{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在前一节的例子中，我们只有一个自变量，也就是只有一个特征 $(X)$，但是通过数学变换，我们可以扩展到多个特征 $(X, X^2, ..., X^n)$，并得到多项式回归。模型的结果如下图所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "# 创建图形，并将图形划分成 2*2 四格\n",
    "plt.figure(figsize=(15,8))\n",
    "ax1 = plt.subplot(2,2,1)\n",
    "ax2 = plt.subplot(2,2,2)\n",
    "ax3 = plt.subplot(2,2,3)\n",
    "ax4 = plt.subplot(2,2,4)\n",
    "\n",
    "def draw_polynomial(X, Y, degree):\n",
    "    polynomial = PolynomialFeatures(degree = degree)\n",
    "    X_t = polynomial.fit_transform(X)\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_t, Y)\n",
    "    x = np.linspace(30, 60, 100).reshape(-1, 1)\n",
    "    x_t = polynomial.fit_transform(x.reshape(x.shape[0], 1))\n",
    "    y = model.predict(x_t)\n",
    "    plt.xlim(30, 60)\n",
    "    plt.ylim(100, 600)\n",
    "    plt.plot(x, y)\n",
    "\n",
    "X = np.array([39.93, 42.05, 43.18, 44.68, 49.87, 53.57]).reshape(-1, 1)\n",
    "Y = np.array([199,   290,   298,   310,   399,   420]).reshape(-1, 1)\n",
    "\n",
    "# 一次回归\n",
    "plt.sca(ax1)\n",
    "plt.scatter(X, Y)\n",
    "plt.text(31,540,r'$y=a_0+a_1x$',fontsize=12)\n",
    "draw_polynomial(X, Y, 1)\n",
    "\n",
    "# 二次回归\n",
    "plt.sca(ax2)\n",
    "plt.scatter(X, Y)\n",
    "plt.text(31,540,r'$y=a_0+a_1x+a_2x^2$',fontsize=12)\n",
    "draw_polynomial(X, Y, 2)\n",
    "\n",
    "# 三次回归\n",
    "plt.sca(ax3)\n",
    "plt.scatter(X, Y)\n",
    "plt.text(31,540,r'$y=a_0+a_1x+a_2x^2+a_3x^3$',fontsize=12)\n",
    "draw_polynomial(X, Y, 3)\n",
    "\n",
    "# 十次回归\n",
    "plt.sca(ax4)\n",
    "plt.scatter(X, Y)\n",
    "plt.text(31,540,r'$y=a_0+a_1x+...+a_{10}x^{10}$',fontsize=12)\n",
    "draw_polynomial(X, Y, 10)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从图中的拟合程度来看，似乎是特征越多，模型越复杂，拟合效果越好。很显然这是不可取的，在前面讲到过拟合时我们提到，用非常复杂的模型可以把训练误差降的很低，甚至为0，而我们其实是希望模型在新样本上表现的很好，也就是泛化误差要小，当我们把模型训练的太复杂时，模型的泛化能力反而会下降。\n",
    "\n",
    "这里我们犯了一个很严重的错误，既将样本数据当作训练数据，又把这些数据拿来评估模型的好坏，这有点像是在自娱自乐。为了解决这个问题，我们通常将数据集划分成两部分：**训练集**（training set）和**测试集**（testing set）。机器学习是关于算法的算法，根据输入的数据，生成 **模型**（model），这个模型可以接收新的输入数据，从而对未知的情况作出预测。生成模型的过程称为 **学习**（learning）或 **训练**（training），训练所使用的数据集合称为 **训练集**。生成模型之后，我们要对模型进行 **测试**（testing），测试所使用的数据集合称为 **测试集**。\n",
    "\n",
    "我们将数据划分成训练集和测试集之后，模型在训练集上的误差称为 **训练误差**（testing error），模型在测试集上的误差称为 **测试误差**（testing error），然后以测试误差作为泛化误差的一个近似，再根据模型的评估方法，找到测试误差最小的一个模型。\n",
    "\n",
    "那么这里就引申出两个问题：如何将数据划分成训练集和测试集？如何在测试集上评估模型的好坏？"
   ]
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