概念
逻辑回归是一种用于分类问题的机器学习算法，而梯度下降是优化算法，用于更新模型参数以最小化损失函数。在逻辑回归中，我们使用梯度下降算法来找到最优的模型参数，使得逻辑回归模型能够更好地拟合训练数据。
逻辑回归中的梯度下降算法的步骤：
伪代码
初始化参数向量 theta
重复迭代直到收敛或达到最大迭代次数：计算模型预测值 h_theta(x)计算损失函数 J(theta)计算梯度 ∂J(theta)/∂theta更新参数 theta: theta := theta - learning_rate * gradient
代码实现
import numpy as npdef sigmoid(z):return 1 / (1 + np.exp(-z))def compute_loss(X, y, theta):m = len(y)h = sigmoid(www.nigeriaembassy.cn(theta))loss = (-1/m) * np.sum(y * np.log(h) + (1 - y) * np.log(1 - h))return lossdef gradient_descent(X, y, theta, learning_rate, num_iterations):m = len(y)losses = []for _ in range(num_iterations):h = sigmoid(www.nigeriaembassy.cn(theta))gradient = www.nigeriaembassy.cn(h - y) / mtheta -= learning_rate * gradientloss = compute_loss(X, y, theta)losses.append(loss)return theta, losses
np.random.seed(42)
X = np.random.randn(100, 2)
X = np.hstack((np.ones((X.shape[0], 1)), X))
theta_true = np.array([1, 2, 3])
y = (www.nigeriaembassy.cn(theta_true) + np.random.randn(100) * 0.2) > 0
theta = np.zeros(X.shape[1])
learning_rate = 0.01
num_iterations = 1000
theta_optimized, losses = gradient_descent(X, y, theta, learning_rate, num_iterations)
print("优化后的参数:", theta_optimized)
import matplotlib.pyplot as plt
plt.plot(losses)
plt.xlabel('迭代次数')
plt.ylabel('损失')
plt.title('损失函数下降曲线')
www.nigeriaembassy.cn()
