notebooks/Aula_005_Introdução_ao_Deep_Learning.ipynb

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      "name": "Aula 005: Introdução ao Deep Learning.ipynb",
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        "<a href=\"https://colab.research.google.com/github/carlosfab/escola-data-science/blob/master/notebooks/Aula_005_Introdu%C3%A7%C3%A3o_ao_Deep_Learning.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "<p align=\"center\"><img src=\"https://raw.githubusercontent.com/carlosfab/escola-data-science/master/img/eds.png\" height=\"100px\"></p>\n",
        "\n",
        "# Aula 005: Introdução ao Deep Learning\n",
        "\n",
        "Nesta aula começaremos a falar sobre os princípios do Deep Learning, passando pelos conceitos de Modelos Paramétricos, Regressão Logística (com perspectiva de *deep learning*), *score function* e entender como uma rede neural é capaz de classificar uma imagem.\n",
        "\n",
        "Na próxima aula iremos entrar em cost function e um algoritmo conhecido como ***Gradient Descente*** **(GD)** -  a cereja do bolo!\n",
        "\n",
        "Para você ter uma ideia a respeito da motivação em aprendê-lo, veja o que diz *Goodfellow et al (2016)*  em seu livro *Deep Learning*, referência em referência absoluta na área:\n",
        "\n",
        "\n",
        "> *Praticamente, tudo que se chama deep learning é movido por um algoritmo muito importante: Stochastic Gradient Descent (SGD).*\n",
        "\n",
        "Mas antes de entrar no SGD diretamente, vamos dar uma olhada em alguns conceitos primários.\n",
        "\n",
        "\n",
        "\n"
      ]
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      "metadata": {
        "id": "Ub1ehmI7hKlB",
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      "source": [
        "## Modelos Paramétricos\n",
        "\n",
        "Um modelo de *machine learning* tem a capacidade de aprender padrões a partir de dados de *input* durante uma etapa conhecida como treinamento. \n",
        "\n",
        "Esse modelo é representado não por todos os dados que o alimentam, mas por um número limitado de parâmetros. Ou seja, independente do tamanho do meus dados de treino, é possível **generalizar**, representar os mesmos por meio de parâmetros.\n",
        "\n",
        "\n",
        "<p align=\"center\">\n",
        "<img height=\"500\" src=\"https://raw.githubusercontent.com/carlosfab/escola-data-science/master/img/classificacao-anvs.png\">\n",
        "</p>\n",
        "\n",
        "Considere que você queira treinar um modelo de *deep learning* para reconhecer se há uma aeronave em uma imagem. As seguintes classificações são possíveis:\n",
        "\n",
        "* **1:** Quando é detectada uma aeronave na imagem; e \n",
        "* **2:** Quando não é detectada uma aeronave na imagem.\n",
        "\n",
        "Basicamente, as imagens normais que usaremos é composta por 3 canais de cores (RGB). Se formos olhar mais de perto, veremos temos 3 matrizes (uma para cada canal) e que cada pixel é representado por um número entre $0-255$.\n",
        "\n",
        "<p align=\"center\">\n",
        "<img height=\"350\" src=\"https://raw.githubusercontent.com/carlosfab/escola-data-science/master/img/anv-rgb.png\">\n",
        "</p>\n",
        "\n",
        "## Classificação Binária \n",
        "\n",
        "Claramente, nós seres humanos podemos identificar que existe algum tipo de padrão que faz com que nosso cérebro reconheça rapidamente se uma imagem é um avião ou não. Trazendo para o lado da matemática, assuma que existe uma função $y = f^{*}(x)$ que mapeia o nosso *input* $x$ para uma categoria $y \\in \\{0, 1 \\}$.\n",
        "\n",
        "A imagem do caça acima tem dimensões iguais a $64 \\times 64$ *pixels*. No lugar de termos 3 matrizes  $64 \\times 64$ *pixels*, podemos gerar um vetor $x$ único contendo todos seus valores:\n",
        "\n",
        "$$\n",
        "\\begin{equation}\n",
        "\\begin{aligned}\n",
        "x&=\n",
        "    \\begin{bmatrix}\n",
        "        123 \\\\ 250 \\\\ \\vdots \\\\ 70 \\\\ 100 \\\\ \\vdots \\\\130\n",
        "    \\end{bmatrix} \n",
        "&&n_x = 64 \\times 64 \\times 3 = 12288\n",
        "\\end{aligned}\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "Dependendo a literatura adotada, você vai ter notações matemáticas e teóricas divergentes. Essas divergências podem ser puramente relacionadas aos símbolos e letras convencionadas ou em algum conceito.\n",
        "\n",
        "Também não é minha ideia mergulhar fundo nessa parte mais matemática, então resolvi simplificar o que poderia ser simplificado (com menos rigor acadêmico), mas sem perder a essência. Vamos ver as convenções e notações que eu irei usar.\n",
        "\n",
        "* Uma única amostra de treino é representado pela tupla:\n",
        "\n",
        "$$\n",
        "\\begin{align}\n",
        "(x, y) && onde && x& \\in \\rm I\\!R^{n_x}, \\\\\n",
        "&& && y& \\in \\{0, 1\\}\n",
        "\\end{align}\n",
        "$$\n",
        "\n",
        "* Para um conjunto de $m$ amostras de treinamento:\n",
        "\n",
        "$$\n",
        "m\\text{-amostras: } \\{ (x^{(1)}, y^{(1)}), (x^{(2)}, y^{(2)}), \\dots, (x^{(m)}, y^{(m)}) \\}\n",
        "$$\n",
        "\n",
        "Essa notação acima é muito didática, porém você também consegue representar a mesma coisa, porém de forma mais compacta usando a notação da Álgebra Linear. Veja como eu represento matricialmente um conjunto de dados de treino contendo $m$ amostras diferentes.\n",
        "\n",
        "$$\n",
        "\\begin{aligned}\n",
        "X&=\n",
        "\\begin{bmatrix}\n",
        "    \\bigg\\rvert & \\bigg\\rvert &  & \\bigg\\rvert \\\\\n",
        "    x^{(1)} & x^{(2)} & \\dots & x^{(m)} \\\\\n",
        "    \\bigg\\rvert & \\bigg\\rvert &  & \\bigg\\rvert\n",
        "\\end{bmatrix}\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Um detalhe que devemos sempre nos atentar diz respeito à dimensionalidade. Tenha em mente que $X \\in \\rm I\\!R^{n_x \\ \\times \\ m}$, o que pode ser verificado diretamente no código checando o atributo do *array* com `X.shape` $= (n_x, m)$.\n",
        "\n",
        "Convenientemente, para facilitar implementações e operações matriciais, usaremos um vetor horizontal $y$ contendo os *outputs labels*.\n",
        "\n",
        "$$\n",
        "\\begin{equation}\n",
        "\\begin{aligned}\n",
        "Y&=\n",
        "    \\begin{bmatrix}\n",
        "        y^{(1)}, y^{(1)}, \\dots, y^{(m)}\n",
        "    \\end{bmatrix} \n",
        "\\end{aligned}\n",
        "\\end{equation}\n",
        "$$\n",
        "\n",
        "Em relação à dimensionalidade do vetor, temos que $Y \\in \\rm I\\!R^{1 \\ \\times \\ m}$, o que pode ser verificado diretamente no código checando `Y.shape` $= (1, m)$."
      ]
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        "## Classificador Linear: Das Imagens para os *Labels*\n",
        "\n",
        "Dentro do campo de *machine learning* (ML), temos uma classe de problemas conhecida como classificação estatística. Um classificador linear consegue tomar a decisão de classificar um determinado objeto mediante combinação linear das suas características (*features*).\n",
        "\n",
        "Nesta seção, eu irei falar sobre Regressão Logística, um algoritmo de ML amplamente usado para classificação em problemas de aprendizado supervisionado.\n",
        "\n",
        "### Regressão Logística\n",
        "\n",
        "\n",
        "No exemplo de identificar se nossa foto é um avião ou não, temos um problema de classificação binária onde você recebe um vetor $x \\in \\rm I\\!R^{n_x}$ contendo as *features* (os *pixels* da imagem) e o algoritmo de Regressão Logística retorna a probabilidade $\\hat{y} = P(y=1 | x)$ de ser um avião.\n",
        "\n",
        "Para entender o algoritmo GD, precisamos entrar em dois conceitos-chaves:\n",
        "\n",
        "1. *Score Function*\n",
        "2. *Cost Function*\n",
        "\n",
        "#### 1. *Score Function*\n",
        "\n",
        "*Machine learning*, ou aprendizado de máquina é o nosso campo de estudo. O \"*learning*\" significa que de alguma maneira o computador é capaz de aprender. Essa maneira é por meio da otimização dos parâmetros $\\theta \\in \\rm I\\!R^{n_x}$ e $b \\in \\rm I\\!R$.\n",
        "\n",
        "A *score function* é uma função que vai receber o nosso *input* (no exemplo usado aqui, uma imagem) e mapear os dados para as classes de *labels*. A função mais simples possível para fazer isso é o **mapeamento linear**:\n",
        "\n",
        "$$\n",
        "f(x, \\theta, b) = \\hat{y} = \\theta^Tx + b\n",
        "$$\n",
        "\n",
        "**Uma pausa.**\n",
        "\n",
        "Lembra que estamos falando de classificação de imagens, e da probabilidade dessa imagem ser um avião ou não?\n",
        "\n",
        "O problema é que a nossa *score function*, do jeito que está, pode retornar qualquer valor. Só que se eu espero obter uma probabilidade como *output*, é esperado que $0 \\leq \\hat{y} \\leq 1$.\n",
        "\n",
        "Uma das maneiras de fazer isso é usando uma função de ativação conhecida como **função sigmóide**.\n",
        "\n",
        "$$\n",
        "\\sigma(z) = \\frac{1}{1 + e^{-z}}\n",
        "$$"
      ]
    },
    {
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      "metadata": {
        "id": "bG-vzlQ3MJ6h",
        "colab_type": "code",
        "outputId": "67e0ae0d-ae21-4dfa-8598-8668dc504361",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
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      "source": [
        "# importar pacotes necessários\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# criar um set entre -10 e 10 e aplicar a função sigmóide\n",
        "x = np.arange(-10, 10)\n",
        "y = 1 / (1 + np.exp(-x))\n",
        "\n",
        "# plotar a curva sigmoidal\n",
        "plt.plot(x, y)\n",
        "plt.vlines(0, 0, 1, colors='r', linestyles='dashed')\n",
        "plt.show()"
      ],
      "execution_count": 1,
      "outputs": [
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NZlBWus+FiajLRSQ6De9ejfuHHfUcO9nO0vPU3SLJQWfoIr1UXlnHiLwsPjy50O9SRAAF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\ndBGRFKFAFxFJEQp0EZEUoUAXEUkR/x/5uOGO4hH7zgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vmZqgr2XX36k",
        "colab_type": "text"
      },
      "source": [
        "Em suma, o *output* que queremos estará no formato \n",
        "\n",
        "$$\\hat{y} = \\sigma(\\theta^Tx + b) = \\frac{1}{1 + e^{-(\\theta^Tx + b)}}$$\n",
        "\n",
        "\n",
        "Como estamos falando de NN (*feedforward neural networks*, mais especificamente), o nosso objetivo é aproximar essa função $f(x, \\theta, b) = f^{*}(x, \\theta, b)$. Isso significa que durante a fase de treinamento nós conduzimos $f(x, \\theta, b)$ para equiparar $f^{*}(x, \\theta, b)$.\n",
        "\n",
        "Voltando a função de ativação, utilizamos a mesma para (1) inserir não-lineariedade no problema e (2) gerar probabilidade para um problema de classificação binária.\n",
        "\n",
        "Utilizando a função de ativação aplicada na *score function*, ou seja $\\sigma( \\theta^T x + b)$, conseguiremos mapear qualquer valor para dentro do intervalo $0 \\leq \\hat{y} \\leq 1$. Veja um exemplo de onde usamos essa teoria para prever se uma imagem é um avião ou não.\n",
        "\n",
        "<p align=\"center\">\n",
        "<img height=\"350\" src=\"https://raw.githubusercontent.com/carlosfab/escola-data-science/master/img/passe-nn.png\">\n",
        "</p>\n",
        "\n",
        "As etapas ilustradas na imagem acima são:\n",
        "\n",
        "1. Transformar a imagem em um vetor.\n",
        "2. Multiplicar o valor de cada pixel de $x$ por um peso de $w$.\n",
        "3. Obter o valor de $z = w^T x + b$.\n",
        "4. Obter a probabilidade $\\hat{y} = P(y=1 | x)$ de ser um avião. Ou seja, obter o valor de $\\hat{y} = \\sigma(z)$.\n",
        "5. Classificar a imagem com o label `avião` ($0.91 \\gt 0.5)$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UMvjlUbled9V",
        "colab_type": "text"
      },
      "source": [
        "## Visualizando uma imagem\n",
        "\n",
        "Para mostrar os *pixels* de uma imagem, vamos importar um exemplo com o OpenCV e ver o *array* que representa a intensidade de cada um."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4KXAkw9L7S-T",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# importar o OpenCV\n",
        "import cv2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FFU5oyYONcYg",
        "colab_type": "code",
        "outputId": "8fc70f55-99f7-45b9-eba8-bf84875c28f7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 233
        }
      },
      "source": [
        "# baixar uma imagem de exemplo\n",
        "!wget https://raw.githubusercontent.com/carlosfab/escola-data-science/master/img/aviao_64x64.jpg\n",
        "!ls"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2020-03-28 08:45:48--  https://raw.githubusercontent.com/carlosfab/escola-data-science/master/img/aviao_64x64.jpg\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 151.101.0.133, 151.101.64.133, 151.101.128.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|151.101.0.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 14272 (14K) [image/jpeg]\n",
            "Saving to: ‘aviao_64x64.jpg’\n",
            "\n",
            "aviao_64x64.jpg     100%[===================>]  13.94K  --.-KB/s    in 0.01s   \n",
            "\n",
            "2020-03-28 08:45:53 (1.15 MB/s) - ‘aviao_64x64.jpg’ saved [14272/14272]\n",
            "\n",
            "aviao_64x64.jpg  sample_data\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2rOM869r7S02",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# ler a imagem usando o OpenCV\n",
        "img = cv2.imread(\"aviao_64x64.jpg\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LhET5mbf7StH",
        "colab_type": "code",
        "outputId": "ddd4fe47-5c59-4cca-8a26-0c3dee88842a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# ver suas dimensões\n",
        "img.shape"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(64, 64, 3)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XgoLIoQvNvCP",
        "colab_type": "code",
        "outputId": "96f2c85d-4e34-4c0a-aea9-bc9de1f23b41",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "# plotar a imagem usando o `matplotlib`\n",
        "plt.imshow(cv2.cvtColor(img, cv2.COLOR_BGR2RGB))\n",
        "plt.show()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dMhX10lR4LqmU7FPrYQMRzytp7uD8AuvVY2PsIttl3JOz8hzEmDAhyEK6knwt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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cE31rpw0JpsH",
        "colab_type": "text"
      },
      "source": [
        "#### **Referências**\n",
        "\n",
        "*Goodfellow, I.; Bengio, Y.; Courville, A. **Deep Learning**. MIT Press, 2016.*"
      ]
    }
  ]
}