao`, fica mais fácil ou mais difícil decidir por uma hipótese?\n",
    "\n",
    "c) Quando diminuimos o `desvio_padrao_da_medicao`, fica mais fácil ou mais difícil decidir por uma hipótese?\n",
    "\n",
    "d) Quando aumentamos o número de pontos medidos, fica mais fácil ou mais difícil decidir por uma hipótese?\n",
    "\n",
    "e) Quando diminuímos o número de pontos medidos, fica mais fácil ou mais difícil decidir por uma hipótese?\n",
    "\n",
    "f) Se as hipóteses forem muito próximas umas das outras, é mais fácil ou mais difícil escolher uma delas?\n",
    "\n",
    "g) Se as hipóteses forem muito próximas umas das outras, é mais relevante ou menos relevante escolher exatamente a hipótese correta?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "c = 300 # velocidade do som, em metros por segundo - esse valor foi absolutamente inventado para fins de exemplo\n",
    "delta_s = np.linspace(60,100,20) # medimos 20 distâncias, indo de 60 a 100 metros\n",
    "t = (1/c) * delta_s\n",
    "\n",
    "desvio_padrao_da_medicao = 0.01 # Desvio padrão, em segundos - esse número também é inventado!\n",
    "t_medido = t + np.random.randn(20) * desvio_padrao_da_medicao\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.scatter(delta_s, t_medido)\n",
    "plt.plot(delta_s, (1/280) * delta_s, 'r')\n",
    "plt.plot(delta_s, (1/290) * delta_s, 'r')\n",
    "plt.plot(delta_s, (1/300) * delta_s, 'r')\n",
    "plt.plot(delta_s, (1/310) * delta_s, 'r')\n",
    "plt.plot(delta_s, (1/320) * delta_s, 'r')\n",
    "plt.xlabel('Distância (m)')\n",
    "plt.ylabel('Tempo de propagação (s)')\n",
    "plt.legend(['Medições', 'Hipóteses'])\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 2\n",
    "*Objetivo: encontrar e analisar o erro de aproximação entre modelo e medidas*\n",
    "\n",
    "Uma característica dos modelos teóricos é que eles existem somente no mundo das abstrações. É claro que, se quisermos usar nosso modelo teórico para fazer algum tipo de predição, então precisamos de um modelo teórico que se aproxime da realidade. Em outras palavras, ao compararmos dois modelos teóricos, como nas curvas abaixo, gostaríamos de escolher o modelo da curva azul, e não o da curva vermelha:\n",
    "\n",
    "<img src=\"teoria_boa_vs_nao_boa.png\" />\n",
    "\n",
    "Claro que não podemos usar o critério de \"olho\" ou \"intuição\" para fazer essa escolha (até podemos no sentido de capacidade, ou mesmo de legalidade, mas com certeza não deveríamos). Ao invés disso, queremo usar um critério objetivo, isto é, encontrar um número que nos diga o quão bom é um modelo. Uma das propostas mais comuns para isso é o **erro quadrático médio**, ou EQM, que funciona da seguinte forma:\n",
    "\n",
    "    Para cada ponto medido (x,y), com o modelo y_est=a*x_medido+b:\n",
    "        estime o valor fornecido pelo modelo y_est = a*x_medido + b\n",
    "        calcule o erro quadrático EQ = (y_est-y_medido)**2\n",
    "    \n",
    "    Após:\n",
    "        calcule o EQM como a média de todos os EQs\n",
    "\n",
    "Outra maneira de entender o EQM é como uma equação:\n",
    "\n",
    "$$\n",
    "\\text{EQM} = \\frac{1}{N} \\sum_{n=1}^N (y_n - (ax_n + b))^2\n",
    "$$\n",
    "\n",
    "Nesta atividade, vamos analisar como o EQM se comporta quando variamos os coeficientes do modelo.\n",
    "\n",
    "1. No código abaixo, complete a função `EQM` para que ela calcule o EQM de um modelo linear frente a medições recebidas como entrada.\n",
    "1. Na figura que é gerada, qual é o coeficiente angular teórico que leva ao menor EQM? Como ele se compara com o EQM teórico?\n",
    "1. Aumente o `desvio_padrao_da_medicao`. Como isso afeta o valor mínimo do EQM?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def erro( parametros ):\n",
    "    medidas_x, medidas_y, coef_angular_modelo, coef_linear_modelo = parametros\n",
    "    # Complete esta função\n",
    "\n",
    "    return 0\n",
    "\n",
    "# Gerando a medição\n",
    "medidas_x = np.linspace(10,30,5)\n",
    "coef_linear_real = 0\n",
    "coef_angular_real = 1.7\n",
    "desvio_padrao_da_medicao = 0.1 # Desvio padrão, em segundos - esse número também é inventado!\n",
    "medidas_y = coef_linear_real + coef_angular_real * medidas_x + np.random.randn(len(medidas_x)) * desvio_padrao_da_medicao\n",
    "\n",
    "# Gerando o modelo\n",
    "coef_linear_modelo = 0\n",
    "coef_angular_modelo = 1.8\n",
    "\n",
    "# Candidatos\n",
    "candidatos_coef_angular = np.linspace(0,3,1000)\n",
    "eqms = []\n",
    "for idx, a_ in enumerate(candidatos_coef_angular):\n",
    "    erro_quadratico_medio = erro( (medidas_x, medidas_y, a_, coef_linear_modelo) )\n",
    "    eqms.append(erro_quadratico_medio)\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(candidatos_coef_angular, eqms)\n",
    "plt.xlabel('Coeficiente angular do modelo')\n",
    "plt.ylabel('EQM')\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 3\n",
    "*Objetivo: Calcular a derivada do erro em relação aos parâmetros da reta*\n",
    "\n",
    "Em várias aplicações, sabemos de antemão que o coeficiente linear do modelo é zero. Isso significa que o erro do modelo é simplesmente:\n",
    "\n",
    "$$\n",
    "\\text{EQM} = \\frac{1}{N} \\sum_{n=1}^N (y_n - a x_n)^2 = \\frac{1}{N} \\sum_{n=1}^N y_n^2 - 2 a x_n y_n + a^2 x_n^2\n",
    "$$\n",
    "\n",
    "1. Calcule a derivada de EQM em relação ao coeficiente angular $a$, isto é, calcule (no papel) $e'(a) = \\frac{d\\text{EQM}}{da}$. DICA: calcule a derivada para um único ponto (por exemplo, $n=1$), e então some as derivadas para todos os pontos.\n",
    "1. Implemente o cálculo de $e'(a)$ na função abaixo. Quais são os valores de $e'(a)$ quando $a$ (o coeficiente angular do modelo) é muito superior ao coeficiente angular \"real\"? E se $a$ é inferior ao coeficiente angular \"real\"?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def deqm_da(medidas_x, medidas_y, coef_angular_tentativa):\n",
    "    # Complete esta função\n",
    "\n",
    "    return 0\n",
    "\n",
    "# Gerando a medição\n",
    "medidas_x = np.linspace(10,30,5)\n",
    "coef_angular_teorico = 1.7\n",
    "desvio_padrao_da_medicao = 0.1 # Desvio padrão, em segundos - esse número também é inventado!\n",
    "medidas_y = coef_angular_teorico * medidas_x + np.random.randn(len(medidas_x)) * desvio_padrao_da_medicao\n",
    "\n",
    "# Gerando o modelo\n",
    "coef_angular_modelo = 1.8\n",
    "\n",
    "# Candidatos\n",
    "candidatos_coef_angular = np.linspace(0,3,1000)\n",
    "eqms = []\n",
    "for idx, a_ in enumerate(candidatos_coef_angular):\n",
    "    erro_quadratico_medio = deqm_da(medidas_x, medidas_y, a_)\n",
    "    eqms.append(erro_quadratico_medio)\n",
    "\n",
    "plt.figure(figsize=(7,3))\n",
    "plt.plot(candidatos_coef_angular, eqms)\n",
    "plt.xlabel('a')\n",
    "plt.ylabel(\"e'(a)\")\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercício 4\n",
    "*Objetivo: entender o processo de descida pelo gradiente*\n",
    "\n",
    "Partindo de um modelo linear com coeficiente angular $a$, podemos estimar um novo modelo usando:\n",
    "\n",
    "$a_{\\text{novo}} = a_{\\text{atual}} + \\alpha e'(a)$, onde $\\alpha$ é um valor pequeno e positivo como $0.01$.\n",
    "\n",
    "1. O modelo com coeficiente linear $a_{\\text{novo}}$ deve ter EQM maior ou menor que o modelo com $a_{\\text{atual}}$?\n",
    "1. Como poderíamos mudar o procedimento de estimativa de forma que o modelo novo tenha EQM menor que o modelo antigo?\n",
    "1. Usando as funções que você já implementou, complete a função `melhorar_modelo` no código abaixo de forma a implementar o cálculo de um $a_{\\text{novo}}$.\n",
    "1. Aplicando sucessivamente a função melhorar_modelo, verifique se você consegue aproximar o coeficiente angular teórico dos dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coeficiente angular encontrado: 0.00013280699443793772\n",
      "Coeficiente angular real: 1.7\n"
     ]
    }
   ],
   "source": [
    "def melhorar_modelo(medidas_x, medidas_y, alpha, a_atual):\n",
    "    a_novo = a_atual * 0.9 #Modifique isso \n",
    "    return a_novo\n",
    "\n",
    "# Gerando a medição\n",
    "medidas_x = np.linspace(10,30,5)\n",
    "coef_angular_teorico = 1.7\n",
    "desvio_padrao_da_medicao = 0.5 # Desvio padrão\n",
    "medidas_y = coef_angular_teorico * medidas_x + np.random.randn(len(medidas_x)) * desvio_padrao_da_medicao\n",
    "\n",
    "# Buscar sucessivamente por coeficientes angulares\n",
    "a_ = 5.0 # Esse é o coeficiente angular tentativa\n",
    "alpha = 0.1\n",
    "for _ in range(100):\n",
    "    a_ = melhorar_modelo(medidas_x, medidas_y, alpha, a_)\n",
    "\n",
    "print(\"Coeficiente angular encontrado:\", a_)\n",
    "print(\"Coeficiente angular real:\", coef_angular_teorico)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 5\n",
    "*Objetivo: estimar um coeficiente angular em dados reais*\n",
    "\n",
    "Neste experimento, estimaremos a aceleração da gravidade ($g$). O experimento funciona da seguinte forma:\n",
    "\n",
    "* Sabemos que o tempo de queda $t$ de um objeto que cai de uma altura $h$ é dado por $t=\\sqrt{\\frac{2h}{g}}$.\n",
    "* Isso significa que $t^2 = \\frac{2}{g} h$\n",
    "* Então, se assumirmos que $y=t^2$ e $x=h$, podemos encontrar uma reta $y=ax$ onde $a=\\frac{2}{g}$.\n",
    "\n",
    "O procedimento experimental, portanto, é:\n",
    "\n",
    "1. Escolha um objeto que pode ser jogado sem quebrar (por exemplo, uma borracha).\n",
    "1. Solte o objeto de uma altura conhecida $h$ e meça o tempo de queda $t$ usando um cronômetro (pode ser, por exemplo, o cronômetro do celular)\n",
    "1. Anote a altura e o tempo de queda.\n",
    "1. Repita o procedimento até juntar algumas dezenas de pontos. Compartilhe suas medições com o restante da turma!!!\n",
    "1. Calcule $y=t^2$ para todos os seus pontos\n",
    "1. Use o procedimento que fizemos no exercício anterior para estimar o valor do coeficiente $a$ no modelo linear\n",
    "1. À partir do coeficiente $a$, calcule o valor da aceleração da gravidade usando $a=\\frac{2}{g}$.\n",
    "\n",
    "Quanto vale a aceleração da gravidade $g$ na sua sala de aula?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 6\n",
    "**Objetivo: Encontrar a derivada de uma função**\n",
    "\n",
    "Até o momento, estamos encontrando os parâmetros do nosso modelo dando pequenos passos na direção contrária à derivada do erro em relação ao parâmetro, isto é, a n-ésima iteração do parâmetro $a$ é encontrada usando:\n",
    "\n",
    "$$\n",
    "a_n = a_{n-1} - \\alpha \\frac{dE}{da},\n",
    "$$\n",
    "\n",
    "onde $E$ é o erro que calculamos (por exemplo o EQM) e $\\alpha$ é um número real bem pequeno.\n",
    "\n",
    "Podemos calcular a derivada do erro em relação a todos os parâmetros do nosso modelo, mas é claro que em modelos mais complicados o cálculo desse gradiente vai ficando cada vez mais difícil. Por isso, podemos usar o pacote `autograd`, que calcula automaticamente o gradiente de uma função chamada `loss` em relação aos parâmetros livres de um modelo. Se você quiser saber mais sobre como o autograd funciona, uma boa ideia é começar na própria [página web do autograd](https://github.com/HIPS/autograd/blob/master/docs/tutorial.md).\n",
    "\n",
    "Neste exercício, verificaremos que o autograd, de fato, funciona, e como é sua mecânica, usando uma função polinomial.\n",
    "\n",
    "1. No código abaixo, identifique qual é o polinômio $p(x)$ que está sendo calculado. Quais são os *coeficientes* do polinômio?\n",
    "1. Calcule manualmente a derivada do polinômio em relação a x, e complete a função `derivada`\n",
    "1. Teste sua função `derivada` em alguns pontos e verifique que ela está correta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def polinomio( parametros ):\n",
    "    x, a0, a1, a2 = parametros\n",
    "    px = a0 + a1*x + a2*x**2.0\n",
    "    return px\n",
    "\n",
    "def derivada( parametros ):\n",
    "    x, a0, a1, a2 = parametros\n",
    "    return 0\n",
    "\n",
    "a0 = -1.\n",
    "a1 = 0.\n",
    "a2 = 1.\n",
    "x = 0.\n",
    "print(polinomio ( (x, a0, a1, a2) ))\n",
    "print(derivada ( (x, a0, a1, a2) ))\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercício 7\n",
    "**Objetivo: usar autograd para encontrar a derivada de uma função**\n",
    "\n",
    "Embora calcular derivadas de polinômios seja um caso relativamente simples (quando comparado a outras derivadas), é comum que desejemos calcular derivadas de funções mais complicadas, ou simplesmente que náo queiramos nos preocupar com a derivada de uma função. Para isso, usamos o pacote `autograd`. A função que usaremos é a função `grad`.\n",
    "\n",
    "Veja no código abaixo como a função `grad` funciona. Usando essas ideias, faça uma função `derivada_do_polinomio` que calcula a derivada do polinômio que você encontrou no exercício anterior, e verifique como ela fornece as mesmas informações que a função `derivada` que você já fez."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 12.0\n"
     ]
    }
   ],
   "source": [
    "import autograd.numpy as np_\n",
    "from autograd import grad\n",
    "\n",
    "def funcao_que_quero_derivar ( parametros_como_tupla ):\n",
    "    parametro1, parametro2 = parametros_como_tupla\n",
    "    return parametro1 + parametro2**3 + 1\n",
    "\n",
    "derivada_por_autograd = grad(funcao_que_quero_derivar)\n",
    "\n",
    "derivada1, derivada2 = derivada_por_autograd( (1., 2.) ) # Veja como passei os parametros como uma tupla!\n",
    "print(derivada1, derivada2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 8\n",
    "**Objetivo: usar autograd para minimizar o EQM de uma aproximação**\n",
    "\n",
    "Usando o procedimento de calcular a derivada do erro em relação a cada um dos parâmetros do modelo, use `autograd` para minimizar o EQM da aproximação $y=ax+b$ para os dados medidos abaixo. Os parâmetros $a$ e $b$ do modelo se aproximam dos \"reais\", que foram usados para gerar os dados?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dados \"reais\"\n",
    "a_real = 4\n",
    "b_real = 10\n",
    "x = np.random.random(100) * 100\n",
    "x = np.sort(x)\n",
    "y = a_real * x + b_real\n",
    "\n",
    "# Dados \"medidos\"\n",
    "ym = y + np.random.randn(y.shape[0])*250"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 0.0\n"
     ]
    }
   ],
   "source": [
    "import autograd.numpy as np_\n",
    "from autograd import grad\n",
    "\n",
    "def erro( parametros ):\n",
    "    a, b, x, y_medido = parametros\n",
    "    yhat = a * x + b\n",
    "    mse = 0 # modifique esta linha!!\n",
    "    return mse\n",
    "\n",
    "g = grad(erro)\n",
    "\n",
    "a_modelo, b_modelo = 0.0, 0.0\n",
    "alpha = 0.1\n",
    "for _ in range(100): # por 10 iterações...\n",
    "    pass\n",
    "    # Calcular gradiente\n",
    "\n",
    "    # Modificar parametros do modelo para reduzir o erro\n",
    "\n",
    "print(a_modelo, b_modelo)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 9\n",
    "**Objetivo: usar autograd para realizar um experimento científico**\n",
    "\n",
    "Usando os dados que você já tem do tempo de queda de objetos, re-faça o experimento de descobrir a gravidade usando `autograd`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import autograd.numpy as np_\n",
    "from autograd import grad\n",
    "\n",
    "# Faça seu código aqui"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 3"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 10\n",
    "*Objetivo: entender o problema de classificação linear*\n",
    "\n",
    "Podemos calcular um valor para cada ponto em um plano cartesiano fazendo uma função. Por exemplo, podemos dizer que o ponto $(x,y)$ tem um \"valor\" $f(x,y) = x+y$. Uma possibilidade para esse tipo de função é que ela seja uma função linear, ou seja:\n",
    "\n",
    "$$\n",
    "f(x,y) = Ax + By + C\n",
    "$$\n",
    "\n",
    "Nos pontos em que $f(x,y)=0$, encontramos que $Ax + By + C=0$, que é a equação de uma reta.\n",
    "\n",
    "O código abaixo mostra como isso divide o plano entre o lado \"positivo\" e o \"negativo\".\n",
    "\n",
    "1. Adicione ao *plot* o desenho da reta $Ax+By+C$ que realiza a divisão dos lados positivo e negativo.\n",
    "1. Se as variáveis $x$ e $y$ representam a altura e o peso de personagens (em alguma unidade imaginária em que nossos números fazem sentido), e queremos identificar elfos e anões do Senhor dos Anéis, relacione os grupos (azul e vermelho) a suas categorias (elfos ou anões)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 237) (2, 263)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "A = 1.0\n",
    "B = -1.0\n",
    "C = -0.5\n",
    "\n",
    "pontos = np.random.random( (2,500) )*20+.5\n",
    "funcao = A*pontos[0,:] + B*pontos[1,:] + C\n",
    "\n",
    "pontos_pos = pontos[:, funcao > 0]\n",
    "pontos_neg = pontos[:, funcao < 0]\n",
    "print(pontos_pos.shape, pontos_neg.shape)\n",
    "plt.figure()\n",
    "plt.scatter(pontos_pos[0,:], pontos_pos[1,:], c='b')\n",
    "plt.scatter(pontos_neg[0,:], pontos_neg[1,:], c='r')\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 11\n",
    "**Objetivo: Usar autograd para modelar sistema de classificação usando EQM**\n",
    "\n",
    "Veja que agora fizemos um classificador cujos parâmetros são $A$, $B$ e $C$, e cujas entradas são $x$ e $y$. Em situações reais, raramente sabemos os parâmetros $A$, $B$ e $C$, e gostaríamos de identificá-los através de dados. Para isso, vamos usar a estratégia de descida pelo gradiente, assim como temos feito para o problema de regressão.\n",
    "\n",
    "Gostaríamos de estimar uma função $f(x,y) = Ax+By+C$ de tal forma que $f(x_p,y_p)=1$ se $(x_p,y_p)$ for um ponto da categoria (ou classe) 1, e  $f(x_p,y_p)=-1$ se $(x_p,y_p)$ caso os pontos sejam da categoria 2.\n",
    "\n",
    "O erro do nosso modelo é o EQM que relaciona $f(x,y)$ estimado pelo nosso modelo com os valores desejados 1 e -1.\n",
    "\n",
    "1. Usando o que já fizemos, use o `autograd` para estimar o modelo $f(x,y) = Ax+By+C$ à partir dos dados abaixo.\n",
    "1. Faça um plot semelhante ao do exercício 6 mostrando os pontos de cada categoria de dados com uma cor diferente e a reta estimada.\n",
    "1. Modifique o valor da contante `SEP` para que tenha valores menores e valores maiores. O que acontece com o modelo estimado?\n",
    "1. Modifique seu código para que ele passe a ter muito mais elementos da categoria 1 que elementos da categoria 2. O que acontece com o modelo estimado?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "SEP =3\n",
    "\n",
    "dados_c1 = np.random.randn(2,50) + SEP\n",
    "dados_c2 = np.random.randn(2,50) - SEP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 50) (2, 50)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import autograd.numpy as np_   # Thinly-wrapped version of Numpy\n",
    "from autograd import grad\n",
    "\n",
    "def loss( parametros ):\n",
    "    A, B, C, pontos, val = parametros\n",
    "    est = A*pontos[0,:] + B*pontos[1,:] + C\n",
    "    mse = np_.mean( (est - val)**2)\n",
    "    return mse\n",
    "\n",
    "g = grad(loss)\n",
    "\n",
    "pontos = np.hstack ( (dados_c1, dados_c2))\n",
    "alvos = np.hstack ( (np.ones(50), -1*np.ones(50)))\n",
    "\n",
    "A, B, C = 0.0, 0.1, 0.2\n",
    "alpha = 10**-2\n",
    "\n",
    "for n in range(100):\n",
    "    grad_ = g( (A, B, C, pontos, alvos) )\n",
    "    A -= alpha*grad_[0]\n",
    "    B -= alpha*grad_[1]\n",
    "    C -= alpha*grad_[2]\n",
    "\n",
    "\n",
    "funcao = A*pontos[0,:] + B*pontos[1,:] + C\n",
    "\n",
    "# Reta:\n",
    "# y = -A/B x + C/B\n",
    "x = np.linspace(-3,3,100)\n",
    "y = -A*x/B - C/B\n",
    "\n",
    "pontos_pos = pontos[:, funcao > 0]\n",
    "pontos_neg = pontos[:, funcao < 0]\n",
    "print(pontos_pos.shape, pontos_neg.shape)\n",
    "plt.figure()\n",
    "plt.scatter(pontos_pos[0,:], pontos_pos[1,:], c='b')\n",
    "plt.scatter(pontos_neg[0,:], pontos_neg[1,:], c='r')\n",
    "plt.plot(x, y)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 12\n",
    "**Objetivo: fazer uma formulação matricial para o classificador linear**\n",
    "\n",
    "Até o momento, a função que executamos para o classificador linear é:\n",
    "\n",
    "$$\n",
    "f(x,y) = Ax + By + C\n",
    "$$\n",
    "\n",
    "Nessa formulação, estamos assumindo que nossa entrada tem duas dimensões ($x$ e $y$).\n",
    "\n",
    "Veja como $f(x,y)$ funciona como se $A$ é o \"peso\" atribuído a $x$, e $B$ é o \"peso\" atribuído a $y$. $C$ é uma variável que nos dá uma tendência que é independente das entradas.\n",
    "\n",
    "Essa interpretação funciona para pontos em $2$ dimensões. Se quisermos, podemos assumir que nossa entrada tem $N$ dimensões, expressas em um vetor-coluna $\\boldsymbol x$. Nesse caso, os coeficientes do nosso classificador devem ser colocados também em um vetor-coluna $\\boldsymbol w$, e então ficamos com:\n",
    "\n",
    "$$\n",
    "f(\\boldsymbol x) = b + \\sum_n w_n x_n = \\begin{bmatrix} w_0 & w_1 & ... & w_{N-1} \\end{bmatrix} \\begin{bmatrix} x_0 \\\\ x_1 \\\\ ... \\\\ x_{N-1} \\end{bmatrix} + b = \\boldsymbol w^T \\boldsymbol x + b\n",
    "$$\n",
    "\n",
    "Usando uma formulação matricial, faça um classificador linear para separar os dados abaixo. Quais são os pesos $\\boldsymbol w$ do classificador que você encontrou?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "SEP = 10\n",
    "N_DIMENSOES = 5\n",
    "N_DADOS = 500\n",
    "\n",
    "dados_c1 = np.random.randn(N_DIMENSOES,N_DADOS) + SEP\n",
    "dados_c2 = np.random.randn(N_DIMENSOES,N_DADOS) - SEP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.16123034]\n",
      " [ 0.10122426]\n",
      " [ 0.22259538]\n",
      " [-0.11248491]\n",
      " [ 0.04905519]]\n",
      "-0.024619064692574955\n"
     ]
    }
   ],
   "source": [
    "import autograd.numpy as np_   # Thinly-wrapped version of Numpy\n",
    "from autograd import grad\n",
    "\n",
    "def loss( parametros ):\n",
    "    w, b, pontos, val = parametros\n",
    "    est = w.T @ pontos + b\n",
    "    mse = np_.mean( (est - val)**2)\n",
    "    return mse\n",
    "\n",
    "g = grad(loss)\n",
    "\n",
    "pontos = np.hstack ( (dados_c1, dados_c2))\n",
    "alvos = np.hstack ( (np.ones(N_DADOS), -1*np.ones(N_DADOS)))\n",
    "\n",
    "w = np.random.randn( N_DIMENSOES,1)\n",
    "b = 0.0\n",
    "alpha = 10**-3\n",
    "\n",
    "for n in range(1000):\n",
    "    grad_ = g( (w, b, pontos, alvos) )\n",
    "    w -= alpha*grad_[0]\n",
    "    b -= alpha*grad_[1]\n",
    "\n",
    "print(w)\n",
    "print(b)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 13\n",
    "**Objetivo: avaliar o classificador**\n",
    "\n",
    "Neste momento, já somos capazes de encontrar os pesos $\\boldsymbol w$ e o *bias* $b$ do nosso classificador. Porém: ele funciona bem, na prática?\n",
    "\n",
    "Para saber disso, precisamos de dois conjuntos de dados. Um deles, chamado *conjunto de treino*, será usado para encontrar os pesos do classificador. O outro, chamado *conjunto de teste*, será usado para avaliar se o classificador funciona bem em dados que ele ainda não encontrou. Ambos os conjuntos têm pares de entradas e saídas.\n",
    "\n",
    "Neste exercício, começaremos com dados que já foram pré-processados. Eles foram extraídos do [breast cancer dataset](https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+(Diagnostic)), e já estão organizados para que as entradas e saídas correspondam ao que fizemos nesta aula.\n",
    "\n",
    "1. Verifique as dimensões dos dados no conjunto de treino e no conjunto de teste.\n",
    "1. Inicialize uma vetor de pesos e um *bias* para a classificação.\n",
    "1. Com as inicializações aleatórias, execute o classificador no conjunto de teste e verifique o accuracy.\n",
    "1. Ajuste o vetor de pesos e o *bias* através de reduzir o erro de classificação para o conjunto de *treino*. Ajuste a taxa de aprendizado $\\alpha$ e o número de iterações que serão realizadas.\n",
    "1. Com os pesos e *bias* ajustados, execute o classificador no conjunto de teste e verifique o accuracy. O treino foi efetivo?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "import joblib\n",
    "X_train, X_test, y_train, y_test = joblib.load('./dados_classificacao.joblib')\n",
    "\n",
    "def accuracy(y_test, y_est):\n",
    "    return np.mean(np.sign(y_test)==np.sign(y_est))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Resolva o exercício aqui\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parte 4\n",
    "\n",
    "## Exercício 14\n",
    "*Objetivo: entender o que são decisões binárias em sequência*\n",
    "\n",
    "Vamos jogar um jogo de adivinhações usando um baralho comum, com quatro naipes e 13 cartas por naipe (de \"ás\" a 10, e, adicionalmente, Q, J, K).\n",
    "\n",
    "Neste jogo, teremos dois jogadores. \n",
    "\n",
    "* O jogador 1 deve escolher uma das cartas e manter sua escolha em segredo. \n",
    "* Em seguida, o jogador 2 deve fazer perguntas para tentar adivinhar qual carta foi escolhida.\n",
    "* As perguntas devem ter resposta \"sim\" ou \"não\". Exemplos de perguntas válidas são:\n",
    "    * A carta é um número?\n",
    "    * A carta é um número ímpar?\n",
    "    * A carta é do naipe \"espadas\"?\n",
    "    * A carta é de um naipe preto ou vermelho?\n",
    "    * A carta é uma figura?\n",
    "    * A carta é uma \"dama\"?\n",
    "    * A carta é uma dama de copas?\n",
    "* Não é permitido perguntar se a carta é \"maior que\" outra carta!\n",
    "* O objetivo do jogador 2 é conseguir encontrar a carta com o mínimo de perguntas.\n",
    "* O objetivo do jogador 1 é conseguir escolher a carta que é obriga o jogador 2 a fazer o máximo de perguntas antes de encontrar a carta.\n",
    "\n",
    "## Exercício 15\n",
    "*Objetivo: comparar duas estratégias para o jogo de adivinhações*\n",
    "\n",
    "Uma estratégia direta para o jogo de adivinhações é simplesmente fazer uma lista de todas as cartas e então perguntar sobre elas, uma por uma: \"é um ás de esoadas? é um dois de espadas?\", etc.\n",
    "\n",
    "Uma outra estratégia é a de escolher perguntas que, independente da resposta, eliminam o maior número de possibilidades: \"é uma carta vermelha?\", \"é uma carta de espadas?\", \"é um número ímpar?\", e assim por diante.\n",
    "\n",
    "1. Desenhe *árvores binárias* mostrando como as decisões são progressivamente aplicadas para escolher as cartas.\n",
    "1. Analisando a árvore de cada, responda: qual dessas duas estratégias mais provavelmente leva a encontrar a carta com o mínimo de perguntas? \n",
    "1. Qual característica da árvore binária está ligada ao número de perguntas necessário para encontrar a carta?\n",
    "\n",
    "\n",
    "## Exercício 16\n",
    "*Objetivo: entender o que é entropia de Shannon e sua relação com o jogo de adivinhação*\n",
    "\n",
    "Uma possível maneira de definir o \"poder de decisão\" de uma pergunta é usar a Entropia de Shannnon. A entropia é um conceito ligado à quantidade de informação de uma decisão ou de uma resposta, e foi refinada por [Shannon (1948)](https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf). Não vamos deduzir os *motivos* que levam à formulação proposta por Shannon, mas, se você quiser, pode ler o artigo original - ele é difícil, porém muito claro.\n",
    "\n",
    "A Entropia de Shannon é um valor $H(X)$ ligado a uma variável aleatória $X$. No caso discreto (que é o que nos interessa), a entropia é a soma de $- P(X=x_i) \\log_2(P(X=x_i))$ para cada observação possível $x_i$, ou:\n",
    "\n",
    "$$\n",
    "H(X) = -\\sum_i P(X=x_i) \\log _2(P(X=x_i)).\n",
    "$$\n",
    "\n",
    "Uma formulação que é muito comum encontrar em livros é substituir $P(X=x_i)$ por $p(x_i)$, encontrando:\n",
    "\n",
    "$$\n",
    "H(X) = -\\sum_i p(x_i) \\log _2(p(x_i)).\n",
    "$$\n",
    "\n",
    "A Entropia de Shannon é medida em *bits* (ao longo das próximas aulas vamos entender melhor o motivo disso).\n",
    "\n",
    "**EXEMPLO**\n",
    "\n",
    "Se tivermos uma moeda honesta, temos uma variável aleatória $X$ com p(CARA)=0.5 e p(COROA)=0.5. Então, a Entropia de Shannon da moeda é:\n",
    "\n",
    "$$\n",
    "H(X) = - (0.5 \\log _2(0.5) + 0.5 \\log _2(0.5)) \n",
    "$$\n",
    "\n",
    "Como $\\log _2(0.5)=-1$, então:\n",
    "\n",
    "$$\n",
    "H(X) = - (-0.5 + (-0.5)) = - (-1) = 1 \n",
    "$$\n",
    "\n",
    "**EXEMPLO 2**\n",
    "\n",
    "Se tivermos uma moeda desonesta, com p(CARA)=0.7 e p(COROA)=0.3, então temos uma Entropia de Shannon igual a:\n",
    "\n",
    "$$\n",
    "H(X) = - (0.3 \\log _2(0.3) + 0.7 \\log _2(0.7)) \n",
    "$$\n",
    "\n",
    "Como $\\log _2(0.3)$ é um número mais difícil de calcular, vamos recorrer ao recurso computacional:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8812908992306927\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "print(stats.entropy([0.3, 0.7], base=2))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Isso significa que, ao jogar uma moeda completamente honesta, ganhamos 1 bit de informação, ao passo que, se a moeda for enviesada (com o viés 0.3-0.7), ganhamos somente 0.88 bit de informação.\n",
    "\n",
    "No limite do viés da moeda, temos uma moeda que sempre dá cara. Nesse caso, temos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "print(stats.entropy([0, 1], base=2))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "isto é, jogar uma moeda que sabemos que sempre dá cara (ou que sempre dá coroa) não nos fornece nenhuma informação nova sobre o sistema.\n",
    "\n",
    "Usando a função `stats.entropy`, sem se esquecer de usar `base=2`:\n",
    "\n",
    "1. Encontre a entropia relacionada a jogar uma moeda enviesada com P(CARA) = 0.9.\n",
    "1. No jogo de cartas, *fazer uma pergunta*, sob o ponto de vista do jogador que pergunta, pode ser entendida como *jogar uma moeda*, com probabilidade de \"sim\" e probabilidade de \"não\". Para a pergunta: *a carta é de um naipe vermelho?*, qual é P(sim) e qual é P(não)?\n",
    "1. Qual é a entropia relacionada à pergunta: *a carta é de um naipe vermelho*?\n",
    "1. Qual é a entropia relacionada à pergunta: *a carta é um rei de copas*?\n",
    "1. Como a entropia se relaciona à \"utilidade\" de uma pergunta para nosso jogo de adivinhações?\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercício 17\n",
    "*Objetivo: usar a entropia para otimizar a estratégia do jogo de adivinhações*\n",
    "\n",
    "Vamos organizar nossas perguntas da seguinte forma:\n",
    "\n",
    "1. Sabemos todas as cartas que podem ser candidatas à escolha. São $N$ cartas (começamos com $N=52$)\n",
    "1. Para cada pergunta que podemos fazer, calculamos sua entropia.\n",
    "1. Escolhemos a pergunta usando aquela que dá a máxima entropia.\n",
    "1. Para a possibilidade da resposta ter sido SIM, temos $N \\times P(SIM)$ cartas. Para a possibilidade da resposta ter sido NAO, temos $N \\times P(NAO)$ cartas.\n",
    "1. Após termos nossa resposta, refazemos a estratégia, agora considerando apenas as cartas que restaram.\n",
    "\n",
    "Usando esta estratégia, tente jogar o jogo novamente. Quantas perguntas você conseguiu fazer?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 18\n",
    "*Objetivo: usar uma árvore de decisão*\n",
    "\n",
    "Veja que as decisões que tomamos em nosso jogo de adivinhações estão organizadas em uma árvore. Por isso, esse tipo de algoritmo é chamado de \"árvore de decisão\". No exemplo abaixo, vamos usar uma árvore de decisão para adivinhar números de 1 a 10 à partir das características:\n",
    "\n",
    "* é um número primo?\n",
    "* é divisível por 2? por 3? por 5? por 7?\n",
    "* o número faz parte da [sequência de fibonacci](https://pt.wikipedia.org/wiki/Sequ%C3%AAncia_de_Fibonacci)?\n",
    "\n",
    "Acompanhe o código passo a passo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   número  primo  fibo  div2  div3  div5  div7\n",
      "0       1      0     1     0     0     0     0\n",
      "1       2      1     1     1     0     0     0\n",
      "2       3      1     1     0     1     0     0\n",
      "3       4      0     0     1     0     0     0\n",
      "4       5      1     1     0     0     1     0\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Primeiro, vamos ler nossos dados e colocar o rótulo (ou: o número em si) em uma variável,\n",
    "# e as suas características em outra variável:\n",
    "df = pd.read_excel('numeros.xlsx')\n",
    "#print(df.head())\n",
    "df_rotulo = df['número']\n",
    "df_features = df[ ['primo', 'fibo', 'div2', 'div3', 'div5', 'div7'] ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 2000x2000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Depois, vamos instanciar uma árvore de decisão usando o pacote sklearn:\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "tree = DecisionTreeClassifier(criterion='entropy')\n",
    "\n",
    "# Agora, vamos usar o método .fit() para ajustar os parâmetros da árvore:\n",
    "tree.fit(df_features, df_rotulo)\n",
    "\n",
    "# Podemos visualizar a árvore de decisão em uma figura!\n",
    "from sklearn.tree import plot_tree\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure( figsize=(20,20) )\n",
    "a = plot_tree(tree, feature_names=df_features.columns, fontsize=15, \n",
    "              node_ids=False, impurity=False, filled=True)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Usando a árvore de decisão que foi montada automaticamente, jogue um jogo de \"adivinhar o número\". Quais números sáo mais difíceis de adivinhar, isto é, quais números precisam de mais perguntas para serem adivinhados?\n",
    "1. Como seria uma árvore de decisão para a estratégia de perguntar número por número?\n",
    "1. Qual é a propriedade da árvore que mede a \"dificuldade\" em encontrar um número?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 19\n",
    "*Objetivo: calcular a entropia para diferentes dados em jogos de RPG*\n",
    "\n",
    "Em jogos de RPG, particularmente Dungeons & Dragons, é comum usar dados diferentes do comum, de seis lados. O jogo usa dados de 4 faces, 6, 8, 10, 12 e 20 faces, e eles são referidos como d4, d6, d8, d10, d12 e d20:\n",
    "\n",
    "<img src=\"6dice(cropped).jpg\" height=300  />\n",
    "\n",
    "1. Calcule a entropia relacionada a jogar cada um desses dados, assumindo que são dados honestos (lembre-se de usar base 2!)\n",
    "1. Como a entropia do d4 se relaciona com a entropia da jogada da moeda? E a entropia do d8?\n",
    "1. Em um sistema digital, quantos bits são necessários para representar números que variam de 0 a 1? E de 0 a 3? E de 0 a 7?\n",
    "1. Quantas faces tem um dado cuja jogada tem uma entropia de 5 bits?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "N=2\n",
    "stats.entropy(np.ones(N)/N, base=2)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercício 20\n",
    "*Objetivo: relacionar a entropia à ideia de surpresa*\n",
    "\n",
    "Provavelmente, você teria mais \"surpresa\" com o resultado de um d20 (que pode ser qualquer uma das 20 possibilidades) que com o resultado de uma moeda (que só tem dois resultados possíveis). Escreva com suas palavras um parágrafo relacionando a entropia (que é uma característica mensurável) com a surpresa (que é uma sensação subjetiva)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Projeto\n",
    "\n",
    "Neste projeto, vamos usar classificadores para identificar *quais são os fatores de risco para o acidente vascular cerebral (AVC)*. Um AVC (*stroke*) é um dano cerebral causado pela interrupção de seu fluxo sanguíneo. Ter um AVC é um problema sério porque pode levar a sequelas, então é melhor preveni-lo do que tentar lidar com suas consequências.\n",
    "\n",
    "Temos à nossa disposição um conjunto de dados para [predição de AVCs](https://www.kaggle.com/datasets/fedesoriano/stroke-prediction-dataset). O que faremos é:\n",
    "\n",
    "1. Treinar um classificador para predizer se houve ou não houve AVCs\n",
    "1. Verificar a acurácia do classificador\n",
    "1. Identificar quais são os fatores que mais provavelmente estão ligados a ter AVCs\n",
    "\n",
    "## Teoria\n",
    "\n",
    "### Separando linhas de dados em treino e teste\n",
    "\n",
    "O que faremos será avaliar um classificador. Lembre-se que para fazer o classificador tivemos que usar uma base de dados pré-classificada. Porém, o que gostaríamos de saber é se, ao ser colocado em produção, o classificador terá um bom desempenho.\n",
    "\n",
    "Para isso, vamos partir de uma premissa (vou chamar de *premissa número 1* mas esse não é um nome oficial) que é muito importante: a de que nossa base de dados é composta de elementos amostrados aleatoriamente do conjunto total de dados. Nessas condições, a distribuição dos dados na nossa base de dados é a mesma distribuição dos dados que encontraremos no mundo real.\n",
    "\n",
    "Claro que gostaríamos de saber como nosso classificador se comporta no mundo real, e não na amostra dele que compõe nossa base de dados! Então, precisamos ao menos de ter alguns dados que seguem a mesma distribuição dos dados do mundo real, e que serão usados nas mesmas condições que os dados do mundo real.\n",
    "\n",
    "Por isso, dividimos nosso conjunto de dados em dois conjuntos: treino e teste. O conjunto de treino é o que será usado para treinar (`fit`) os nossos classificadores. O conjunto de teste será usado para testar (`score`) os classificadores. O conjunto de teste existe para simular uma situação de produção (como se o classificador estivesse operando), então ele não pode ser usado em hipótese alguma para nenhum tipo de ajuste de parâmetros. Ao mesmo tempo, o conjunto de treino é aquele que foi usado para \"ensinar\" rótulos corretos aos classificadores, então o desempenho dos classificadores no conjunto de treino não é representativo de seu desempenho em produção.\n",
    "\n",
    "Para dividir os conjuntos de treino e teste, você pode usar a função `train_test_split` do scikit-learn:\n",
    "\n",
    "    from sklearn.model_selection import train_test_split\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.5)\n",
    "\n",
    "### Analisando os dados\n",
    "\n",
    "Antes de começar qualquer coisa, vamos (como sempre) olhar para os dados que temos. Na nossa tabela, temos uma coluna com a identificação do paciente - essa é uma ID única, anônima, que permite referenciar ao paciente. Também, temos várias colunas com características do paciente: idade, sexo, se fuma, etc. Por fim, temos uma coluna com o *outcome*, que é a coluna `stroke`. Para usar corretamente os classificadores do scikit-learn, você deve separar suas tabelas entre as que têm dados de \"entrada\" (as features) das que têm dados de \"saída\" (os *outcomes*).\n",
    "\n",
    "Outra coisa importante é que os dados deste dataset podem ser categóricos, e nossos sistemas não lidam bem com eles. Por isso, precisamos convertê-los para dados numéricos, por exemplo usando one-hot encoding. Pandas implementa a conversão para one-hot encoding usando `pd.get_dummies(df)`. Um exemplo de seu uso é o seguinte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coluna_de_teste</th>\n",
       "      <th>coluna_que_fica_inalterada_porque_ja_era_numerica</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>categoria_1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>categoria_2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>categoria_3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>categoria_1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  coluna_de_teste  coluna_que_fica_inalterada_porque_ja_era_numerica\n",
       "0     categoria_1                                                  3\n",
       "1     categoria_2                                                  2\n",
       "2     categoria_3                                                  1\n",
       "3     categoria_1                                                  2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df['coluna_de_teste'] = ['categoria_1', 'categoria_2', 'categoria_3', 'categoria_1']\n",
    "df['coluna_que_fica_inalterada_porque_ja_era_numerica'] = [3, 2, 1, 2]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>coluna_que_fica_inalterada_porque_ja_era_numerica</th>\n",
       "      <th>coluna_de_teste_categoria_1</th>\n",
       "      <th>coluna_de_teste_categoria_2</th>\n",
       "      <th>coluna_de_teste_categoria_3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   coluna_que_fica_inalterada_porque_ja_era_numerica  \\\n",
       "0                                                  3   \n",
       "1                                                  2   \n",
       "2                                                  1   \n",
       "3                                                  2   \n",
       "\n",
       "   coluna_de_teste_categoria_1  coluna_de_teste_categoria_2  \\\n",
       "0                            1                            0   \n",
       "1                            0                            1   \n",
       "2                            0                            0   \n",
       "3                            1                            0   \n",
       "\n",
       "   coluna_de_teste_categoria_3  \n",
       "0                            0  \n",
       "1                            0  \n",
       "2                            1  \n",
       "3                            0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_ = pd.get_dummies(df)\n",
    "df_.head()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Avaliando o classificador\n",
    "\n",
    "Quando o classificador atua sobre dados, encontramos, para cada entrada, uma saída predita, ou:\n",
    "\n",
    "$$\n",
    "\\hat{y} = f(X),\n",
    "$$\n",
    "onde $f(.)$ é a função que implementa o classificador, $X$ são os dados de entrada e $\\hat{y}$ são os dados de saída.\n",
    "\n",
    "Neste momento, o que gostaríamos é de saber quantas vezes o classificador *acertou* dentre todas aquelas, isto é, precisamos:\n",
    "\n",
    "1. Comparar cada valor de $\\hat{y}$ a cada valor correspondente de $y$ (a saída \"gabarito\"),\n",
    "1. Dividir o número de vezes que a saída é igual pelo número total de valores\n",
    "\n",
    "O nome desta medida é acurácia (*accuracy*). Se você quiser, pode usar o [accuracy implementado pelo scikit-learn](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html) para fazer essa avaliação.\n",
    "\n",
    "#### Hipótese nula\n",
    "\n",
    "A acurácia é uma medida válida de desempenho do classificador, mas é importante sempre colocá-la em contraste com as características do próprio conjunto de dados que foram utilizados. Um caso bastante patológico é o de termos um dataset no qual, por exemplo, 70% dos exemplos são da classe A e 30% são da classe B. Nesse caso, se nosso classificador sempre dizer que qualquer elemento é da classe A, ele terá acurácia de 70%, mas essa acurácia não significa um bom desempenho. Por isso, sempre que usamos a acurácia como medida de desempenho, usamos como base para comparação um classificador que sempre \"chuta\" a classe mais frequente no dataset.\n",
    "\n",
    "### Referências bibliográficas\n",
    "\n",
    "Na nossa análise de dados, podemos encontrar vários elementos ligados ao fenômeno que estamos analisando. Por exemplo, podemos descobrir que o fato de alguém preferir suco de laranja ao suco de maracujá é um fator que pode determinar o AVC. O problema disso é que não podemos saber, só com base nisso, se essa ligação é uma característica dos nossos dados ou se é uma característica geral do fenômeno. Por isso, sempre buscamos saber mais e verificar se há outros trabalhos que também apontam as mesmas ligações que encontramos. Para este tipo de análise, é importante encontrar trabalhos que foram publicados em veículos com revisão por pares (conferências e revistas são válidos, mas não materiais auto-publicados como blogs, vídeos ou *pre-prints*). Em especial, neste trabalho, vamos nos restringir apenas a materiais que estão disponíveis gratuitamente (open access), isto é, não utilizaremos materiais que precisam do pagamento de assinatura.\n",
    "\n",
    "\n",
    "## Descrição do projeto\n",
    "\n",
    "Neste projeto, o grupo deverá projetar e avaliar o classificador linear e o classificador por árvore de decisão no problema de predizer AVCs à partir da base de dados que está disponível no Kaggle. Também, deverá avaliar quais foram os fatores de risco identificados por cada um dos classificadores e, após, deverá verificar se esses fatores de risco identificados pelos classificadores já foram identificados anteriormente por algum estudo na área.\n",
    "\n",
    "Anotações importantes:\n",
    "\n",
    "1. O grupo deve enviar um link para o repositório GitHub onde está localizado o projeto.\n",
    "2. No diretório principal do repositório, deve haver um *notebook* comentado `demo.ipynb`, que, quando executado, executa todos os testes que geram os resultados alcançados.\n",
    "\n",
    "**ENTREGAS**\n",
    "* Link para o repositório onde está o projeto.\n",
    "* No `README.md` do repositório, deve haver um resumo, com até 400 palavras, explicando qual foi a metodologia usada, quais foram os principais resultados encontrados, e o que o grupo descobriu sobre AVCs à partir da análise dos dados.\n",
    "* O `demo.ipynb` deve estar comentado, célula a célula, em Markdown, explicando em linguagem natural a importância de cada passo e comentanto os resultados da execução de cada célula.\n",
    "* O `demo.ipynb` deve ser colocado no repositório já executado, isto é, com todos os dados já gerados, de forma que seja possível visualizá-lo inteiramente sem executar as células.\n",
    "\n",
    "\n",
    "**RUBRICA**\n",
    "\n",
    "O projeto será avaliado usando três rubricas. [Duas delas dizem respeito à redação e ao código apresentado](rubricas.md), e são compartilhados por todos os projetos. Em especial, a rubrica de *argumentação* será aplicada ao conjundo do `README.md` e das células em markdown do `demo.ipynb`. Este projeto tem ainda requisitos específicos que estão na rubrica abaixo. Os níveis são cumulativos, isto é, para passar de um nível, *todos* os requisitos dele devem ser cumpridos. A nota final é baseada na rubrica em que o trabalho obtiver o *menor* desempenho. As rubricas foram inspiradas nos níveis da [Taxonomia de Bloom](https://cft.vanderbilt.edu/guides-sub-pages/blooms-taxonomy/).\n",
    "\n",
    "| Nível | Descrição | [Tax. de Bloom](https://cft.vanderbilt.edu/guides-sub-pages/blooms-taxonomy/) |\n",
    "| --- | --- | --- |\n",
    "| F | Não entregue, entregue sem completar o `README.md`, entregue sem o `demo.ipynb`, entregue sem resolver o problema que foi proposto.  | Não fez |\n",
    "| E | Entregue, mas comete erros metodológicos graves: deixar de separar treino e teste, deixar de escolher as features relevantes, deixar de usar as variáveis categóricas em one-hot encoding | Entender |\n",
    "| D | O projeto tem erros na avaliação de desempenho (accuracy) ou deixa de comparar o accuracy obtido com o classificador da hipótese nula. | Compreender |\n",
    "| C | O projeto avalia corretamente o accuracy, mas deixa de verificar quais são as features mais relevantes para a classificação | Compreender |\n",
    "| B | O método foi aplicado corretamente e o grupo encontrou quais são fatores de risco para AVC à partir da analise de seu dataset com uma metodologia consistente | Aplicar |\n",
    "| A | Além da aplicação correta do método, o grupo encontrou uma ou mais referências bibliográficas (citadas no `README.md`) que corroboram com suas descobertas, ou, alternativamente, encontrou referências que encontraram o oposto do que foi descoberto pelo grupo | Analisar |\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "42e34ec1a81382d7a35a13fd98192c35dabe0890684b7b0a474deec672e3df02"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}