{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 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", "FIXME: this figure is wrong\n", "![LogisticFunction](images/fig2.gif)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 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": { "text/plain": [ "Text(0.5,1,'Logistic function')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "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\")" ] }, { "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$g(z)$将最为假设函数来预测。$g(z)$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": [ "### 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": [ "### 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:\n", "$$\n", "\\theta_j := \\theta_j + \\alpha(y^i - h_\\theta(x^i)) x_j^i\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Program" ] }, { "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": 3, "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", " \"\"\"\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)\n", " plt.scatter(data[:, 0], data[:, 1], c=label, cmap=plt.cm.Spectral)\n", " plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "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", " 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", " for j in range(num_iteration):\n", " data_index = list(range(self.data_num))\n", " for i in range(self.data_num):\n", " # 学习速率\n", " alpha = 0.01\n", " rand_index = int(np.random.uniform(0, len(data_index)))\n", " error = self.label[rand_index] - 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": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": [ "## How to use sklearn to resolve the problem\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "accuracy train = 0.825000\n", "accuracy test = 0.900000\n" ] }, { "data": { "image/png": "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\n", 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" ] }, "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*0.8)\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": [ "## Multi-class recognition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load & show the data" ] }, { "cell_type": "code", "execution_count": 15, "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": [ "### Visualizing the Data\n", "\n", "A good first-step for many problems is to visualize the data using one of the Dimensionality Reduction techniques we saw earlier. We'll start with the most straightforward one, Principal Component Analysis (PCA).\n", "\n", "PCA seeks orthogonal linear combinations of the features which show the greatest variance, and as such, can help give you a good idea of the structure of the data set. Here we'll use RandomizedPCA, because it's faster for large N." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "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": [ "A weakness of PCA is that it produces a linear dimensionality reduction:\n", "this may miss some interesting relationships in the data. If we want to\n", "see a nonlinear mapping of the data, we can use one of the several\n", "methods in the `manifold` module. Here we'll use [Isomap](https://blog.csdn.net/VictoriaW/article/details/78497316) (a concatenation\n", "of Isometric Mapping) which is a manifold learning method based on\n", "graph theory:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "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": [ "## Program" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(1797, 64)\n", "accuracy train = 0.998608, accuracy_test = 0.897222\n", "score_train = 0.998608, score_test = 0.897222\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", "# 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": 21, "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": [ "## Exercise - How to draw mis-classfied data?\n", "\n", "1. How to obtain the mis-classified index?\n", "2. How to draw them?" ] }, { "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 2 }