python实现对数几率回归

对数几率回归(Logistic Regression)是一种常用的分类算法，可以用于二分类和多分类任务。下面是Python实现对数几率回归的示例代码：

import numpy as np

class LogisticRegression:
    def __init__(self, learning_rate=0.01, num_iterations=100000, fit_intercept=True, verbose=False):
        self.learning_rate = learning_rate
        self.num_iterations = num_iterations
        self.fit_intercept = fit_intercept
        self.verbose = verbose
        
    def __add_intercept(self, X):
        intercept = np.ones((X.shape[0], 1))
        return np.concatenate((intercept, X), axis=1)
    
    def __sigmoid(self, z):
        return 1 / (1 + np.exp(-z))
    
    def __loss(self, h, y):
        return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()
    
    def fit(self, X, y):
        if self.fit_intercept:
            X = self.__add_intercept(X)
            
        self.theta = np.zeros(X.shape[1])
        
        for i in range(self.num_iterations):
            z = np.dot(X, self.theta)
            h = self.__sigmoid(z)
            gradient = np.dot(X.T, (h - y)) / y.size
            self.theta -= self.learning_rate * gradient
            
            if self.verbose and i % 10000 == 0:
                z = np.dot(X, self.theta)
                h = self.__sigmoid(z)
                print(f'loss: {self.__loss(h, y)} \t')
    
    def predict_prob(self, X):
        if self.fit_intercept:
            X = self.__add_intercept(X)
            
        return self.__sigmoid(np.dot(X, self.theta))
    
    def predict(self, X, threshold=0.5):
        return self.predict_prob(X) >= threshold

以上代码使用了NumPy库，其中fit()方法用于拟合模型，predict_prob()方法用于预测样本属于正类的概率，predict()方法用于预测样本的类别。需要注意的是，在使用对数几率回归之前应该对数据进行标准化处理，以避免数值计算上的不稳定性。