diff --git a/analysis of regression.ipynb b/analysis of regression.ipynb new file mode 100644 index 0000000..074c14e --- /dev/null +++ b/analysis of regression.ipynb @@ -0,0 +1,3246 @@ +{ + "cells": [ + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": { + "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19", + "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5" + }, + "source": [ + "![image.png](attachment:image.png)\n", + "\n", + "\n", + "**什么是回归算法? .**\n", + "\n", + "在机器学习中,回归算法试图估计从输入变量 (x) 到数值或连续输出变量 (y) 的映射函数 (f)。\n", + "在这种情况下,y 是一个实数值,可以是整数或浮点值。 因此,回归预测问题通常是数量或大小。\n", + "例如,当提供有关房屋的数据集,并且要求您预测它们的价格时,这是一项回归任务,因为价格将是一个连续输出。" + ] + }, + { + "attachments": { + "%E5%9B%BE%E7%89%87.png": { + "image/png": "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" + }, + "CSDN_1640862400617.jpg": { + "image/jpeg": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 任务要求\n", + "\n", + "通过用数学的方式解释10种不同类型的回归算法使用,如:\n", + "\n", + "任务1:线性回归进行拟合,使用梯度下降法来获得全局最小值。\n", + "\n", + "任务2:多项式回归对比线性回归进行拟合\n", + "\n", + "任务3:逻辑回归\n", + "\n", + "\n", + "回答问题区\n", + "\n", + "\n", + "1,老师其实有讲过。。。在下面的代码注释中我们也有写到,梯度下降法是一种确定线性回归中最佳截距和斜率的一种办法,即先随机确定a,b,再通过梯度下降法求出不同的a,b\n", + "给定初始的a,b值,对于 任 何 一 个 点 ( x i , y i ) , 称 为 样 本 , 计 算 其 函 数 值 f ( x i ) 与 y i 的 差 异 , 称 为 误 差 , 误 差函数就是老师PPT里那个,F(a,b)=1/2(a*xi+b-yi)**2,此时的未知数是a和b, 使用梯度下降法对(a,b)进行迭代,只要找到最合适的a,b值使得对于所有的数据点(样本点)误差函数值最小化,就求得了线性拟合函数。因此线性拟合问题转换为误差函数求 最小值问题,找出合适的(a,b)值使得 F(a,b)最小。具体来写可以采用每个数据点计算一次F(a,b),迭代一次(a,b),所有数据点采集完毕标志整体数据进一轮迭代,在对整体数据进行N轮迭代,取平均值\n", + "本质就是一种优化算法,我们平时使用的from sklearn.linear_model import LinearRegression本质上就是内置了这种算法,在数学上称之为最小二乘法\n", + "\n", + "\n", + "2,在下面的代码里也做出了较详细的解释,欠拟合是指模型的复杂程度不足以描述自变量与因变量之间的函数关系,比如一个二阶关系式我们用一阶方程去解决就会出现。。\n", + "![%E5%9B%BE%E7%89%87.png](attachment:%E5%9B%BE%E7%89%87.png)\n", + "典型的欠拟合,为了克服欠拟合,我们需要增加模型的复杂程度,比如添加通过from sklearn.preprocessing import PolynomialFeatures\n", + "poly_features=PolynomialFeatures(degree=2,include_bias=False) #添加二次特征\n", + "相对的,过拟合是指模型复杂程度过高,导致模型对于训练集表现良好和对于测试集表现不佳,说明这也不能很好的进行回归分析,我们需要做的就是降低模型的复杂程度,通过添加惩罚项使得模型的高次参数趋近0,自然过渡到第三个问题\n", + "\n", + "\n", + "3.过拟合: 当多元线性回归中有用矩阵解线性方程组的时有无穷多的解时会出现共线(表现为原始特征过多,存在一些嘈杂特征)的问题,使得最小二乘法系数不稳定。\n", + "通过交叉验证可以判断数据是否过拟合(轮换训练集和测试集),正则化可以尽量减小高次项的影响,达到解决过拟合的问题。\n", + " 岭回归中我们采用L2 正则化,即我们尝试通过向 *系数平方和* 添加惩罚项来最小化目标函数\n", + "![CSDN_1640862400617.jpg](attachment:CSDN_1640862400617.jpg)\n", + "总结来说,岭回归就是通过舍弃掉一部分数据,使得整体数据的方差变小,所有相应的参数波动范围变小,变得更加稳定,但是它不能完全解决多元线性回归中解的共线性问题,我们可以在主成分回归 (PCR)或xgboost中得到比较好的解决" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "首先让我们从非常熟悉的回归算法开始\n", + "\n", + "**1. 线性回归**\n", + "\n", + "它是最简单的回归形式。 它是一种因变量本质上是连续的技术。 假设因变量和自变量之间的关系本质上是线性的。目标是设计一个模型,如果给定研究的小时数,可以预测分数。 使用训练数据,得到一条回归线,该回归线将给出最小误差。 然后将该线性方程用于任何新数据。 也就是说,如果我们将学生学习的小时数作为输入,我们的模型应该以最小的错误预测他们的分数。\n", + "\n", + "Y(pred) = b0 + b1*x" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np \n", + "import pandas as pd \n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0", + "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[3.01152699e-01]\n", + " [1.76345696e+00]\n", + " [1.26704805e+00]\n", + " [1.55325574e+00]\n", + " [1.83628537e+00]\n", + " [4.17812907e-01]\n", + " [1.74945762e-01]\n", + " [1.80509245e+00]\n", + " [1.32136397e+00]\n", + " [9.11535493e-01]\n", + " [1.70891223e+00]\n", + " [1.37178575e+00]\n", + " [9.02808337e-01]\n", + " [5.58446894e-01]\n", + " [6.67409600e-01]\n", + " [1.97443944e+00]\n", + " [1.57227002e+00]\n", + " [7.94792821e-01]\n", + " [3.71628230e-01]\n", + " [1.22641152e+00]\n", + " [3.09745187e-01]\n", + " [3.98025788e-01]\n", + " [1.20445456e+00]\n", + " [1.27713674e+00]\n", + " [3.08383377e-01]\n", + " [2.94450243e-02]\n", + " [2.41871739e-01]\n", + " [1.69454621e+00]\n", + " [1.18195300e+00]\n", + " [3.67716893e-01]\n", + " [1.28380475e+00]\n", + " [1.37825996e+00]\n", + " [4.70169915e-01]\n", + " [5.30329894e-01]\n", + " [1.32820252e+00]\n", + " [1.87577582e-01]\n", + " [1.05210780e+00]\n", + " [1.31630480e+00]\n", + " [9.88056271e-01]\n", + " [3.77173842e-02]\n", + " [1.75056276e+00]\n", + " [9.75834114e-01]\n", + " [3.18015537e-01]\n", + " [1.21553291e+00]\n", + " [1.07114774e+00]\n", + " [6.39169166e-01]\n", + " [1.51402594e+00]\n", + " [1.61030158e+00]\n", + " [1.69033297e+00]\n", + " [1.32201532e+00]\n", + " [4.86356901e-04]\n", + " [1.17239230e+00]\n", + " [1.04779532e+00]\n", + " [7.63517503e-01]\n", + " [2.63458433e-01]\n", + " [4.74152271e-01]\n", + " [6.06973843e-01]\n", + " [1.27715350e-01]\n", + " [1.82110459e+00]\n", + " [5.90364283e-01]\n", + " [2.35010165e-02]\n", + " [1.90972938e+00]\n", + " [3.24405628e-01]\n", + " [6.31845146e-01]\n", + " [1.08576732e+00]\n", + " [1.10151398e+00]\n", + " [1.81845580e+00]\n", + " [1.11099087e+00]\n", + " [5.22296713e-02]\n", + " [9.92161074e-01]\n", + " [1.81178511e+00]\n", + " [3.35604946e-01]\n", + " [9.39720942e-01]\n", + " [1.17784867e-01]\n", + " [2.56789821e-01]\n", + " [1.62938613e+00]\n", + " [1.20565191e+00]\n", + " [1.05029978e+00]\n", + " [1.57715039e+00]\n", + " [1.10355677e+00]\n", + " [4.38817531e-01]\n", + " [1.84831982e+00]\n", + " [1.35285645e-01]\n", + " [6.11232495e-02]\n", + " [3.08230816e-01]\n", + " [9.49362101e-01]\n", + " [1.93341067e-01]\n", + " [1.23472368e+00]\n", + " [7.86792693e-02]\n", + " [1.93875502e+00]\n", + " [1.00411949e-01]\n", + " [1.32811713e+00]\n", + " [1.01014569e+00]\n", + " [1.19910187e+00]\n", + " [1.11823659e-01]\n", + " [1.89560179e+00]\n", + " [4.80658802e-01]\n", + " [1.88420745e+00]\n", + " [6.77667246e-01]\n", + " [7.96649514e-02]]\n", + "[[ 3.45714031]\n", + " [11.15058596]\n", + " [ 8.24438472]\n", + " [ 9.46942386]\n", + " [ 9.72978492]\n", + " [ 6.2865314 ]\n", + " [ 5.36524685]\n", + " [10.33295654]\n", + " [ 6.7623038 ]\n", + " [ 6.1012076 ]\n", + " [ 9.20858849]\n", + " [ 7.7373074 ]\n", + " [ 5.82432279]\n", + " [ 6.80345046]\n", + " [ 6.59717973]\n", + " [11.2859678 ]\n", + " [ 9.0264083 ]\n", + " [ 6.26105903]\n", + " [ 5.12010661]\n", + " [ 7.65756323]\n", + " [ 6.61819085]\n", + " [ 4.43491678]\n", + " [ 6.72514607]\n", + " [ 9.43109346]\n", + " [ 2.72112689]\n", + " [ 1.3482176 ]\n", + " [ 6.18665771]\n", + " [ 8.82151324]\n", + " [ 8.96329424]\n", + " [ 3.91196859]\n", + " [ 7.74350379]\n", + " [ 7.80715896]\n", + " [ 6.62462881]\n", + " [ 5.06884211]\n", + " [ 7.69794878]\n", + " [ 3.90661064]\n", + " [ 6.6397907 ]\n", + " [ 7.88949395]\n", + " [ 6.15235171]\n", + " [ 5.28763699]\n", + " [10.35658702]\n", + " [ 5.43041395]\n", + " [ 4.67183768]\n", + " [ 7.15152221]\n", + " [ 5.98173954]\n", + " [ 4.84160904]\n", + " [ 7.33239779]\n", + " [ 8.37990578]\n", + " [ 8.0316349 ]\n", + " [ 7.8874427 ]\n", + " [ 4.07577241]\n", + " [ 8.4986357 ]\n", + " [ 6.11537298]\n", + " [ 8.47954562]\n", + " [ 5.37770379]\n", + " [ 6.63188018]\n", + " [ 5.45798207]\n", + " [ 5.35949829]\n", + " [10.28339143]\n", + " [ 5.6646844 ]\n", + " [ 4.77607742]\n", + " [11.64902504]\n", + " [ 5.87073356]\n", + " [ 4.20973725]\n", + " [ 5.61392707]\n", + " [ 6.1961858 ]\n", + " [ 9.12535332]\n", + " [ 7.73243328]\n", + " [ 5.31788666]\n", + " [ 5.19915321]\n", + " [ 9.23858711]\n", + " [ 6.76468624]\n", + " [ 7.14301649]\n", + " [ 5.57928609]\n", + " [ 4.45379033]\n", + " [ 8.13484257]\n", + " [ 7.16781814]\n", + " [ 6.30416232]\n", + " [ 9.27430077]\n", + " [ 7.66687411]\n", + " [ 5.15646771]\n", + " [ 8.83858289]\n", + " [ 3.6729317 ]\n", + " [ 3.97003778]\n", + " [ 6.24158582]\n", + " [ 7.01282421]\n", + " [ 5.5770889 ]\n", + " [ 5.80804927]\n", + " [ 5.80647895]\n", + " [ 7.79132842]\n", + " [ 3.32902477]\n", + " [ 9.07473196]\n", + " [ 5.93231781]\n", + " [ 8.76506155]\n", + " [ 3.40278011]\n", + " [ 8.81317726]\n", + " [ 3.54488193]\n", + " [ 9.78283504]\n", + " [ 6.11627985]\n", + " [ 4.35032318]]\n" + ] + } + ], + "source": [ + "X = 2*np.random.rand(100,1)#生成0,1的100个随机数,每个数作为一个维度\n", + "y = 4+3*X+np.random.randn(100,1)#生成100个符合正态分布的随机数\n", + "print(X)\n", + "print(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "使用 numpy 随机生成数据..!" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 2, 0, 15]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(X,y,color=\"blue\",marker=\".\")\n", + "plt.xlabel(\"X\")\n", + "plt.ylabel(\"Y\")\n", + "plt.axis([0,2,0,15])#指定x,y轴坐标" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "X_b=np.c_[np.ones((100, 1)), X] # 创建100个1的数组,再按列链接他们\n", + "\n", + "theta_best=np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)#矩阵求逆" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "正如我所说,如果我们将所有训练数据传递给我们的假设方程,我们就会得到 y 预测\n", + "\n", + "Y(pred) = b0 + b1*x\n", + "\n", + "但是如何选择 b0 和 b1 呢?\n", + "\n", + "必须选择值 b0 和 b1,以使它们最小化误差。 如果将误差平方和作为评估模型的指标,则目标是获得一条最能减少误差的线。\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4.03110973],\n", + " [2.92858453]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta_best" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 0.]\n", + " [1. 2.]]\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[4.03110973],\n", + " [9.88827879]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_new = np.array([[0], [2]])#取两端\n", + "X_new_b = np.c_[np.ones((2, 1)), X_new] \n", + "print(X_new_b)\n", + "y_predict = X_new_b.dot(theta_best)\n", + "y_predict#计算出两端的y预测值" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n", + "plt.plot(X, y, \"b.\")\n", + "plt.xlabel(\"$x_1$\", fontsize=18)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)#y字母与水平夹角为0\n", + "plt.legend(loc=\"upper left\", fontsize=14)\n", + "plt.axis([0, 2, 0, 15])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "因为 python 使我们的生活变得轻松......这是在 **sklearn.linear_model** 中预先构建的" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([[2.85308474]]), array([4.07182529]))" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "lin_reg=LinearRegression()\n", + "lin_reg.fit(X, y)\n", + "lin_reg.coef_,lin_reg.intercept_#输出斜率,截距。和原方程y=3x+4基本一致" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "为此,我们需要使用优化技术来找到全局最小化。 通常我们有很多优化算法,现在我们将使用梯度下降法来获得全局最小值\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "#通过迭代找到目标函数最小值或收敛值\n", + "#对于单变量函数,梯度就是其微分" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "eta=0.1#学习率,每次所走的步长\n", + "n_iterations=1000\n", + "m=100\n", + "theta=np.random.randn(2,1)#初始位置可以任意给定\n", + "\n", + "for iteration in range(n_iterations):\n", + " gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)#求偏导数\n", + " theta = theta - eta * gradients#用初始状态-导数*步长,做循环,一步一步逼近局部最小值" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4.07182529],\n", + " [2.85308474]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[4.07182529],\n", + " [9.77799476]])" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X_new_b.dot(theta)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们继续下一个回归算法\n", + "\n", + "**2. 多项式回归**\n", + "\n", + "线性回归要求因变量和自变量之间的关系是线性的。 如果数据的分布更复杂,如下图所示怎么办?这就是多项式回归的用武之地" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import numpy.random as rnd\n", + "import matplotlib.pyplot as plt\n", + "np.random.seed(42)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "m=100\n", + "X=6 * np.random.rand(m, 1) - 3#生成0,1的m个随机数,每个数作为一个维度\n", + "y=0.5 * X**2 + X + 2 + np.random.randn(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[-3, 3, 0, 10]" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(X, y, \"b.\")\n", + "plt.xlabel(\"$x_1$\", fontsize=18)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.axis([-3, 3, 0, 10])" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'X' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_135328/1653548325.py\u001b[0m in \u001b[0;36m\u001b[1;34m\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlinear_model\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mLinearRegression\u001b[0m\u001b[1;31m#我们可以先做个线性关系来看一下\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[0mlr\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mLinearRegression\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;31m#建立线性回归模型\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mlr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;31m#训练\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 4\u001b[0m \u001b[0my_predict\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;31m#预测\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;31m#画散点图\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'X' is not defined" + ] + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression#我们可以先做个线性关系来看一下\n", + "lr=LinearRegression()#建立线性回归模型\n", + "lr.fit(X, y)#训练\n", + "y_predict=lr.predict(X)#预测\n", + "plt.scatter(X,y)#画散点图\n", + "plt.plot(X,y_predict)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#可以看到拟合效果很不好,欠拟合" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "直线无法捕捉数据中的模式。 这是欠拟合的一个例子。为了克服欠拟合,我们需要增加模型的复杂度。为了生成更高阶的方程,我们可以添加原始特征的幂作为新特征。 线性模型, $Y(pred) = b0 + b1* x$ 应该转化为\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "这仍然被认为是线性模型,因为与特征相关的系数/权重仍然是线性的。 x² 只是一个特征。 然而,我们拟合的曲线本质上是二次的。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "poly_features=PolynomialFeatures(degree=2,include_bias=False)\n", + "#degree=2,添加二次特征\n", + "X_poly=poly_features.fit_transform(X)\n", + "print(X_poly)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "X_poly[0]\n", + "print(\"X_poly的shape是\",X_poly.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#我们已经为X_poly添加了二次特征,下面继续使用线性模型\n", + "lin_reg=LinearRegression()\n", + "lin_reg.fit(X_poly, y)\n", + "lin_reg.intercept_, lin_reg.coef_#截距,系数" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "X_new=np.linspace(-3, 3, 100).reshape(100, 1)#测试集\n", + "X_new_poly=poly_features.transform(X_new)#将X_new也转化成含有二次特征\n", + "y_new=lin_reg.predict(X_new_poly)#得到预测值\n", + "plt.plot(X, y, \"b.\")\n", + "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n", + "plt.xlabel(\"$x_1$\", fontsize=18)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.legend(loc=\"upper left\", fontsize=14)\n", + "plt.axis([-3, 3, 0, 10])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "从图中可以很明显地看出,二次曲线比线性线能够更好地拟合数据......\n", + "\n", + "所以取决于我们必须选择算法的数据:)" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**3.逻辑回归**\n", + "\n", + "在逻辑回归中,因变量本质上是二元的(有两个类别)。 自变量可以是连续的或二进制的。 在多项逻辑回归中,您的因变量可以有两个以上的类别。\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "t=np.linspace(-10, 10, 100)\n", + "sig=1/(1 + np.exp(-t))\n", + "plt.figure(figsize=(9, 3))\n", + "plt.plot([-10, 10], [0, 0], \"k-\")\n", + "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n", + "plt.plot([-10, 10], [1, 1], \"k:\")\n", + "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n", + "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")#转义,转换成数学表达式\n", + "plt.xlabel(\"t\")\n", + "plt.legend(loc=\"upper left\", fontsize=20)\n", + "plt.axis([-10, 10, -0.1, 1.1])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "这是它的样子..!\n", + "\n", + "逻辑回归模型默认类别的概率例如,如果我们根据身高将人们的性别建模为男性或女性,那么第一个类别可能是男性,逻辑回归模型可以写成给定一个人身高的男性概率, 或更正式地:\n", + "\n", + "P(性别=男性|身高)。给定身高,判断为男性的概率(条件概率)\n", + "\n", + "换句话说,我们正在对输入 (X) 属于默认类 (Y=1) 的概率进行建模,我们可以将其形式化地写为:\n", + "\n", + "P(X) = P(Y=1|X)y_proba\n", + "\n", + "我们在预测概率! 我认为逻辑回归是一种分类算法? :)\n", + "\n", + "请注意,必须将概率预测转换为二进制值(0 或 1)才能实际进行概率预测。 稍后当我们谈论进行预测时会详细介绍这一点。" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + }, + { + "data": { + "text/plain": [ + "['data',\n", + " 'target',\n", + " 'frame',\n", + " 'target_names',\n", + " 'DESCR',\n", + " 'feature_names',\n", + " 'filename']" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# 使用 iris 数据集,包含150行记录,前四列是花萼长度,花萼宽度,花瓣长度和花瓣宽度(第五列是花类别,用前四行判断)\n", + "from sklearn import datasets\n", + "iris=datasets.load_iris()#数据集\n", + "print(type(iris))\n", + "list(iris.keys())\n", + "# 了解更多关于数据集的信息\n", + "# print(iris.DESCR)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "X = iris[\"data\"][:, 3:]#花瓣宽度\n", + "y = (iris[\"target\"] == 2).astype(np.int)#为bool型,转化为0,1\n", + "#将概率预测转换为二进制值(0 或 1)才能实际进行概率预测" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LogisticRegression(random_state=42)" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "log_reg=LogisticRegression(random_state=42)#random_state用于控制随机过程,保证生成的模型每次是相同的\n", + "log_reg.fit(X, y)#在花瓣宽度为()的条件下,y为第二型花的概率" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[9.99250016e-01 7.49984089e-04]\n", + " [9.99240201e-01 7.59799387e-04]\n", + " [9.99230257e-01 7.69743043e-04]\n", + " ...\n", + " [3.08374822e-03 9.96916252e-01]\n", + " [3.04400296e-03 9.96955997e-01]\n", + " [3.00476842e-03 9.96995232e-01]]\n" + ] + }, + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "X_new=np.linspace(0, 3, 1000).reshape(-1, 1)#指定为-1,则numpy会根据剩下的维度自动计算出合适的行数\n", + "#这里是1000维的数组,每个维度里面只有一个数\n", + "y_proba=log_reg.predict_proba(X_new)#测试集的预测值\n", + "print(y_proba)\n", + "\n", + "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")#是第二型花的概率\n", + "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")#不是是第二型花的概率" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "与线性回归相同,我们需要制作成本函数并最小化以获得全局最小值。\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "并使用任何优化算法并获得全局最小值" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**4.分位数回归**\n", + "\n", + "分位数回归至少有两个动机:假设我们的因变量是双峰或多峰的,即它有多个驼峰。 如果我们知道是什么导致了多峰性,我们可以对该变量进行分离并进行分层分析,但如果我们不知道,分位数回归可能会很好。 (普通最小二乘法)OLS 回归在这里与依赖均值作为双峰分布的中心性度量一样具有误导性。" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
incomefoodexp
0420.157651255.839425
1541.411707310.958667
2901.157457485.680014
3639.080229402.997356
4750.875606495.560775
\n", + "
" + ], + "text/plain": [ + " income foodexp\n", + "0 420.157651 255.839425\n", + "1 541.411707 310.958667\n", + "2 901.157457 485.680014\n", + "3 639.080229 402.997356\n", + "4 750.875606 495.560775" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import statsmodels.api as sm#横截面模型和方法\n", + "import statsmodels.formula.api as smf#使用公式字符串和Dateframe指定模型的方便接口\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "data = sm.datasets.engel.load_pandas().data#反正就是搞了一些数据过来,收入与食物支出的关系\n", + "data.head()" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在分位数回归中,我们尝试在给定 X 值的情况下估计因变量的分位数。注意因变量应该是连续的。\n", + "\n", + "分位数回归模型:\n", + "对于第 q 个分位数,我们有以下回归模型,\n", + "这似乎类似于线性回归模型,但这里我们考虑最小化的目标函数是:\n", + "![image.png](attachment:image.png)\n", + "其中 q 是第 q 个分位数。\n", + "\n", + "如果 q = 0.5,即如果我们对中位数感兴趣,那么它就变成了中位数回归(或最小绝对偏差回归)并代入上述方程中 q = 0.5 的值,我们得到目标函数为:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**最小绝对偏差**\n", + "\n", + "LAD 模型是分位数回归的一个特例,其中 q=0.5" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " QuantReg Regression Results \n", + "==============================================================================\n", + "Dep. Variable: foodexp Pseudo R-squared: 0.6206\n", + "Model: QuantReg Bandwidth: 64.51\n", + "Method: Least Squares Sparsity: 209.3\n", + "Date: Sat, 25 Dec 2021 No. Observations: 235\n", + "Time: 12:19:12 Df Residuals: 233\n", + " Df Model: 1\n", + "==============================================================================\n", + " coef std err t P>|t| [0.025 0.975]\n", + "------------------------------------------------------------------------------\n", + "Intercept 81.4823 14.634 5.568 0.000 52.649 110.315\n", + "income 0.5602 0.013 42.516 0.000 0.534 0.586\n", + "==============================================================================\n", + "\n", + "The condition number is large, 2.38e+03. This might indicate that there are\n", + "strong multicollinearity or other numerical problems.\n" + ] + } + ], + "source": [ + "mod=smf.quantreg('foodexp ~ income', data)\n", + "res=mod.fit(q=0.5)#训练\n", + "print(res.summary())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**可视化结果**\n", + "\n", + "我们估计 0.05 到 0.95 之间的许多分位数的分位数回归模型,并将这些模型中的每一个的最佳拟合线与普通最小二乘法结果进行比较。\n", + "\n", + "为方便起见,我们将分位数回归结果放在 Pandas DataFrame 中,OLS 结果放在字典中。" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " q a b lb ub\n", + "0 0.05 124.880097 0.343361 0.268632 0.418090\n", + "1 0.15 111.693660 0.423708 0.382780 0.464636\n", + "2 0.25 95.483539 0.474103 0.439900 0.508306\n", + "3 0.35 105.841294 0.488901 0.457759 0.520043\n", + "4 0.45 81.083647 0.552428 0.525021 0.579835\n", + "5 0.55 89.661370 0.565601 0.540955 0.590247\n", + "6 0.65 74.033435 0.604576 0.582169 0.626982\n", + "7 0.75 62.396584 0.644014 0.622411 0.665617\n", + "8 0.85 52.272216 0.677603 0.657383 0.697823\n", + "9 0.95 64.103964 0.709069 0.687831 0.730306\n", + "{'a': 147.47538852370573, 'b': 0.48517842367692354, 'lb': 0.4568738130184233, 'ub': 0.5134830343354237}\n" + ] + } + ], + "source": [ + "quantiles=np.arange(0.05,0.96, 0.1)\n", + "def fit_model(q):#建立在不同q值下训练的函数\n", + " res=mod.fit(q=q)\n", + " return [q, res.params['Intercept'], res.params['income']] + \\\n", + " res.conf_int().loc['income'].tolist()\n", + "\n", + "models = [fit_model(x) for x in quantiles]\n", + "models = pd.DataFrame(models, columns=['q', 'a', 'b', 'lb', 'ub'])#将分位数回归结果放在Pandas DataFrame\n", + "\n", + "ols = smf.ols('foodexp ~ income', data).fit()\n", + "ols_ci = ols.conf_int().loc['income'].tolist()#与list不同,这会把数组的值作为创建列表的元素\n", + "#ols.conf_int()\n", + "# 0 1\n", + "#Intercept 116.036792 178.913985\n", + "#income 0.456874 0.513483\n", + "ols = dict(a=ols.params['Intercept'],\n", + " b=ols.params['income'],\n", + " lb=ols_ci[0],\n", + " ub=ols_ci[1])\n", + "\n", + "print(models)\n", + "print(ols)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "该图将 10 个分位数回归模型的最佳拟合线与最小二乘拟合进行了比较。 正如 Koenker 和 Hallock (2001) 指出的那样,我们看到:\n", + "\n", + "1.食品支出随收入增加\n", + "\n", + "2.食品支出分散度随收入增加\n", + "\n", + "3.最小二乘估计对低收入观察的拟合效果很差(即 OLS 线经过大多数低收入家庭)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Food expenditure')" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.arange(data.income.min(), data.income.max(), 50)\n", + "get_y = lambda a, b: a + b * x\n", + "\n", + "fig, ax = plt.subplots(figsize=(8, 6))\n", + "\n", + "for i in range(models.shape[0]):\n", + " y = get_y(models.a[i], models.b[i])\n", + " ax.plot(x, y, linestyle='dotted', color='grey')\n", + "\n", + "y = get_y(ols['a'], ols['b'])\n", + "\n", + "ax.plot(x, y, color='red', label='OLS')\n", + "ax.scatter(data.income, data.foodexp, alpha=0.2)\n", + "ax.set_xlim((240, 3000))\n", + "ax.set_ylim((240, 2000))\n", + "legend = ax.legend()\n", + "ax.set_xlabel('Income', fontsize=16)\n", + "ax.set_ylabel('Food expenditure', fontsize=16)" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "n = models.shape[0]\n", + "p1 = plt.plot(models.q, models.b, color='black', label='Quantile Reg.')\n", + "p2 = plt.plot(models.q, models.ub, linestyle='dotted', color='black')\n", + "p3 = plt.plot(models.q, models.lb, linestyle='dotted', color='black')\n", + "p4 = plt.plot(models.q, [ols['b']] * n, color='red', label='OLS')\n", + "p5 = plt.plot(models.q, [ols['lb']] * n, linestyle='dotted', color='red')\n", + "p6 = plt.plot(models.q, [ols['ub']] * n, linestyle='dotted', color='red')\n", + "plt.ylabel(r'$\\beta_{income}$')\n", + "plt.xlabel('Quantiles of the conditional food expenditure distribution')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**5.岭回归**\n", + "当多元线性回归中有用矩阵解线性方程组的时有无穷多的解时会出现共线的问题,使得最小二乘法系数不稳定\n", + "\n", + "在跳到岭回归之前理解正则化的概念很重要。\n", + "\n", + "**正则化**\n", + "\n", + "正则化有助于解决过拟合问题,这意味着模型在训练数据上表现良好但在验证(测试)数据上表现不佳。正则化通过向目标函数添加惩罚项并使用该惩罚项控制模型复杂性来解决此问题。\n", + "\n", + "**L1 损失函数或 L1 正则化**\n", + "\n", + "在 L1 正则化中,我们尝试通过将惩罚项添加到 **系数绝对值之和**来最小化目标函数。这也称为最小绝对偏差方法。套索回归利用 L1 正则化。\n", + "\n", + "**L2 损失函数或 L2 正则化**\n", + "\n", + "在 L2 正则化中,我们尝试通过向 **系数平方和** 添加惩罚项来最小化目标函数。RidgeRegression 或收缩回归利用 L2 正则化。\n", + "岭回归就是损失部分信息,减小线性回归的方差\n", + "\n", + "传统的线性拟合涉及最小化 RSS(残差平方和)。在岭回归中,添加了一个新参数,现在参数将最小化:\n", + "\n", + "![image.png](attachment:image.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "['data',\n", + " 'target',\n", + " 'frame',\n", + " 'target_names',\n", + " 'DESCR',\n", + " 'feature_names',\n", + " 'filename']" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn import datasets\n", + "import numpy as np\n", + "iris = datasets.load_iris()#数据集\n", + "list(iris.keys())" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "X = iris[\"data\"][:, 3:]#花瓣宽度\n", + "y = (iris[\"target\"] == 2).astype(np.int)#如果Iris-Virginica为1,否则为0" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "首先让我们做线性回归,然后比较岭" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.15478415224232214\n" + ] + } + ], + "source": [ + "from sklearn.model_selection import cross_val_score#交叉验证\n", + "from sklearn.linear_model import LinearRegression\n", + "\n", + "reg=LinearRegression()#建立线性回归模型\n", + "\n", + "mes=cross_val_score(reg,X,y,scoring='neg_mean_squared_error',cv=5)#cv:每次测试折数,scoring=参数选择指标,这里选择的均方误差\n", + "mean_mes=np.mean(mes)#均值\n", + "print(mean_mes)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们介绍 GridSearchCV。 这将允许我们使用一系列不同的正则化参数自动执行 5 折交叉验证,以便找到 alpha 的最佳值。 alpha就表示正则化程度参数,通过舍弃一部分数据,减小方差来控制模型的复杂度,使高次参数趋近0" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "GridSearchCV(cv=5, estimator=Ridge(),\n", + " param_grid={'alpha': [1e-15, 1e-10, 1e-08, 0.0001, 0.001, 0.01, 1,\n", + " 5, 10, 20]},\n", + " scoring='neg_mean_squared_error')" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.model_selection import GridSearchCV\n", + "from sklearn.linear_model import Ridge#岭回归库\n", + "\n", + "ridge=Ridge()\n", + "\n", + "parameters={'alpha':[1e-15,1e-10,1e-8,1e-4,1e-3,1e-2,1,5,10,20]}\n", + "ridge_reg=GridSearchCV(ridge,parameters,scoring='neg_mean_squared_error',cv=5)\n", + "ridge_reg.fit(X,y)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'alpha': 5}\n", + "-0.15373851579535566\n" + ] + } + ], + "source": [ + "print(ridge_reg.best_params_)\n", + "print(ridge_reg.best_score_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "您应该看到 alpha 的最佳值为 5,负 MSE 为 -0.15373851579535563 。 这是对基本多元线性回归的轻微改进" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**6. 套索回归**\n", + "\n", + "Lasso 代表最小绝对收缩和选择算子。 它在目标函数中使用 L1 正则化技术。 因此,LASSO 回归中的目标函数变为:\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "λ 是正则化参数,截距项没有被正则化。 我们不假设误差项是正态分布的。\n", + "对于估计,我们没有任何特定的数学公式,但我们可以使用一些统计软件获得估计。\n", + "请注意,套索回归也需要标准化。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/lib/python3.6/site-packages/sklearn/linear_model/_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.024374927802504942, tolerance: 0.0029166666666666672\n", + " positive)\n", + "/usr/local/lib/python3.6/site-packages/sklearn/linear_model/_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.005158285777145721, tolerance: 0.0022500000000000003\n", + " positive)\n", + "/usr/local/lib/python3.6/site-packages/sklearn/linear_model/_coordinate_descent.py:532: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.006225388694383938, tolerance: 0.0016666666666666668\n", + " positive)\n" + ] + }, + { + "data": { + "text/plain": [ + "GridSearchCV(cv=5, estimator=Lasso(),\n", + " param_grid={'alpha': [1e-15, 1e-10, 1e-08, 0.0001, 0.001, 0.01, 1,\n", + " 5, 10, 20]},\n", + " scoring='neg_mean_squared_error')" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#losso方法是以缩小变量集(降阶)为思想的压缩估计方法。通过构造惩罚函数,将变量的系数进行压缩并使某些回归系数变为0.从而达到变量选择的目的.\n", + "from sklearn.model_selection import GridSearchCV\n", + "from sklearn.linear_model import Lasso\n", + "\n", + "lasso=Lasso()\n", + "\n", + "parameters={'alpha':[1e-15,1e-10,1e-8,1e-4,1e-3,1e-2,1,5,10,20]}\n", + "lasso_reg=GridSearchCV(lasso,parameters,scoring='neg_mean_squared_error',cv=5)#5折交叉验证\n", + "lasso_reg.fit(X,y)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'alpha': 1e-15}\n", + "-0.15478415224232225\n" + ] + } + ], + "source": [ + "print(ridge_reg.best_params_)\n", + "print(ridge_reg.best_score_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "和ridge基本相同,你能观察到他的变化\n", + "lasso能稀疏矩阵,进行庞大数量下的特征选择,而ridge稍微解决了矩阵求解线性方程组出现无穷解带来的系数不稳定问题。" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**7. ElasticNet 回归**\n", + "\n", + "当处理高度相关的自变量时,ElasticNet 回归优于岭回归和套索回归。\n", + "它是 L1 和 L2 正则化的组合。\n", + "\n", + "Elastic Net Regression 的目标函数是:\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "像岭回归和套索回归一样,它不假设正态性。" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn import datasets\n", + "import numpy as np\n", + "import pandas as pd\n", + "bostan=datasets.load_boston()#波士顿数据集\n", + "# 要了解有关数据集的更多信息\n", + "# print(bostan.DESCR)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTAT
00.0063218.02.310.00.5386.57565.24.09001.0296.015.3396.904.98
10.027310.07.070.00.4696.42178.94.96712.0242.017.8396.909.14
20.027290.07.070.00.4697.18561.14.96712.0242.017.8392.834.03
30.032370.02.180.00.4586.99845.86.06223.0222.018.7394.632.94
40.069050.02.180.00.4587.14754.26.06223.0222.018.7396.905.33
\n", + "
" + ], + "text/plain": [ + " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n", + "0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 \n", + "1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 \n", + "2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 \n", + "3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 \n", + "4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 \n", + "\n", + " PTRATIO B LSTAT \n", + "0 15.3 396.90 4.98 \n", + "1 17.8 396.90 9.14 \n", + "2 17.8 392.83 4.03 \n", + "3 18.7 394.63 2.94 \n", + "4 18.7 396.90 5.33 " + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bostan_df = pd.DataFrame(bostan.data,columns=bostan.feature_names)\n", + "bostan_df.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们添加因变量 house_price" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTAThouse_price
count506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000506.000000
mean3.61352411.36363611.1367790.0691700.5546956.28463468.5749013.7950439.549407408.23715418.455534356.67403212.65306322.532806
std8.60154523.3224536.8603530.2539940.1158780.70261728.1488612.1057108.707259168.5371162.16494691.2948647.1410629.197104
min0.0063200.0000000.4600000.0000000.3850003.5610002.9000001.1296001.000000187.00000012.6000000.3200001.7300005.000000
25%0.0820450.0000005.1900000.0000000.4490005.88550045.0250002.1001754.000000279.00000017.400000375.3775006.95000017.025000
50%0.2565100.0000009.6900000.0000000.5380006.20850077.5000003.2074505.000000330.00000019.050000391.44000011.36000021.200000
75%3.67708312.50000018.1000000.0000000.6240006.62350094.0750005.18842524.000000666.00000020.200000396.22500016.95500025.000000
max88.976200100.00000027.7400001.0000000.8710008.780000100.00000012.12650024.000000711.00000022.000000396.90000037.97000050.000000
\n", + "
" + ], + "text/plain": [ + " CRIM ZN INDUS CHAS NOX RM \\\n", + "count 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 \n", + "mean 3.613524 11.363636 11.136779 0.069170 0.554695 6.284634 \n", + "std 8.601545 23.322453 6.860353 0.253994 0.115878 0.702617 \n", + "min 0.006320 0.000000 0.460000 0.000000 0.385000 3.561000 \n", + "25% 0.082045 0.000000 5.190000 0.000000 0.449000 5.885500 \n", + "50% 0.256510 0.000000 9.690000 0.000000 0.538000 6.208500 \n", + "75% 3.677083 12.500000 18.100000 0.000000 0.624000 6.623500 \n", + "max 88.976200 100.000000 27.740000 1.000000 0.871000 8.780000 \n", + "\n", + " AGE DIS RAD TAX PTRATIO B \\\n", + "count 506.000000 506.000000 506.000000 506.000000 506.000000 506.000000 \n", + "mean 68.574901 3.795043 9.549407 408.237154 18.455534 356.674032 \n", + "std 28.148861 2.105710 8.707259 168.537116 2.164946 91.294864 \n", + "min 2.900000 1.129600 1.000000 187.000000 12.600000 0.320000 \n", + "25% 45.025000 2.100175 4.000000 279.000000 17.400000 375.377500 \n", + "50% 77.500000 3.207450 5.000000 330.000000 19.050000 391.440000 \n", + "75% 94.075000 5.188425 24.000000 666.000000 20.200000 396.225000 \n", + "max 100.000000 12.126500 24.000000 711.000000 22.000000 396.900000 \n", + "\n", + " LSTAT house_price \n", + "count 506.000000 506.000000 \n", + "mean 12.653063 22.532806 \n", + "std 7.141062 9.197104 \n", + "min 1.730000 5.000000 \n", + "25% 6.950000 17.025000 \n", + "50% 11.360000 21.200000 \n", + "75% 16.955000 25.000000 \n", + "max 37.970000 50.000000 " + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bostan_df['house_price']=bostan.target#\n", + "bostan_df.head()\n", + "bostan_df.describe()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "X = bostan_df.drop('house_price',axis=1)\n", + "y = bostan_df['house_price']" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.linear_model import ElasticNet#ElasticNet 回归库,弹性回归模型\n", + "from sklearn.model_selection import train_test_split#拆分测试集和训练集\n", + "els_reg=ElasticNet()" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "X_train,X_test,y_train,y_test = train_test_split(X,y,test_size=0.3,random_state=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "ElasticNet()" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "els_reg.fit(X_train,y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ElasticNet 的 R 方值:\n" + ] + }, + { + "data": { + "text/plain": [ + "69.98" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print('ElasticNet 的 R 方值:')\n", + "np.round(els_reg.score(X_test,y_test)*100,2)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[31.04225224 28.60516169 17.5876487 22.85603308 23.92723348 21.10353412\n", + " 32.24440467 20.06483179 21.30432621 26.16366764 25.38774987 29.66263414\n", + " 21.14571068 27.57815239 23.91477772 22.35262528 14.42494542 32.37657153\n", + " 30.72624958 12.20169369 22.93119233 20.96527599 25.49767055 25.9594289\n", + " 31.88684865 10.42935117 13.97058633 19.33123148 34.51271647 15.99390048\n", + " 24.87025096 16.00043622 39.00216026 19.30919479 22.16121732 20.79133858\n", + " 18.22837653 27.31934997 12.71529113 19.46289807 23.86635636 24.61456375\n", + " 28.65331404 13.17556876 18.01205288 12.57206656 34.44280189 19.23177671\n", + " 26.17992385 20.26264276 22.9656752 24.63378097 27.02796213 25.91907291\n", + " 3.2533114 26.5525057 8.73307157 27.84132854 18.55551286 31.88127544\n", + " 20.23656806 27.01792857 16.98628749 16.55123223 8.28043245 30.77886571\n", + " 32.99545685 23.04430404 24.27735146 25.57380458 25.22864347 9.01645502\n", + " 20.56451561 21.04091119 19.9230722 21.91408838 30.90278823 27.75061379\n", + " 29.61453403 33.48059894 18.37527631 24.10862144 31.49515824 12.53608924\n", + " 24.07685861 30.98504503 16.90433873 25.88146044 20.3963146 16.88707964\n", + " 27.34077947 37.04485807 13.00102034 24.376045 16.41292624 23.53232938\n", + " 23.49102651 28.09263042 32.43140739 19.90923643 16.71837005 17.82073022\n", + " 26.21097528 25.23476095 8.00829131 20.21378261 15.6665747 30.59734365\n", + " 23.93980856 24.500427 36.52874133 27.88123321 13.65191239 32.26833137\n", + " 34.28688248 31.84120768 23.44801718 19.49299521 34.18705577 34.28838673\n", + " 21.77554301 15.22693904 27.26563491 21.0343553 26.89959906 21.67920532\n", + " 25.36230989 23.92855956 23.21225575 28.03142359 20.59859876 24.310501\n", + " 29.0614835 11.84050247 27.05694485 30.68945723 14.66447556 14.75115427\n", + " 29.77966955 14.2367033 23.95727618 15.9592544 16.3858431 28.48555134\n", + " 33.48622692 22.71917081 25.47151311 15.22115043 27.06640698 20.21609042\n", + " 32.49469198 14.94007031]\n" + ] + } + ], + "source": [ + "predict_els = els_reg.predict(X_test)\n", + "print(predict_els)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ElasticNet 测试数据的均方误差:\n" + ] + }, + { + "data": { + "text/plain": [ + "27.51" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn import metrics\n", + "print('ElasticNet 测试数据的均方误差:')\n", + "np.round(metrics.mean_squared_error(y_test,predict_els),2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**8. 主成分回归 (PCR)**\n", + "\n", + "PCR 是一种回归技术,当您的数据中有许多自变量或多重共线性时,它被广泛使用。 它分为2个步骤:\n", + "\n", + " 1.获取主成分\n", + " 2.对主成分运行回归分析\n", + "\n", + "PCR最常见的特点是:\n", + "\n", + " 1.降维\n", + " 2.去除多重共线性,不同于岭回归和锁套回归,可以从根本是解决系数不稳定的问题\n", + " \n", + "**获取主成分**\n", + "主成分分析是一种在原始特征高度相关时提取新特征的统计方法。 我们在原始特征的帮助下创建新特征,使得新特征不相关。\n", + "\n", + "让我们使用击球手数据来做到这一点......" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "_cell_guid": "", + "_uuid": "" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun \\\n", + "0 293 66 1 30 29 14 1 293 66 1 \n", + "1 315 81 7 24 38 39 14 3449 835 69 \n", + "2 479 130 18 66 72 76 3 1624 457 63 \n", + "3 496 141 20 65 78 37 11 5628 1575 225 \n", + "4 321 87 10 39 42 30 2 396 101 12 \n", + "5 594 169 4 74 51 35 11 4408 1133 19 \n", + "6 185 37 1 23 8 21 2 214 42 1 \n", + "7 298 73 0 24 24 7 3 509 108 0 \n", + "8 323 81 6 26 32 8 2 341 86 6 \n", + "9 401 92 17 49 66 65 13 5206 1332 253 \n", + "10 574 159 21 107 75 59 10 4631 1300 90 \n", + "11 202 53 4 31 26 27 9 1876 467 15 \n", + "12 418 113 13 48 61 47 4 1512 392 41 \n", + "13 239 60 0 30 11 22 6 1941 510 4 \n", + "14 196 43 7 29 27 30 13 3231 825 36 \n", + "15 183 39 3 20 15 11 3 201 42 3 \n", + "16 568 158 20 89 75 73 15 8068 2273 177 \n", + "17 190 46 2 24 8 15 5 479 102 5 \n", + "18 407 104 6 57 43 65 12 5233 1478 100 \n", + "19 127 32 8 16 22 14 8 727 180 24 \n", + "20 413 92 16 72 48 65 1 413 92 16 \n", + "21 426 109 3 55 43 62 1 426 109 3 \n", + "22 22 10 1 4 2 1 6 84 26 2 \n", + "23 472 116 16 60 62 74 6 1924 489 67 \n", + "24 629 168 18 73 102 40 18 8424 2464 164 \n", + "25 587 163 4 92 51 70 6 2695 747 17 \n", + "26 324 73 4 32 18 22 7 1931 491 13 \n", + "27 474 129 10 50 56 40 10 2331 604 61 \n", + "28 550 152 6 92 37 81 5 2308 633 32 \n", + "29 513 137 20 90 95 90 14 5201 1382 166 \n", + ".. ... ... ... ... ... ... ... ... ... ... \n", + "292 289 63 7 36 41 44 17 7402 1954 195 \n", + "293 559 141 2 48 61 73 8 3162 874 16 \n", + "294 520 120 17 53 44 21 4 927 227 22 \n", + "295 19 4 1 2 3 1 1 19 4 1 \n", + "296 205 43 2 24 17 20 7 854 219 12 \n", + "297 193 47 10 21 29 24 6 1136 256 42 \n", + "298 181 46 1 19 18 17 5 937 238 9 \n", + "299 213 61 4 17 22 3 17 4061 1145 83 \n", + "300 510 147 10 56 52 53 7 2872 821 63 \n", + "301 578 138 1 56 59 34 3 1399 357 7 \n", + "302 200 51 2 14 29 25 23 9778 2732 379 \n", + "303 441 113 5 76 52 76 5 1546 397 17 \n", + "304 172 42 3 17 14 15 10 4086 1150 57 \n", + "305 580 194 9 91 62 78 8 3372 1028 48 \n", + "306 127 32 4 14 25 12 19 8396 2402 242 \n", + "307 279 69 4 35 31 32 4 1359 355 31 \n", + "308 480 112 18 50 71 44 7 3031 771 110 \n", + "309 600 139 0 94 29 60 2 1236 309 1 \n", + "310 610 186 19 107 98 74 6 2728 753 69 \n", + "311 360 81 5 37 44 37 7 2268 566 41 \n", + "312 387 124 1 67 27 36 7 1775 506 6 \n", + "313 580 207 8 107 71 105 5 2778 978 32 \n", + "314 408 117 11 66 41 34 1 408 117 11 \n", + "315 593 172 22 82 100 57 1 593 172 22 \n", + "316 221 53 2 21 23 22 8 1063 283 15 \n", + "317 497 127 7 65 48 37 5 2703 806 32 \n", + "318 492 136 5 76 50 94 12 5511 1511 39 \n", + "319 475 126 3 61 43 52 6 1700 433 7 \n", + "320 573 144 9 85 60 78 8 3198 857 97 \n", + "321 631 170 9 77 44 31 11 4908 1457 30 \n", + "\n", + " CRuns CRBI CWalks League Division PutOuts Assists Errors Salary \\\n", + "0 30 29 14 A E 446 33 20 NaN \n", + "1 321 414 375 N W 632 43 10 475.000 \n", + "2 224 266 263 A W 880 82 14 480.000 \n", + "3 828 838 354 N E 200 11 3 500.000 \n", + "4 48 46 33 N E 805 40 4 91.500 \n", + "5 501 336 194 A W 282 421 25 750.000 \n", + "6 30 9 24 N E 76 127 7 70.000 \n", + "7 41 37 12 A W 121 283 9 100.000 \n", + "8 32 34 8 N W 143 290 19 75.000 \n", + "9 784 890 866 A E 0 0 0 1100.000 \n", + "10 702 504 488 A E 238 445 22 517.143 \n", + "11 192 186 161 N W 304 45 11 512.500 \n", + "12 205 204 203 N E 211 11 7 550.000 \n", + "13 309 103 207 A E 121 151 6 700.000 \n", + "14 376 290 238 N E 80 45 8 240.000 \n", + "15 20 16 11 A W 118 0 0 NaN \n", + "16 1045 993 732 N W 105 290 10 775.000 \n", + "17 65 23 39 A W 102 177 16 175.000 \n", + "18 643 658 653 A W 912 88 9 NaN \n", + "19 67 82 56 N W 202 22 2 135.000 \n", + "20 72 48 65 N E 280 9 5 100.000 \n", + "21 55 43 62 A W 361 22 2 115.000 \n", + "22 9 9 3 A W 812 84 11 NaN \n", + "23 242 251 240 N W 518 55 3 600.000 \n", + "24 1008 1072 402 A E 1067 157 14 776.667 \n", + "25 442 198 317 A E 434 9 3 765.000 \n", + "26 291 108 180 N E 222 3 3 708.333 \n", + "27 246 327 166 N W 732 83 13 750.000 \n", + "28 349 182 308 N W 262 329 16 625.000 \n", + "29 763 734 784 A W 267 5 3 900.000 \n", + ".. ... ... ... ... ... ... ... ... ... \n", + "292 1115 919 1153 A W 166 211 7 NaN \n", + "293 421 349 359 N E 352 414 9 925.000 \n", + "294 106 80 52 A W 70 144 11 185.000 \n", + "295 2 3 1 N W 692 70 8 920.000 \n", + "296 105 99 71 N E 131 6 1 286.667 \n", + "297 129 139 106 A W 299 13 5 245.000 \n", + "298 88 95 104 A E 37 98 9 NaN \n", + "299 488 491 244 A W 178 45 4 235.000 \n", + "300 307 340 174 N E 810 99 18 1150.000 \n", + "301 149 161 87 N E 133 371 20 160.000 \n", + "302 1272 1652 925 N W 398 29 7 NaN \n", + "303 226 149 191 A W 160 290 11 425.000 \n", + "304 579 363 406 N W 65 0 0 900.000 \n", + "305 604 314 469 N E 270 13 6 NaN \n", + "306 1048 1348 819 N W 167 18 6 500.000 \n", + "307 180 148 158 N E 133 173 9 277.500 \n", + "308 338 406 239 N E 94 270 16 750.000 \n", + "309 201 69 110 N E 300 12 9 160.000 \n", + "310 399 366 286 N E 1182 96 13 1300.000 \n", + "311 279 257 246 N E 170 284 3 525.000 \n", + "312 272 125 194 N E 186 290 17 550.000 \n", + "313 474 322 417 A E 121 267 19 1600.000 \n", + "314 66 41 34 N W 942 72 11 120.000 \n", + "315 82 100 57 A W 1222 139 15 165.000 \n", + "316 107 124 106 N E 325 58 6 NaN \n", + "317 379 311 138 N E 325 9 3 700.000 \n", + "318 897 451 875 A E 313 381 20 875.000 \n", + "319 217 93 146 A W 37 113 7 385.000 \n", + "320 470 420 332 A E 1314 131 12 960.000 \n", + "321 775 357 249 A W 408 4 3 1000.000 \n", + "\n", + " NewLeague \n", + "0 A \n", + "1 N \n", + "2 A \n", + "3 N \n", + "4 N \n", + "5 A \n", + "6 A \n", + "7 A \n", + "8 N \n", + "9 A \n", + "10 A \n", + "11 N \n", + "12 N \n", + "13 A \n", + "14 N \n", + "15 A \n", + "16 N \n", + "17 A \n", + "18 A \n", + "19 N \n", + "20 N \n", + "21 N \n", + "22 A \n", + "23 N \n", + "24 A \n", + "25 A \n", + "26 N \n", + "27 N \n", + "28 N \n", + "29 A \n", + ".. ... \n", + "292 A \n", + "293 N \n", + "294 A \n", + "295 A \n", + "296 N \n", + "297 A \n", + "298 A \n", + "299 A \n", + "300 N \n", + "301 N \n", + "302 N \n", + "303 A \n", + "304 N \n", + "305 N \n", + "306 N \n", + "307 N \n", + "308 N \n", + "309 N \n", + "310 N \n", + "311 N \n", + "312 N \n", + "313 A \n", + "314 N \n", + "315 A \n", + "316 N \n", + "317 N \n", + "318 A \n", + "319 A \n", + "320 A \n", + "321 A \n", + "\n", + "[322 rows x 20 columns]\n" + ] + } + ], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "Hitters=pd.read_csv(\"/data/shixunfiles/e6e58424771007dd312a029742530217_1638264937440.csv\")\n", + "print(Hitters)" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.preprocessing import scale#数据预处理,得到的的结果每列均值为0,方差为1\n", + "from sklearn.decomposition import PCA#PCA算法库\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.cross_decomposition import PLSRegression, PLSSVD#交叉分解\n", + "from sklearn.metrics import mean_squared_error#均方误差" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " League_A League_N Division_E Division_W NewLeague_A NewLeague_N\n", + "0 1 0 1 0 1 0\n", + "1 0 1 0 1 0 1\n", + "2 1 0 0 1 1 0\n", + "3 0 1 1 0 0 1\n", + "4 0 1 1 0 0 1\n", + "5 1 0 0 1 1 0\n", + "6 0 1 1 0 1 0\n", + "7 1 0 0 1 1 0\n", + "8 0 1 0 1 0 1\n", + "9 1 0 1 0 1 0\n", + "10 1 0 1 0 1 0\n", + "11 0 1 0 1 0 1\n", + "12 0 1 1 0 0 1\n", + "13 1 0 1 0 1 0\n", + "14 0 1 1 0 0 1\n", + "15 1 0 0 1 1 0\n", + "16 0 1 0 1 0 1\n", + "17 1 0 0 1 1 0\n", + "18 1 0 0 1 1 0\n", + "19 0 1 0 1 0 1\n", + "20 0 1 1 0 0 1\n", + "21 1 0 0 1 0 1\n", + "22 1 0 0 1 1 0\n", + "23 0 1 0 1 0 1\n", + "24 1 0 1 0 1 0\n", + "25 1 0 1 0 1 0\n", + "26 0 1 1 0 0 1\n", + "27 0 1 0 1 0 1\n", + "28 0 1 0 1 0 1\n", + "29 1 0 0 1 1 0\n", + ".. ... ... ... ... ... ...\n", + "292 1 0 0 1 1 0\n", + "293 0 1 1 0 0 1\n", + "294 1 0 0 1 1 0\n", + "295 0 1 0 1 1 0\n", + "296 0 1 1 0 0 1\n", + "297 1 0 0 1 1 0\n", + "298 1 0 1 0 1 0\n", + "299 1 0 0 1 1 0\n", + "300 0 1 1 0 0 1\n", + "301 0 1 1 0 0 1\n", + "302 0 1 0 1 0 1\n", + "303 1 0 0 1 1 0\n", + "304 0 1 0 1 0 1\n", + "305 0 1 1 0 0 1\n", + "306 0 1 0 1 0 1\n", + "307 0 1 1 0 0 1\n", + "308 0 1 1 0 0 1\n", + "309 0 1 1 0 0 1\n", + "310 0 1 1 0 0 1\n", + "311 0 1 1 0 0 1\n", + "312 0 1 1 0 0 1\n", + "313 1 0 1 0 1 0\n", + "314 0 1 0 1 0 1\n", + "315 1 0 0 1 1 0\n", + "316 0 1 1 0 0 1\n", + "317 0 1 1 0 0 1\n", + "318 1 0 1 0 1 0\n", + "319 1 0 0 1 1 0\n", + "320 1 0 1 0 1 0\n", + "321 1 0 0 1 1 0\n", + "\n", + "[322 rows x 6 columns]\n" + ] + } + ], + "source": [ + "dummies=pd.get_dummies(Hitters[['League', 'Division', 'NewLeague']])#将分类变量转化成虚拟变量或指标矩阵\n", + "#sklearn不能直接分析分类型的变量,常用欧式空间中的距离来衡量相似程度\n", + "#但是当类别很多的时候就会造成多维,因此使用PCA来降维\n", + "print(dummies)" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": {}, + "outputs": [], + "source": [ + "Hitters['Salary'].fillna('0',inplace=True)#填充non为0,inplace=True,会覆盖原数据" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": {}, + "outputs": [], + "source": [ + "y=Hitters.Salary\n", + "X=Hitters.drop(['Salary', 'League', 'Division', 'NewLeague'], axis=1).astype('float64')#去除行,将非主成分和因变量去掉,剩下20个主成分" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": {}, + "outputs": [], + "source": [ + "X=pd.concat([X_, dummies[['League_N', 'Division_W', 'NewLeague_N']]], axis=1)#行对齐,将不同列名称的两张表合并" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "可以使用 PCA() 函数执行主成分回归 (PCR),该函数是 sklearn 库的一部分。 在本实验中,我们将 PCR 应用于击球者数据,以预测薪水..." + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[-3.14857393 -0.39735086 -0.74226115 ... 0.04178935 0.0194595\n", + " -0.00399568]\n", + " [ 0.13528458 1.44872679 1.47931407 ... 0.08877741 0.03885092\n", + " -0.02378335]\n", + " [ 0.68070491 -2.64429774 -1.05413047 ... 0.04031652 0.01448852\n", + " -0.00701455]\n", + " ...\n", + " [-0.87602982 -0.95721001 -0.99858725 ... -0.06874074 0.06521014\n", + " 0.01951883]\n", + " [ 2.17773575 -2.36001164 -0.53069363 ... -0.01586417 0.0184468\n", + " -0.01039176]\n", + " [ 1.97397124 -0.33904516 -1.12557919 ... -0.28076437 -0.07356957\n", + " -0.02410452]]\n", + "322\n" + ] + } + ], + "source": [ + "pca=PCA()\n", + "X_reduced=pca.fit_transform(scale(X))#训练模型,pca是一个无监督算法,可以直接fit_transform\n", + "print(X_reduced)\n", + "print(len(X_reduced))" + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
012345
00.215399-0.3678060.0583830.0277280.017248-0.103710
10.210356-0.3638040.0487680.011653-0.013760-0.115771
20.209753-0.232320-0.190024-0.2667720.056637-0.074143
30.208525-0.366283-0.026125-0.052286-0.029717-0.174071
40.244688-0.303961-0.074444-0.1475220.001853-0.053992
\n", + "
" + ], + "text/plain": [ + " 0 1 2 3 4 5\n", + "0 0.215399 -0.367806 0.058383 0.027728 0.017248 -0.103710\n", + "1 0.210356 -0.363804 0.048768 0.011653 -0.013760 -0.115771\n", + "2 0.209753 -0.232320 -0.190024 -0.266772 0.056637 -0.074143\n", + "3 0.208525 -0.366283 -0.026125 -0.052286 -0.029717 -0.174071\n", + "4 0.244688 -0.303961 -0.074444 -0.147522 0.001853 -0.053992" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pd.DataFrame(pca.components_.T).loc[:4,:5]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在我们将执行 10 折交叉验证,看看它如何影响 MSE:" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[208971.19193682022]\n", + "[208971.19193682022, 144897.84704912142, 138363.498039743, 137418.20834745828, 137169.58213183572, 134905.71227494648, 135877.36069362512, 135727.6189039476, 137378.8965028787, 138499.85382947003, 139735.4129219722, 141464.16312308345, 141901.5061954281, 142738.73023283808, 138578.90930399625, 137844.1022951366, 135008.92288625863, 139793.95192336355, 139008.19141226978, 140393.56782725232]\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn import model_selection\n", + "# 10 折交叉验证,每次划分后都进行洗牌(shuffle)\n", + "n=len(X_reduced)\n", + "kf_10=model_selection.KFold( n_splits=10, shuffle=True, random_state=1)\n", + "\n", + "reg=LinearRegression()\n", + "mse=[]\n", + "\n", + "# 仅使用截距计算 MSE(回归中没有主成分)\n", + "score = -1*model_selection.cross_val_score(regr, np.ones((n,1)), y.ravel(), cv=kf_10, scoring='neg_mean_squared_error').mean() \n", + "mse.append(score)\n", + "#使用ravel对y进行降维\n", + "print(mse)\n", + "# 使用 CV 计算 19 个主要成分的 MSE,一次添加一个成分。\n", + "for i in np.arange(1, 20):\n", + " score = -1*model_selection.cross_val_score(regr, X_reduced[::,:i], y.ravel(), cv=kf_10, scoring='neg_mean_squared_error').mean()\n", + " mse.append(score)\n", + "print(mse)\n", + "# Plot results \n", + "plt.plot(mse, '-v')\n", + "plt.xlabel('Number of principal components in regression')\n", + "plt.ylabel('MSE')\n", + "plt.title('Salary')\n", + "plt.xlim(xmin=-1);#设置x轴的数值显示范围" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们看到,当使用 M=18 组件时,会出现最小的交叉验证错误。 这几乎不小于 M=19 ,这相当于简单地执行最小二乘法,因为当所有组件都用于 PCR 时,不会发生降维。 但是,从图中我们还看到,当模型中仅包含一个组件时,交叉验证误差大致相同。 这表明仅使用少量组件的模型可能就足够了。" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 38.88, 60.89, 71.38, 79.51, 84.78, 89.18, 92.68, 95.18,\n", + " 96.5 , 97.46, 98.12, 98.73, 99.22, 99.53, 99.78, 99.91,\n", + " 99.98, 100. , 100.01])" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)#计算轴向元素累加和,返回由中间结果组成的数组" + ] + }, + { + "attachments": { + "image.png": { + "image/png": "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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**9.随机森林回归**\n", + "有多个决定参数,根据重要性结合多个相同类型的算法,即多个决策树\n", + "\n", + "随机森林是一种集成技术,能够使用多个决策树和一种称为 Bootstrap 聚合(通常称为装袋)的技术来执行回归和分类任务。 你可能会问什么是装袋? 随机森林方法中的 Bagging 涉及在不同的数据样本上训练每个决策树,其中采样是通过替换完成的。\n", + "\n", + "![image.png](attachment:image.png)\n", + "\n", + "\n", + "这背后的基本思想是结合多个决策树来确定最终输出,而不是依赖于单个决策树。 如果您想阅读有关随机森林的更多信息,我提供了一些参考链接,这些链接提供了有关该主题的深入解释。\n", + "1从数据集中中选择N个样本子集,每进行一次交叉验证则会生成一个子集\n", + "2基于N个样本子集构建决策树\n", + "3选择算法中所需要的棵数,然后重复1和2\n", + "回归问题中每棵树都预测Y值,取平均值输出" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.model_selection import cross_val_score, GridSearchCV#交叉验证库\n", + "from sklearn.ensemble import RandomForestRegressor#随机森林\n", + "from sklearn.preprocessing import MinMaxScaler#数据归一化" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def rfr_model(X, y):\n", + "# Perform Grid-Search\n", + " gsc=GridSearchCV( #k折交叉验证\n", + " estimator=RandomForestRegressor(), #使用随机森林的分类器\n", + " param_grid={ # param_grid传入字典或列表,优化参数的取值\n", + " 'max_depth': range(3,7),#决策树深度\n", + " 'n_estimators': (10, 50, 100, 1000),#决策树棵数\n", + " },\n", + " cv=5, scoring='neg_mean_squared_error', verbose=0,n_jobs=-1)#n_jobs并行job个数,-1表示CPU有多少核就启动多少\n", + " \n", + " grid_result=gsc.fit(X, y)#把5折交叉验证的结果都放进去训练模型,得到5组结果\n", + " best_params= grid_result.best_params_#最好的参数设置\n", + " \n", + " rfr=RandomForestRegressor(max_depth=best_params[\"max_depth\"], n_estimators=best_params[\"n_estimators\"],random_state=False, verbose=False)\n", + " #在利用最大平均值来预测之前,你想要子树的数量(用上文得到的);,random_state=False确定的随机数,verbose=False表示不显示详细信息\n", + " scores=cross_val_score(rfr, X, y, cv=10, scoring='neg_mean_absolute_error')#10折交叉验证,得分需要绝对误差最小\n", + "\n", + " return scores" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'X' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrfr_model\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mNameError\u001b[0m: name 'X' is not defined" + ] + } + ], + "source": [ + "rfr_model(X,y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**10.XGBoost**\n", + "\n", + "XGBoost 是当今最流行的机器学习算法之一。 无论手头的预测任务类型如何; 回归或分类\n", + "\n", + "**提升**\n", + "\n", + "Boosting 是一种基于集成原理的顺序技术。 它结合了一组弱学习器并提高了预测精度。 在任何时刻 t,模型结果都基于前一个时刻 t-1 的结果进行加权。 正确预测的结果被赋予较低的权重,而错误分类的结果权重较高。 请注意,弱学习器比随机猜测略好。 例如,预测略好于 50% 的决策树。" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'data': array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,\n", + " 4.9800e+00],\n", + " [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,\n", + " 9.1400e+00],\n", + " [2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,\n", + " 4.0300e+00],\n", + " ...,\n", + " [6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n", + " 5.6400e+00],\n", + " [1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,\n", + " 6.4800e+00],\n", + " [4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,\n", + " 7.8800e+00]]), 'target': array([24. , 21.6, 34.7, 33.4, 36.2, 28.7, 22.9, 27.1, 16.5, 18.9, 15. ,\n", + " 18.9, 21.7, 20.4, 18.2, 19.9, 23.1, 17.5, 20.2, 18.2, 13.6, 19.6,\n", + " 15.2, 14.5, 15.6, 13.9, 16.6, 14.8, 18.4, 21. , 12.7, 14.5, 13.2,\n", + " 13.1, 13.5, 18.9, 20. , 21. , 24.7, 30.8, 34.9, 26.6, 25.3, 24.7,\n", + " 21.2, 19.3, 20. , 16.6, 14.4, 19.4, 19.7, 20.5, 25. , 23.4, 18.9,\n", + " 35.4, 24.7, 31.6, 23.3, 19.6, 18.7, 16. , 22.2, 25. , 33. , 23.5,\n", + " 19.4, 22. , 17.4, 20.9, 24.2, 21.7, 22.8, 23.4, 24.1, 21.4, 20. ,\n", + " 20.8, 21.2, 20.3, 28. , 23.9, 24.8, 22.9, 23.9, 26.6, 22.5, 22.2,\n", + " 23.6, 28.7, 22.6, 22. , 22.9, 25. , 20.6, 28.4, 21.4, 38.7, 43.8,\n", + " 33.2, 27.5, 26.5, 18.6, 19.3, 20.1, 19.5, 19.5, 20.4, 19.8, 19.4,\n", + " 21.7, 22.8, 18.8, 18.7, 18.5, 18.3, 21.2, 19.2, 20.4, 19.3, 22. ,\n", + " 20.3, 20.5, 17.3, 18.8, 21.4, 15.7, 16.2, 18. , 14.3, 19.2, 19.6,\n", + " 23. , 18.4, 15.6, 18.1, 17.4, 17.1, 13.3, 17.8, 14. , 14.4, 13.4,\n", + " 15.6, 11.8, 13.8, 15.6, 14.6, 17.8, 15.4, 21.5, 19.6, 15.3, 19.4,\n", + " 17. , 15.6, 13.1, 41.3, 24.3, 23.3, 27. , 50. , 50. , 50. , 22.7,\n", + " 25. , 50. , 23.8, 23.8, 22.3, 17.4, 19.1, 23.1, 23.6, 22.6, 29.4,\n", + " 23.2, 24.6, 29.9, 37.2, 39.8, 36.2, 37.9, 32.5, 26.4, 29.6, 50. ,\n", + " 32. , 29.8, 34.9, 37. , 30.5, 36.4, 31.1, 29.1, 50. , 33.3, 30.3,\n", + " 34.6, 34.9, 32.9, 24.1, 42.3, 48.5, 50. , 22.6, 24.4, 22.5, 24.4,\n", + " 20. , 21.7, 19.3, 22.4, 28.1, 23.7, 25. , 23.3, 28.7, 21.5, 23. ,\n", + " 26.7, 21.7, 27.5, 30.1, 44.8, 50. , 37.6, 31.6, 46.7, 31.5, 24.3,\n", + " 31.7, 41.7, 48.3, 29. , 24. , 25.1, 31.5, 23.7, 23.3, 22. , 20.1,\n", + " 22.2, 23.7, 17.6, 18.5, 24.3, 20.5, 24.5, 26.2, 24.4, 24.8, 29.6,\n", + " 42.8, 21.9, 20.9, 44. , 50. , 36. , 30.1, 33.8, 43.1, 48.8, 31. ,\n", + " 36.5, 22.8, 30.7, 50. , 43.5, 20.7, 21.1, 25.2, 24.4, 35.2, 32.4,\n", + " 32. , 33.2, 33.1, 29.1, 35.1, 45.4, 35.4, 46. , 50. , 32.2, 22. ,\n", + " 20.1, 23.2, 22.3, 24.8, 28.5, 37.3, 27.9, 23.9, 21.7, 28.6, 27.1,\n", + " 20.3, 22.5, 29. , 24.8, 22. , 26.4, 33.1, 36.1, 28.4, 33.4, 28.2,\n", + " 22.8, 20.3, 16.1, 22.1, 19.4, 21.6, 23.8, 16.2, 17.8, 19.8, 23.1,\n", + " 21. , 23.8, 23.1, 20.4, 18.5, 25. , 24.6, 23. , 22.2, 19.3, 22.6,\n", + " 19.8, 17.1, 19.4, 22.2, 20.7, 21.1, 19.5, 18.5, 20.6, 19. , 18.7,\n", + " 32.7, 16.5, 23.9, 31.2, 17.5, 17.2, 23.1, 24.5, 26.6, 22.9, 24.1,\n", + " 18.6, 30.1, 18.2, 20.6, 17.8, 21.7, 22.7, 22.6, 25. , 19.9, 20.8,\n", + " 16.8, 21.9, 27.5, 21.9, 23.1, 50. , 50. , 50. , 50. , 50. , 13.8,\n", + " 13.8, 15. , 13.9, 13.3, 13.1, 10.2, 10.4, 10.9, 11.3, 12.3, 8.8,\n", + " 7.2, 10.5, 7.4, 10.2, 11.5, 15.1, 23.2, 9.7, 13.8, 12.7, 13.1,\n", + " 12.5, 8.5, 5. , 6.3, 5.6, 7.2, 12.1, 8.3, 8.5, 5. , 11.9,\n", + " 27.9, 17.2, 27.5, 15. , 17.2, 17.9, 16.3, 7. , 7.2, 7.5, 10.4,\n", + " 8.8, 8.4, 16.7, 14.2, 20.8, 13.4, 11.7, 8.3, 10.2, 10.9, 11. ,\n", + " 9.5, 14.5, 14.1, 16.1, 14.3, 11.7, 13.4, 9.6, 8.7, 8.4, 12.8,\n", + " 10.5, 17.1, 18.4, 15.4, 10.8, 11.8, 14.9, 12.6, 14.1, 13. , 13.4,\n", + " 15.2, 16.1, 17.8, 14.9, 14.1, 12.7, 13.5, 14.9, 20. , 16.4, 17.7,\n", + " 19.5, 20.2, 21.4, 19.9, 19. , 19.1, 19.1, 20.1, 19.9, 19.6, 23.2,\n", + " 29.8, 13.8, 13.3, 16.7, 12. , 14.6, 21.4, 23. , 23.7, 25. , 21.8,\n", + " 20.6, 21.2, 19.1, 20.6, 15.2, 7. , 8.1, 13.6, 20.1, 21.8, 24.5,\n", + " 23.1, 19.7, 18.3, 21.2, 17.5, 16.8, 22.4, 20.6, 23.9, 22. , 11.9]), 'feature_names': array(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD',\n", + " 'TAX', 'PTRATIO', 'B', 'LSTAT'], dtype='\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTATPRICE
00.0063218.02.310.00.5386.57565.24.09001.0296.015.3396.904.9824.0
10.027310.07.070.00.4696.42178.94.96712.0242.017.8396.909.1421.6
20.027290.07.070.00.4697.18561.14.96712.0242.017.8392.834.0334.7
30.032370.02.180.00.4586.99845.86.06223.0222.018.7394.632.9433.4
40.069050.02.180.00.4587.14754.26.06223.0222.018.7396.905.3336.2
\n", + "" + ], + "text/plain": [ + " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n", + "0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 \n", + "1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 \n", + "2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 \n", + "3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 \n", + "4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 \n", + "\n", + " PTRATIO B LSTAT PRICE \n", + "0 15.3 396.90 4.98 24.0 \n", + "1 17.8 396.90 9.14 21.6 \n", + "2 17.8 392.83 4.03 34.7 \n", + "3 18.7 394.63 2.94 33.4 \n", + "4 18.7 396.90 5.33 36.2 " + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "data['PRICE'] = boston.target#加入因变量一列" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "RangeIndex: 506 entries, 0 to 505\n", + "Data columns (total 14 columns):\n", + "CRIM 506 non-null float64\n", + "ZN 506 non-null float64\n", + "INDUS 506 non-null float64\n", + "CHAS 506 non-null float64\n", + "NOX 506 non-null float64\n", + "RM 506 non-null float64\n", + "AGE 506 non-null float64\n", + "DIS 506 non-null float64\n", + "RAD 506 non-null float64\n", + "TAX 506 non-null float64\n", + "PTRATIO 506 non-null float64\n", + "B 506 non-null float64\n", + "LSTAT 506 non-null float64\n", + "PRICE 506 non-null float64\n", + "dtypes: float64(14)\n", + "memory usage: 55.4 KB\n" + ] + } + ], + "source": [ + "data.info()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "import xgboost as xgb#xgboost库\n", + "from sklearn.metrics import mean_squared_error#均方误差\n", + "import pandas as pd\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "X, y = data.iloc[::,:-1],data.iloc[::,-1]#x取自变量,y取因变量" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "现在,您将数据集转换为 XGBoost 支持的名为 **Dmatrix** 的优化数据结构,并为其带来广受赞誉的性能和效率提升。 您将在本教程后面使用它。" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "data_dmatrix = xgb.DMatrix(data=X,label=y)\n", + "#Dmatrix是xgboost自定义数据矩阵,用于封装数据,可以优化储存和运算速度,data为数据,label为标签" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=123)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "xg_reg=xgb.XGBRegressor(objective ='reg:linear', colsample_bytree = 0.3, learning_rate = 0.1,max_depth = 5, alpha = 10, n_estimators = 10)\n", + "#建立xgboost模型\n", + "#objective为损失函数的类型 colsample_bytree构造每棵树是随机特征占所有特征的比例,learning_rate防止过拟合要乘以一个小数,决策树最大深度=5,\n", + "#正则化系数L1=10,n_estimators表示迭代次数" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[14:18:44] WARNING: ../src/objective/regression_obj.cu:171: reg:linear is now deprecated in favor of reg:squarederror.\n" + ] + } + ], + "source": [ + "xg_reg.fit(X_train,y_train)#训练\n", + "\n", + "preds = xg_reg.predict(X_test)#预测" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RMSE: 10.496021\n" + ] + } + ], + "source": [ + "rmse=np.sqrt(mean_squared_error(y_test, preds))#输出预测值的均方标准差\n", + "print(\"RMSE: %f\" % (rmse))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "好吧,您可以看到价格预测的 RMSE 大约为每 1000 美元 10.8。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}