用梯度下降算法实现Logistic回归的L1正则化和L2正则化python代码

下面是用梯度下降算法实现Logistic回归的L1正则化和L2正则化的Python代码：

import numpy as np

class LogisticRegression:
    def __init__(self, lr=0.1, num_iter=1000, fit_intercept=True, regularization=None, lambda_=0.1):
        self.lr = lr
        self.num_iter = num_iter
        self.fit_intercept = fit_intercept
        self.regularization = regularization
        self.lambda_ = lambda_
    
    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 __l1_regularization(self, w):
        return self.lambda_ * np.abs(w[1:]).sum()
    
    def __l2_regularization(self, w):
        return self.lambda_ * np.sum(w[1:] ** 2)
    
    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_iter):
            z = np.dot(X, self.theta)
            h = self.__sigmoid(z)
            
            if self.regularization == 'l1':
                # L1正则化
                grad = np.dot(X.T, (h - y)) / y.size + self.lambda_ * np.sign(self.theta)
            elif self.regularization == 'l2':
                # L2正则化
                grad = np.dot(X.T, (h - y)) / y.size + self.lambda_ * self.theta
            else:
                grad = np.dot(X.T, (h - y)) / y.size
            
            self.theta -= self.lr * grad
    
    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

其中，lr是学习率，num_iter是迭代次数，fit_intercept表示是否拟合截距，regularization表示正则化方法，lambda_是正则化系数。在fit方法中，通过判断regularization的取值，来实现L1正则化和L2正则化。在L1正则化中，使用np.sign函数计算符号函数，而在L2正则化中，直接对参数的平方和进行惩罚。在predict_prob方法中，对X进行截距拟合和sigmoid变换，返回预测概率。在predict方法中，对预测概率进行阈值处理，返回预测结果。