神经网络基础-神经网络补充概念-10-向量化

概念

向量化是一种优化技术，通过将循环操作替换为向量运算，以利用底层硬件的并行计算能力，从而提高代码的性能。在机器学习中，向量化可以显著加速训练过程，特别是在处理大规模数据集时。

代码实现

import numpy as np

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

def compute_loss(X, y, theta):
    m = len(y)
    h = sigmoid(X.dot(theta))
    loss = (-1/m) * np.sum(y * np.log(h) + (1 - y) * np.log(1 - h))
    return loss

def batch_gradient_descent(X, y, theta, learning_rate, num_iterations):
    m = len(y)
    losses = []
    
    for _ in range(num_iterations):
        h = sigmoid(X.dot(theta))
        gradient = X.T.dot(h - y) / m
        theta -= learning_rate * gradient
        
        loss = compute_loss(X, y, theta)
        losses.append(loss)
        
    return theta, losses

# 生成一些模拟数据
np.random.seed(42)
m = 100
n = 2
X = np.random.randn(m, n)
X = np.hstack((np.ones((m, 1)), X))
theta_true = np.array([1, 2, 3])
y = (X.dot(theta_true) + np.random.randn(m) * 0.2) > 0

# 初始化参数和超参数
theta = np.zeros(X.shape[1])
learning_rate = 0.01
num_iterations = 1000

# 执行批量梯度下降（向量化）
theta_optimized, losses = batch_gradient_descent(X, y, theta, learning_rate, num_iterations)

# 打印优化后的参数
print("优化后的参数:", theta_optimized)

# 绘制损失函数下降曲线
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')
plt.show()