逻辑回归梯度下降代码实现

以下是逻辑回归梯度下降的Python代码实现：

import numpy as np

def sigmoid(z):
    """
    sigmoid函数
    """
    return 1 / (1 + np.exp(-z))

def gradient_descent(X, y, theta, alpha, num_iters):
    """
    梯度下降函数
    """
    m = len(y)
    for i in range(num_iters):
        h = sigmoid(np.dot(X, theta))
        theta = theta - (alpha / m) * np.dot(X.T, h - y)
    return theta

# 测试
X = np.array([[1, 2, 3], [1, 3, 4], [1, 4, 5], [1, 5, 6]])
y = np.array([[0], [0], [1], [1]])
theta = np.zeros((3, 1))
alpha = 0.1
num_iters = 1000
theta = gradient_descent(X, y, theta, alpha, num_iters)
print(theta)

相关问题

逻辑回归梯度下降代码

逻辑回归是一种常用的分类算法，梯度下降是逻辑回归中常用的优化算法。下面是逻辑回归梯度下降的代码示例：

import numpy as np

class LogisticRegression:
    def __init__(self, learning_rate=0.01, num_iterations=1000):
        self.learning_rate = learning_rate
        self.num_iterations = num_iterations
        self.weights = None
        self.bias = None
    
    def sigmoid(self, z):
        return 1 / (1 + np.exp(-z))
    
    def initialize_parameters(self, n_features):
        self.weights = np.zeros(n_features)
        self.bias = 0
    
    def fit(self, X, y):
        n_samples, n_features = X.shape
        self.initialize_parameters(n_features)
        
        for _ in range(self.num_iterations):
            linear_model = np.dot(X, self.weights) + self.bias
            y_predicted = self.sigmoid(linear_model)
            
            dw = (1 / n_samples) * np.dot(X.T, (y_predicted - y))
            db = (1 / n_samples) * np.sum(y_predicted - y)
            
            self.weights -= self.learning_rate * dw
            self.bias -= self.learning_rate * db
    
    def predict(self, X):
        linear_model = np.dot(X, self.weights) + self.bias
        y_predicted = self.sigmoid(linear_model)
        y_predicted_cls = [1 if i > 0.5 else 0 for i in y_predicted]
        return y_predicted_cls

上述代码实现了一个简单的逻辑回归类，其中包括了sigmoid函数、参数初始化、模型训练和预测等功能。你可以根据自己的需求进行调整和扩展。

逻辑回归梯度下降的的Python代码

以下是逻辑回归梯度下降的Python代码示例：

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)
        
        # 初始化权重
        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 == True 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):
        return self.predict_prob(X) >= threshold

其中，`fit`函数用于拟合模型，`predict_prob`函数用于预测概率，`predict`函数用于根据设定的阈值进行预测。在使用时，需要先初始化一个`LogisticRegression`对象，然后调用其`fit`函数拟合模型，并根据需要调用`predict_prob`或`predict`函数进行预测。