{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 逻辑回归 Logistic Regression\n", "\n", "逻辑回归(Logistic Regression, LR)模型其实仅在线性回归的基础上,套用了一个逻辑函数,但也就由于这个逻辑函数,使得逻辑回归模型成为了机器学习领域一颗耀眼的明星,更是计算广告学的核心。本节主要详述逻辑回归模型的基础。\n", "\n", "\n", "## 1. 逻辑回归模型\n", "回归是一种比较容易理解的模型,就相当于$y=f(x)$,表明自变量$x$与因变量$y$的关系。最常见问题有如医生治病时的望、闻、问、切,之后判定病人是否生病或生了什么病,其中的望闻问切就是获取自变量$x$,即特征数据,判断是否生病就相当于获取因变量$y$,即预测分类。\n", "\n", "最简单的回归是线性回归,在此借用Andrew NG的讲义,有如图所示,$X$为数据点——肿瘤的大小,$Y$为观测值——是否是恶性肿瘤。通过构建线性回归模型,如$h_\\theta(x)$所示,构建线性回归模型后,即可以根据肿瘤大小,预测是否为恶性肿瘤$h_\\theta(x)) \\ge 0.5$为恶性,$h_\\theta(x) \\lt 0.5$为良性。\n", "\n", "![LinearRegression](images/fig1.gif)\n", "\n", "然而线性回归的鲁棒性很差,例如在上图的数据集上建立回归,因最右边噪点的存在,使回归模型在训练集上表现都很差。这主要是由于线性回归在整个实数域内敏感度一致,而分类范围,需要在$[0,1]$。\n", "\n", "逻辑回归就是一种减小预测范围,将预测值限定为$[0,1]$间的一种回归模型,其回归方程与回归曲线如图2所示。逻辑曲线在$z=0$时,十分敏感,在$z>>0$或$z<<0$处,都不敏感,将预测值限定为$(0,1)$。\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.figure()\n", "plt.axis([-10,10,0,1])\n", "plt.grid(True)\n", "X=np.arange(-10,10,0.1)\n", "y=1/(1+np.e**(-X))\n", "plt.plot(X,y,'b-')\n", "plt.title(\"Logistic function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1 逻辑回归表达式\n", "\n", "这个函数称为Logistic函数(logistic function),也称为Sigmoid函数(sigmoid function)。函数公式如下:\n", "\n", "$$\n", "g(z) = \\frac{1}{1+e^{-z}}\n", "$$\n", "\n", "Logistic函数当z趋近于无穷大时,g(z)趋近于1;当z趋近于无穷小时,g(z)趋近于0。Logistic函数的图形如上图所示。Logistic函数求导时有一个特性,这个特性将在下面的推导中用到,这个特性为:\n", "$$\n", "g'(z) = \\frac{d}{dz} \\frac{1}{1+e^{-z}} \\\\\n", " = \\frac{1}{(1+e^{-z})^2}(e^{-z}) \\\\\n", " = \\frac{1}{(1+e^{-z})} (1 - \\frac{1}{(1+e^{-z})}) \\\\\n", " = g(z)(1-g(z))\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "plt.figure()\n", "plt.axis([-10,10,0,1])\n", "plt.grid(True)\n", "X=np.arange(-10,10,0.1)\n", "y=1/(1+np.e**(-X))\n", "plt.plot(X,y,'b-')\n", "plt.title(\"Logistic function\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "逻辑回归本质上是线性回归,只是在特征到结果的映射中加入了一层函数映射,即先把特征线性求和,然后使用函数$g(z)$将做为假设函数来预测。$g(z)$可以将连续值映射到0到1之间。线性回归模型的表达式带入$g(z)$,就得到逻辑回归的表达式:\n", "\n", "$$\n", "h_\\theta(x) = g(\\theta^T x) = \\frac{1}{1+e^{-\\theta^T x}}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2 逻辑回归的软分类\n", "\n", "现在我们将y的取值$h_\\theta(x)$通过Logistic函数归一化到(0,1)间,$y$的取值有特殊的含义,它表示结果取1的概率,因此对于输入$x$分类结果为类别1和类别0的概率分别为:\n", "\n", "$$\n", "P(y=1|x,\\theta) = h_\\theta(x) \\\\\n", "P(y=0|x,\\theta) = 1 - h_\\theta(x)\n", "$$\n", "\n", "对上面的表达式合并一下就是:\n", "\n", "$$\n", "p(y|x,\\theta) = (h_\\theta(x))^y (1 - h_\\theta(x))^{1-y}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3 梯度上升\n", "\n", "得到了逻辑回归的表达式,下一步跟线性回归类似,构建似然函数,然后最大似然估计,最终推导出$\\theta$的迭代更新表达式。只不过这里用的不是梯度下降,而是梯度上升,因为这里是最大化似然函数。\n", "\n", "我们假设训练样本相互独立,那么似然函数表达式为:\n", "![Loss](images/eq_loss.png)\n", "\n", "同样对似然函数取log,转换为:\n", "![LogLoss](images/eq_logloss.png)\n", "\n", "转换后的似然函数对$\\theta$求偏导,在这里我们以只有一个训练样本的情况为例:\n", "![LogLossDiff](images/eq_logloss_diff.png)\n", "\n", "这个求偏导过程中:\n", "* 第一步是对$\\theta$偏导的转化,依据偏导公式:$y=lnx$, $y'=1/x$。\n", "* 第二步是根据g(z)求导的特性g'(z) = g(z)(1 - g(z)) 。\n", "* 第三步就是普通的变换。\n", "\n", "这样我们就得到了梯度上升每次迭代的更新方向,那么$\\theta$的迭代表达式为:(FIXME: `j`)\n", "$$\n", "\\theta_j = \\theta_j + \\alpha(y^i - h_\\theta(x^i)) x_j^i\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.4 示例程序" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "#from __future__ import division\n", "import numpy as np\n", "import sklearn.datasets\n", "import matplotlib.pyplot as plt\n", "\n", "np.random.seed(0)\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "data = [[ 0.694565 0.42666408]\n", " [ 1.68353008 -0.80016643]\n", " [-0.25046823 0.24392224]\n", " [-1.13337973 -0.6112787 ]\n", " [ 1.76905577 -0.31025439]\n", " [ 2.00225511 -0.18592 ]\n", " [ 0.91169861 0.46995543]\n", " [ 0.88211794 -0.46701178]\n", " [ 0.75006972 0.33995342]\n", " [ 1.30208867 -0.72334923]]\n", "label = [0 1 1 0 1 1 0 1 0 1]\n" ] }, { "data": { "text/plain": [ "Text(0.5, 1.0, 'Original Data')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# load sample data\n", "data, label = sklearn.datasets.make_moons(200, noise=0.30)\n", "\n", "print(\"data = \", data[:10, :])\n", "print(\"label = \", label[:10])\n", "\n", "plt.scatter(data[:,0], data[:,1], c=label)\n", "plt.title(\"Original Data\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def plot_decision_boundary(predict_func, data, label):\n", " \"\"\"画出结果图\n", " Args:\n", " pred_func (callable): 预测函数\n", " data (numpy.ndarray): 训练数据集合\n", " label (numpy.ndarray): 训练数据标签\n", " 散开数据,但是不在原来的数据上做修改\n", " \"\"\"\n", " x_min, x_max = data[:, 0].min() - .5, data[:, 0].max() + .5\n", " y_min, y_max = data[:, 1].min() - .5, data[:, 1].max() + .5\n", " h = 0.01\n", "\n", " xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n", "\n", " Z = predict_func(np.c_[xx.ravel(), yy.ravel()])\n", " Z = Z.reshape(xx.shape)\n", "\n", " plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) #画出登高线并填充\n", " plt.scatter(data[:, 0], data[:, 1], c=label, cmap=plt.cm.Spectral)\n", " plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# FIXME: function sample\n", "\n", "\n", "def sigmoid(x):\n", " return 1.0 / (1 + np.exp(-x))\n", "\n", "class Logistic(object):\n", " \"\"\"logistic回归模型\"\"\"\n", " def __init__(self, data, label):\n", " self.data = data\n", " self.label = label\n", "\n", " # FIXME: n -> d\n", " self.data_num, n = np.shape(data)\n", " self.weights = np.ones(n)\n", " self.b = 1\n", "\n", " def train(self, num_iteration=150):\n", " \"\"\"随机梯度上升算法\n", " Args:\n", " data (numpy.ndarray): 训练数据集\n", " labels (numpy.ndarray): 训练标签\n", " num_iteration (int): 迭代次数\n", " \"\"\"\n", " # 学习速率\n", " alpha = 0.01\n", " \n", " for j in range(num_iteration):\n", " data_index = list(range(self.data_num))\n", " for i in range(self.data_num):\n", " rand_index = int(np.random.uniform(0, len(data_index)))\n", " error = self.label[rand_index] - \\\n", " sigmoid(sum(self.data[rand_index] * self.weights + self.b))\n", " self.weights += alpha * error * self.data[rand_index]\n", " self.b += alpha * error\n", " del(data_index[rand_index])\n", "\n", " def predict(self, predict_data):\n", " \"\"\"预测函数\"\"\"\n", " result = list(map(lambda x: 1 if sum(self.weights * x + self.b) > 0 else 0,\n", " predict_data))\n", " return np.array(result)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "logistic = Logistic(data, label)\n", "logistic.train(200)\n", "plot_decision_boundary(lambda x: logistic.predict(x), data, label)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.如何用sklearn解决逻辑回归问题?" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accuracy train = 0.850000\n", "accuracy test = 0.825000\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.linear_model.logistic import LogisticRegression\n", "from sklearn.metrics import confusion_matrix\n", "from sklearn.metrics import accuracy_score\n", "import matplotlib.pyplot as plt\n", "\n", "# calculate train/test data number\n", "N = len(data)\n", "N_train = int(N*0.6)\n", "N_test = N - N_train\n", "\n", "# split train/test data\n", "x_train = data[:N_train, :]\n", "y_train = label[:N_train]\n", "x_test = data[N_train:, :]\n", "y_test = label[N_train:]\n", "\n", "# do logistic regression\n", "lr=LogisticRegression()\n", "lr.fit(x_train,y_train)\n", "\n", "pred_train = lr.predict(x_train)\n", "pred_test = lr.predict(x_test)\n", "\n", "# calculate train/test accuracy\n", "acc_train = accuracy_score(y_train, pred_train)\n", "acc_test = accuracy_score(y_test, pred_test)\n", "print(\"accuracy train = %f\" % acc_train)\n", "print(\"accuracy test = %f\" % acc_test)\n", "\n", "# plot confusion matrix\n", "cm = confusion_matrix(y_test,pred_test)\n", "\n", "plt.matshow(cm)\n", "plt.title(u'Confusion Matrix')\n", "plt.colorbar()\n", "plt.ylabel(u'Groundtruth')\n", "plt.xlabel(u'Predict')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. 多类识别问题" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1 加载显示数据" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt \n", "from sklearn.datasets import load_digits\n", "\n", "# load data\n", "digits = load_digits()\n", "\n", "# copied from notebook 02_sklearn_data.ipynb\n", "fig = plt.figure(figsize=(6, 6)) # figure size in inches\n", "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n", "\n", "# plot the digits: each image is 8x8 pixels\n", "for i in range(64):\n", " ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n", " ax.imshow(digits.images[i], cmap=plt.cm.binary)\n", " \n", " # label the image with the target value\n", " ax.text(0, 7, str(digits.target[i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2 可视化特征\n", "\n", "针对机器学习的问题,一个比较好的方法是通过降维的方法将原始的高维特征降到2-3维并可视化处理,通过这样的方法可以对所要处理的数据有一个初步的认识。这里介绍最简单的降维方法主成分分析(Principal Component Analysis, PCA).\n", "\n", "PCA寻求具有最大方差的特征的正交线性组合,因此可以更好地了解数据的结构。在这里,我们将使用Randomized PCA,因为当数据个数$N$比较大时,计算的效率更好。\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.decomposition import PCA\n", "pca = PCA(n_components=2, svd_solver=\"randomized\")\n", "proj = pca.fit_transform(digits.data)\n", "\n", "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PCA的一个缺点是它可能会丢失数据中一些有趣的相互关系。如果想看到非线性的降维与映射\n", "我们可以使用几种流形模块中的方法。在这里,我们将使用[Isomap](https://blog.csdn.net/VictoriaW/article/details/78497316)(串联\n", "等距映射)是一种基于图论的流形降维方法。" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.manifold import Isomap\n", "iso = Isomap(n_neighbors=5, n_components=2)\n", "proj = iso.fit_transform(digits.data)\n", "\n", "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3 示例程序" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1797, 64)\n", "accuracy train = 1.000000, accuracy_test = 0.905556\n", "score_train = 1.000000, score_test = 0.905556\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/bushuhui/virtualenv/dl/lib/python3.6/site-packages/sklearn/linear_model/_logistic.py:764: ConvergenceWarning: lbfgs failed to converge (status=1):\n", "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n", "\n", "Increase the number of iterations (max_iter) or scale the data as shown in:\n", " https://scikit-learn.org/stable/modules/preprocessing.html\n", "Please also refer to the documentation for alternative solver options:\n", " https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n", " extra_warning_msg=_LOGISTIC_SOLVER_CONVERGENCE_MSG)\n" ] } ], "source": [ "from sklearn.datasets import load_digits\n", "from sklearn.linear_model.logistic import LogisticRegression\n", "from sklearn.metrics import accuracy_score\n", "\n", "import matplotlib.pyplot as plt \n", "\n", "# load digital data\n", "digits, dig_label = load_digits(return_X_y=True)\n", "print(digits.shape)\n", "\n", "# calculate train/test data number\n", "N = len(digits)\n", "N_train = int(N*0.8)\n", "N_test = N - N_train\n", "\n", "# split train/test data\n", "x_train = digits[:N_train, :]\n", "y_train = dig_label[:N_train]\n", "x_test = digits[N_train:, :]\n", "y_test = dig_label[N_train:]\n", "\n", "# FIXME: need to use Isomap to transform data\n", "\n", "# do logistic regression\n", "lr=LogisticRegression()\n", "lr.fit(x_train,y_train)\n", "\n", "pred_train = lr.predict(x_train)\n", "pred_test = lr.predict(x_test)\n", "\n", "# calculate train/test accuracy\n", "acc_train = accuracy_score(y_train, pred_train)\n", "acc_test = accuracy_score(y_test, pred_test)\n", "print(\"accuracy train = %f, accuracy_test = %f\" % (acc_train, acc_test))\n", "\n", "score_train = lr.score(x_train, y_train)\n", "score_test = lr.score(x_test, y_test)\n", "print(\"score_train = %f, score_test = %f\" % (score_train, score_test))\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.metrics import confusion_matrix\n", "\n", "# plot confusion matrix\n", "cm = confusion_matrix(y_test,pred_test)\n", "\n", "plt.matshow(cm)\n", "plt.title(u'Confusion Matrix')\n", "plt.colorbar()\n", "plt.ylabel(u'Groundtruth')\n", "plt.xlabel(u'Predict')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. 练习 - 如何画出错误分类的数据?\n", "\n", "1. 如何得到错误分类数据的下标?\n", "2. 如何根据下标,将这些错误的数据可视化出来?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "* [逻辑回归模型(Logistic Regression, LR)基础](https://www.cnblogs.com/sparkwen/p/3441197.html)\n", "* [逻辑回归(Logistic Regression)](http://www.cnblogs.com/BYRans/p/4713624.html)" ] } ], "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": "3.6.9" } }, "nbformat": 4, "nbformat_minor": 2 }