本文共 4196 字，大约阅读时间需要 13 分钟。

在上一篇博客中我们学习了的理论。那么在这篇博客中，我们用代码展示一下，如何用梯度下降法获取逻辑回归的参数

步骤1：我们加载sklearn中的鸢尾花数据进行测试，由于为了数据可视化，我们选择2种类型的鸢尾花，并且只选择2个特征。 

import numpy as np    import matplotlib.pyplot as plt    from sklearn import datasets    X, y = datasets.load_iris(return_X_y=True)    X = X[y < 2, :2]    y = y[y < 2]    plt.scatter(X[y == 0, 0], X[y == 0, 1], color="red")    plt.scatter(X[y == 1, 0], X[y == 1, 1], color="blue")    plt.show()

可视化一下：

步骤二： 我们编写自己的回归算法

# -*- encoding: utf-8 -*-import numpy as npfrom .metrics import accuracy_scoreclass LogisticRegression:    def __init__(self):        """初始化Logistic Regression模型"""        self.coef_ = None        self.intercept_ = None        self._theta = None    def _sigmoid(self, t):        return 1. / (1. + np.exp(-t))    def fit(self, X_train, y_train, eta=0.01, n_iters=1e4):        """根据训练数据集X_train, y_train, 使用梯度下降法训练Logistic Regression模型"""        assert X_train.shape[0] == y_train.shape[0], \            "the size of X_train must be equal to the size of y_train"        def J(theta, X_b, y):            y_hat = self._sigmoid(X_b.dot(theta))            try:                return - np.sum(y*np.log(y_hat) + (1-y)*np.log(1-y_hat)) / len(y)            except:                return float('inf')        def dJ(theta, X_b, y):            return X_b.T.dot(self._sigmoid(X_b.dot(theta)) - y) / len(y)        def gradient_descent(X_b, y, initial_theta, eta, n_iters=1e4, epsilon=1e-8):            theta = initial_theta            cur_iter = 0            while cur_iter < n_iters:                gradient = dJ(theta, X_b, y)                last_theta = theta                theta = theta - eta * gradient                if (abs(J(theta, X_b, y) - J(last_theta, X_b, y)) < epsilon):                    break                cur_iter += 1            return theta        X_b = np.hstack([np.ones((len(X_train), 1)), X_train])        initial_theta = np.zeros(X_b.shape[1])        self._theta = gradient_descent(X_b, y_train, initial_theta, eta, n_iters)        self.intercept_ = self._theta[0]        self.coef_ = self._theta[1:]        return self    def predict_proba(self, X_predict):        """给定待预测数据集X_predict，返回表示X_predict的结果概率向量"""        assert self.intercept_ is not None and self.coef_ is not None, \            "must fit before predict!"        assert X_predict.shape[1] == len(self.coef_), \            "the feature number of X_predict must be equal to X_train"        X_b = np.hstack([np.ones((len(X_predict), 1)), X_predict])        return self._sigmoid(X_b.dot(self._theta))    def predict(self, X_predict):        """给定待预测数据集X_predict，返回表示X_predict的结果向量"""        assert self.intercept_ is not None and self.coef_ is not None, \            "must fit before predict!"        assert X_predict.shape[1] == len(self.coef_), \            "the feature number of X_predict must be equal to X_train"        proba = self.predict_proba(X_predict)        return np.array(proba >= 0.5, dtype='int')    def score(self, X_test, y_test):        """根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""        y_predict = self.predict(X_test)        return accuracy_score(y_test, y_predict)    def __repr__(self):        return "LogisticRegression()"

步骤三、进行测试

from logisticregression import LogisticRegression    iris = load_iris()    X = iris.data    y = iris.target    X = X[y < 2, :2]    y = y[y < 2]    log_reg = LogisticRegression()    X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)    log_reg.fit(X_train, y_train)    print log_reg.theta_    print log_reg.predict_probality(X_test)    print log_reg.predict(X_test)    print log_reg.scores(X_test, y_test)

运行结果：

参数： 第1个表示截距， 第2,3表示参数： [ 0.          2.93348784 -5.10537984]

预测出来的概率：

[0.92944114 0.98777304 0.15845401 0.18960373 0.03911344 0.02054764

 0.05175747 0.99672293 0.9787036  0.7523886  0.04525759 0.003409

 0.28048662 0.03911344 0.83661026 0.81299828 0.83506118 0.34328248

 0.06419014 0.22523806 0.02384776 0.17983628 0.9787036  0.98804275

 0.08845609]

把概率进行映射出来的结果：

[1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0]

准确率为：

1

这个主要是由于数据比较少，并且我们只取了2个特征，不复杂。所以评分高。

 

总结：

1、在代码实现过程中，梯度下降方法中初始化init_theta错了，后来参考了一下老师的代码，重新改正过来了。

init_theta = np.zeros(X_b.shape[1]) 这里面X_b已经增加了一列。 这个要注意。

要是你在西安，感兴趣一起学习AIOPS，欢迎加入QQ群 860794445

转载地址：http://fekai.baihongyu.com/