bp神经网络多元回归预测单层隐藏层relu函数代码

以下是使用单层隐藏层和ReLU函数的BP神经网络多元回归预测的Python代码示例：

import numpy as np

# 定义ReLU函数
def relu(x):
    return np.maximum(0, x)

# 定义BP神经网络类
class BPNeuralNetwork:
    def __init__(self, input_size, hidden_size, output_size):
        # 初始化权重和偏置
        self.weights_input_hidden = np.random.randn(input_size, hidden_size) * 0.1
        self.bias_input_hidden = np.zeros((1, hidden_size))
        self.weights_hidden_output = np.random.randn(hidden_size, output_size) * 0.1
        self.bias_hidden_output = np.zeros((1, output_size))

    # 前向传播
    def forward(self, X):
        self.hidden_layer = relu(np.dot(X, self.weights_input_hidden) + self.bias_input_hidden)
        self.output_layer = np.dot(self.hidden_layer, self.weights_hidden_output) + self.bias_hidden_output
        return self.output_layer

    # 反向传播
    def backward(self, X, y, learning_rate):
        # 计算输出层误差
        output_error = self.output_layer - y
        # 计算隐藏层误差
        hidden_error = np.dot(output_error, self.weights_hidden_output.T) * (self.hidden_layer > 0)

        # 更新权重和偏置
        self.weights_hidden_output -= learning_rate * np.dot(self.hidden_layer.T, output_error)
        self.bias_hidden_output -= learning_rate * np.sum(output_error, axis=0, keepdims=True)
        self.weights_input_hidden -= learning_rate * np.dot(X.T, hidden_error)
        self.bias_input_hidden -= learning_rate * np.sum(hidden_error, axis=0, keepdims=True)

    # 训练模型
    def train(self, X, y, epochs, learning_rate):
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, learning_rate)

            # 每1000次迭代输出一次损失函数值
            if i % 1000 == 0:
                loss = np.mean((output - y) ** 2)
                print("Epoch {0}: loss = {1}".format(i, loss))

# 测试代码
if __name__ == '__main__':
    # 生成随机数据
    X = np.random.randn(100, 5)
    y = np.random.randn(100, 1)

    # 初始化BP神经网络
    nn = BPNeuralNetwork(5, 10, 1)

    # 训练模型
    nn.train(X, y, 10000, 0.01)

    # 预测
    test_X = np.random.randn(10, 5)
    preds = nn.forward(test_X)
    print("Predictions: \n", preds)