{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### 一.过拟合\n", "建模的目的是让模型学习到数据的一般性规律，但有时候可能会学过头，学到一些噪声数据的特性，虽然模型可以在训练集上取得好的表现，但在测试集上结果往往会变差，这时称模型陷入了**过拟合**，接下来造一些伪数据进行演示：" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import os\n", "os.chdir('../')\n", "from ml_models.linear_model import *\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "#造伪样本\n", "X=np.linspace(0,100,100)\n", "X=np.c_[X,np.ones(100)]\n", "w=np.asarray([3,2])\n", "Y=X.dot(w)\n", "X=X.astype('float')\n", "Y=Y.astype('float')\n", "X[:,0]+=np.random.normal(size=(X[:,0].shape))*3#添加噪声\n", "Y=Y.reshape(100,1)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#拟合数据并可视化\n", "lr=LinearRegression()\n", "lr.fit(X[:,:-1],Y)\n", "lr.plot_fit_boundary(X[:,:-1],Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "目前看起来效果还是可以的，但如果加入几个异常点，再看看效果呢" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X=np.concatenate([X,np.asanyarray([[100,1],[101,1],[102,1],[103,1],[104,1]])])\n", "Y=np.concatenate([Y,np.asanyarray([[3000],[3300],[3600],[3800],[3900]])])\n", "lr=LinearRegression()\n", "lr.fit(X[:,:-1],Y)\n", "lr.plot_fit_boundary(X[:,:-1],Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 二.正则化\n", "可以看到，仅仅加入了几个很离谱的异常点，就会对预测产生很大的影响，且偏离很远，这在实际情况中是很常见的；通常可以通过对模型参数添加正则化约束来避免这种情况，使其不会太“飘”，做法是在loss函数中为权重$w$添加$L_1$或者$L_2$约束，借用上一节的公式推导，直接推出loss部分： \n", "\n", "1.线性回归中添加$L_1$约束称为Lasso回归，其损失函数如下： \n", "$$\n", "L(w)=\\sum_{i=1}^m(y_i-f(x_i))^2+\\lambda||w||_1\n", "$$ \n", "2.线性回归中添加$L_2$约束称为Ridge回归，其损失函数如下： \n", "$$\n", "L(w)=\\sum_{i=1}^m(y_i-f(x_i))^2+\\alpha||w||_2\n", "$$ \n", "3.如果不太确定用$L_1$好，还是$L_2$好，可以用它们的组合，称作ElasticNet，损失函数如下： \n", "$$\n", "L(w)=\\sum_{i=1}^m(y_i-f(x_i))^2+\\lambda||w||_1+\\alpha||w||_2\n", "$$ \n", "可以发现通过调整超参，可以控制$w$的大小，如果$\\lambda$或$\\alpha$设置很大，$w$会被约束的很小，而如果$\\alpha$或$\\lambda$设置为0，等价于原始的不带正则项的线性回归；通常可以通过交叉验证，根据验证集上的表现来设置一个合适的超参；接下来在上一节线性回归代码的基础上实现Lasso,Ridge,ElasticNet模型，另外设置两个参数`l1_ratio`以及`l2_ratio`，分别用来控制$L_1$和$L_2$的loss部分的权重\n", "### 三.代码实现" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "class LinearRegression(object):\n", " def __init__(self, fit_intercept=True, solver='sgd', if_standard=True, epochs=10, eta=1e-2, batch_size=1,\n", " l1_ratio=None, l2_ratio=None):\n", " \"\"\"\n", " :param fit_intercept: 是否训练bias\n", " :param solver:\n", " :param if_standard:\n", " \"\"\"\n", " self.w = None\n", " self.fit_intercept = fit_intercept\n", " self.solver = solver\n", " self.if_standard = if_standard\n", " if if_standard:\n", " self.feature_mean = None\n", " self.feature_std = None\n", " self.epochs = epochs\n", " self.eta = eta\n", " self.batch_size = batch_size\n", " self.l1_ratio = l1_ratio\n", " self.l2_ratio = l2_ratio\n", " # 注册sign函数\n", " self.sign_func = np.vectorize(utils.sign)\n", "\n", " def init_params(self, n_features):\n", " \"\"\"\n", " 初始化参数\n", " :return:\n", " \"\"\"\n", " self.w = np.random.random(size=(n_features, 1))\n", "\n", " def _fit_closed_form_solution(self, x, y):\n", " \"\"\"\n", " 直接求闭式解\n", " :param x:\n", " :param y:\n", " :return:\n", " \"\"\"\n", " if self.l1_ratio is None and self.l2_ratio is None:\n", " self.w = np.linalg.pinv(x).dot(y)\n", " elif self.l1_ratio is None and self.l2_ratio is not None:\n", " self.w = np.linalg.inv(x.T.dot(x) + self.l2_ratio * np.eye(x.shape[1])).dot(x.T).dot(y)\n", " else:\n", " self._fit_sgd(x, y)\n", "\n", " def _fit_sgd(self, x, y):\n", " \"\"\"\n", " 随机梯度下降求解\n", " :param x:\n", " :param y:\n", " :param epochs:\n", " :param eta:\n", " :param batch_size:\n", " :return:\n", " \"\"\"\n", " x_y = np.c_[x, y]\n", " # 按batch_size更新w,b\n", " for _ in range(self.epochs):\n", " np.random.shuffle(x_y)\n", " for index in range(x_y.shape[0] // self.batch_size):\n", " batch_x_y = x_y[self.batch_size * index:self.batch_size * (index + 1)]\n", " batch_x = batch_x_y[:, :-1]\n", " batch_y = batch_x_y[:, -1:]\n", "\n", " dw = -2 * batch_x.T.dot(batch_y - batch_x.dot(self.w)) / self.batch_size\n", "\n", " # 添加l1和l2的部分\n", " dw_reg = np.zeros(shape=(x.shape[1] - 1, 1))\n", " if self.l1_ratio is not None:\n", " dw_reg += self.l1_ratio * self.sign_func(self.w[:-1]) / self.batch_size\n", " if self.l2_ratio is not None:\n", " dw_reg += 2 * self.l2_ratio * self.w[:-1] / self.batch_size\n", " dw_reg = np.concatenate([dw_reg, np.asarray([[0]])], axis=0)\n", " dw += dw_reg\n", " self.w = self.w - self.eta * dw\n", "\n", " def fit(self, x, y):\n", " # 是否归一化feature\n", " if self.if_standard:\n", " self.feature_mean = np.mean(x, axis=0)\n", " self.feature_std = np.std(x, axis=0) + 1e-8\n", " x = (x - self.feature_mean) / self.feature_std\n", " # 是否训练bias\n", " if self.fit_intercept:\n", " x = np.c_[x, np.ones_like(y)]\n", " # 初始化参数\n", " self.init_params(x.shape[1])\n", " # 训练模型\n", " if self.solver == 'closed_form':\n", " self._fit_closed_form_solution(x, y)\n", " elif self.solver == 'sgd':\n", " self._fit_sgd(x, y)\n", "\n", " def get_params(self):\n", " \"\"\"\n", " 输出原始的系数\n", " :return: w,b\n", " \"\"\"\n", " if self.fit_intercept:\n", " w = self.w[:-1]\n", " b = self.w[-1]\n", " else:\n", " w = self.w\n", " b = 0\n", " if self.if_standard:\n", " w = w / self.feature_std.reshape(-1, 1)\n", " b = b - w.T.dot(self.feature_mean.reshape(-1, 1))\n", " return w.reshape(-1), b\n", "\n", " def predict(self, x):\n", " \"\"\"\n", " :param x:ndarray格式数据: m x n\n", " :return: m x 1\n", " \"\"\"\n", " if self.if_standard:\n", " x = (x - self.feature_mean) / self.feature_std\n", " if self.fit_intercept:\n", " x = np.c_[x, np.ones(shape=x.shape[0])]\n", " return x.dot(self.w)\n", "\n", " def plot_fit_boundary(self, x, y):\n", " \"\"\"\n", " 绘制拟合结果\n", " :param x:\n", " :param y:\n", " :return:\n", " \"\"\"\n", " plt.scatter(x[:, 0], y)\n", " plt.plot(x[:, 0], self.predict(x), 'r')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Lasso" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lasso=LinearRegression(l1_ratio=100)\n", "lasso.fit(X[:,:-1],Y)\n", "lasso.plot_fit_boundary(X[:,:-1],Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ridge" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ridge=LinearRegression(l2_ratio=10)\n", "ridge.fit(X[:,:-1],Y)\n", "ridge.plot_fit_boundary(X[:,:-1],Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ElasticNet" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n"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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "elastic=LinearRegression(l1_ratio=100,l2_ratio=10)\n", "elastic.fit(X[:,:-1],Y)\n", "elastic.plot_fit_boundary(X[:,:-1],Y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "将sign函数整理到ml_models.utils中" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }