Q03_Pratica_IA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 03. Regularização"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Importação das bibliotecas utilizadas na questão:\n",
    "1. Numpy = Fornece um grande conjunto de funções e operações de biblioteca \n",
    "que auxiliam na realização de cálculos numéricos e manipulação de matrizes.\n",
    "\n",
    "2. Matplotlib = Trata-se de uma biblioteca que é utilizada para plotar gráficos\n",
    "\"\"\"\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Carregue os dados contidos no arquivo ex1data3.txt. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Função responsável por fazer a leitura dos datasets.\n",
    "Parâmetros da função: file_name = nome do arquivo, \n",
    "delimeter_ = trata-se do que tá separando cada valor do dataset e o \n",
    "encoding_ = Trata-se do código em que o dataset foi codificado \n",
    "\"\"\"\n",
    "def load_dataset(file_name, delimiter_, encoding_):\n",
    "    return np.genfromtxt(file_name, delimiter = delimiter_, encoding=encoding_)\n",
    "\n",
    "data = load_dataset('./datasets/ex1data3.txt', ' ','UTF-8')\n",
    "data # Exibe os valores do dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- O arquivo contem 47 linhas e 6 colunas de dados. Cada coluna se refere a uma variável. Neste problema, deve-se desenvolver um modelo onde a variável da coluna 6 será estimada a partir das demais variáveis. Os dados apresentados referem-se a um problema de estimação do preço de casas. As variáveis 1, 2, 3, 4 e 5 são características dos imóveis e serão utilizadas como entrada do problema de regressão. A variável 6 é o preço do imóvel.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pega todos os valores do dataset, exceto os valores da última coluna e cria uma nova coluna com valores 1\n",
    "def get_x(data):\n",
    "    x = data[:, :-1]\n",
    "    m = x.shape[0]\n",
    "    ones = np.ones((m, 1))\n",
    "    return np.concatenate((ones, x), axis = 1)\n",
    "\n",
    "# Pega os últimos valores da coluna do dataset e faz a transposta\n",
    "def get_y(data):\n",
    "    y = data[:, -1]\n",
    "    y = np.array([y])\n",
    "    return y.T\n",
    "\n",
    "# Função responsável por calcular os mínimos quadrados regulares\n",
    "def min_squares_regularized(data, reg_coef):\n",
    "    X = get_x(data)\n",
    "    y = get_y(data)\n",
    "    gram = X.T.dot(X)\n",
    "    identity = np.identity(len(gram))\n",
    "    identity[0,0] = 0\n",
    "    temp = gram + identity*reg_coef\n",
    "    return np.linalg.inv(temp).dot(X.T.dot(y)) \n",
    "\n",
    "# Função responsável por cálcular o error quadrado médio\n",
    "def mqe(data, w):\n",
    "    X = get_x(data)\n",
    "    y = get_y(data)\n",
    "    m = X.shape[0]\n",
    "    return (1.0/(2.0*m))*np.sum((X.dot(w) - y)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Divida o conjunto de dados entre treino e teste. Para este problema, os primeiros 30 dados serão utilizados para treino e o restante será usado para teste.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# No treino pegamos os 30 primeiros valores do dataset e no teste do 31 até o fim\n",
    "treino = data[:30, :]\n",
    "teste = data[30:, :]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Encontre os coeficientes da regressão utilizando o método dos mínimos quadrados regularizado para os seguintes valores de λ = [0 1 2 3 4 5]. Utilize o conjunto de treinamento.\n",
    "  - **Apresentar**: Valores finais dos coeficientes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Criamos um array que ficou com os valores dos coeficientes de regressão\n",
    "coeficientes_de_regressao = [0, 1, 2, 3, 4, 5]\n",
    "\n",
    "# O laço de repetição ele percorre todo o array criado anteriormente e aplica na função do mínimos quadrados\n",
    "for coef in coeficientes_de_regressao:\n",
    "    print(\"Valores do coeficiente {}:\".format(coef))\n",
    "    print(min_squares_regularized(treino, coef))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quais variáveis parecem ser menos relevantes para a regressão?\n",
    "\n",
    "Ao realizar a análise dos pesos finais da regressão com o coeficiente de regularização 5, percebe-se que as variáveis menos relevantes são as de número 4 e 5. Porque os valores de ambas variáveis ficaram uma casa decimal abaixo dos valores das demais variáveis. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Encontrar o valor do EQM para os dados de treinamento e de teste para cada um dos valores de λ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Criação de dois arrays para armazenar os erros quadráticos médio\n",
    "mqe_treino = []\n",
    "mqe_teste = []\n",
    "\n",
    "\"\"\"\n",
    "Nesse laço de repetição, criamos a váriavel coef e iremos percorrer todo o array do coeficiente de regressão.\n",
    "Dentro do laço chamos duas funções que criamos anteriormente, a primeira é a dos minimos quadráticos, onde passamos os 30 primeiros elementos do dataset e \n",
    "o seu coefiente. \n",
    "Com base nas duas variáveis criadas anteriormente, adicionamos ao array os valores do erro quadrático médio\n",
    "\"\"\"\n",
    "for coef in coeficientes_de_regressao:\n",
    "    w = min_squares_regularized(treino, coef)\n",
    "    mqe_treino.append(mqe(treino, w))\n",
    "    mqe_teste.append(mqe(teste, w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Apresentar: Dois gráficos. EQM x λ no conjunto de treinamento e EQM x λ no conjunto de teste"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotagem do gráfico, utilizamos o matplotlib para nos auxiliar na plotagem do gráfico.\n",
    "treino_plt, = plt.plot(coeficientes_de_regressao, mqe_treino, color = 'r', label=\"Treino\")\n",
    "teste_plt, = plt.plot(coeficientes_de_regressao, mqe_teste, color = 'g', label=\"Teste\")\n",
    "primeira_legenda = plt.legend(handles=[treino_plt], loc=3)\n",
    "ax = plt.gca().add_artist(primeira_legenda)\n",
    "plt.legend(handles=[teste_plt], loc=2)\n",
    "plt.xlabel('Coeficientes')\n",
    "plt.ylabel('Erro Quadrático Médio (EQM)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Como os valores dos coeficientes variam com λ ? Explique o motivo.\n",
    "\n",
    "Ficou percepitível que os pesos diminuiam conforme o valor do coeficiente de regularização aumentava. Isso acorre pois o coeficiente de regularização funciona como uma espécie de penalização para cada um dos pesos. Sendo assim, os pesos que contribuiem para a diminuição do erro serão os menos penalizados e os pesos que menos contribuiem serão os mais penalizados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comente o crescimento/decrescimento dos erros presente nas figuras EQM x λ\n",
    "\n",
    "No gráfico plotado anteriormente, vemos que o erro no conjunto de teste diminuiu e por sua vez o erro no conjunto de treinamento aumentou seguindo o aumento do coeficiente de regularização. Isso ocorre devido ao modelo inicial com λ=0 ter sofrido um overfitting em relação ao processo de treinamento dos dados. Entretanto, conforme o aumento do λ, esse overfitting acaba diminuindo e o modelo passa a ter uma capacidade de generalização melhor, fazendo com que esse erro no conjunto de testes diminua enquanto o erro no conjunto de treinamento aumenta."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.10 64-bit",
   "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": "3.8.10"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}