bp神经网络回归正则化代码

下面是一个示例 BP 神经网络回归正则化代码，其中使用 L2 正则化来减小模型的复杂度并避免过拟合：

import numpy as np

class NeuralNetwork:
    def __init__(self, input_dim, hidden_dim, output_dim, reg_lambda=0.01):
        # 初始化网络参数
        self.input_dim = input_dim
        self.hidden_dim = hidden_dim
        self.output_dim = output_dim
        self.reg_lambda = reg_lambda

        # 初始化权重和偏置
        self.weights1 = np.random.randn(self.input_dim, self.hidden_dim) / np.sqrt(self.input_dim)
        self.bias1 = np.zeros((1, self.hidden_dim))
        self.weights2 = np.random.randn(self.hidden_dim, self.output_dim) / np.sqrt(self.hidden_dim)
        self.bias2 = np.zeros((1, self.output_dim))

    def forward(self, X):
        # 前向传播
        self.z1 = np.dot(X, self.weights1) + self.bias1
        self.a1 = np.tanh(self.z1)
        self.z2 = np.dot(self.a1, self.weights2) + self.bias2
        self.y_hat = self.z2
        return self.y_hat

    def backward(self, X, y, y_hat):
        # 反向传播
        error = y_hat - y
        delta2 = error
        delta1 = np.dot(delta2, self.weights2.T) * (1 - np.power(self.a1, 2))

        # 计算梯度
        grad_weights2 = np.dot(self.a1.T, delta2) + self.reg_lambda * self.weights2
        grad_bias2 = np.sum(delta2, axis=0, keepdims=True)
        grad_weights1 = np.dot(X.T, delta1) + self.reg_lambda * self.weights1
        grad_bias1 = np.sum(delta1, axis=0)

        # 更新权重和偏置
        self.weights2 -= learning_rate * grad_weights2
        self.bias2 -= learning_rate * grad_bias2
        self.weights1 -= learning_rate * grad_weights1
        self.bias1 -= learning_rate * grad_bias1

    def train(self, X, y, epochs=10000, learning_rate=0.01):
        for i in range(epochs):
            # 前向传播
            y_hat = self.forward(X)

            # 反向传播
            self.backward(X, y, y_hat)

            # 计算损失函数和精度
            loss = np.mean(np.square(y - y_hat))
            if i % 1000 == 0:
                print("Epoch:", i, "Loss:", loss)

在上面的代码中，`reg_lambda` 参数表示正则化强度。在前向传播和反向传播过程中，我们需要计算正则化项的梯度，并将其加入到原始梯度中。在计算梯度时，我们需要将权重矩阵除以样本数，以避免梯度爆炸或消失的问题。