bp神经网络多元回归预测三层，要有激活函数定义损失函数和优化器代码用numpy库和pandas库

以下是使用numpy和pandas库实现三层神经网络进行多元回归预测的代码，包括激活函数、损失函数和优化器的定义：

import numpy as np
import pandas as pd

# 定义激活函数sigmoid
def sigmoid(x):
    return 1 / (1 + np.exp(-x))

# 定义损失函数均方误差
def mse_loss(y_true, y_pred):
    return np.mean(np.square(y_true - y_pred))

# 定义优化器随机梯度下降
def sgd_optimizer(w, b, dw, db, learning_rate):
    w -= learning_rate * dw
    b -= learning_rate * db
    return w, b

# 数据准备
data = pd.read_csv("data.csv")
X = data.iloc[:, :-1]
Y = data.iloc[:, -1]
X = np.array(X)
Y = np.array(Y)
Y = Y.reshape(-1, 1)

# 参数初始化
input_dim = X.shape[1]
hidden_dim = 4
output_dim = 1
learning_rate = 0.01
epochs = 1000

# 初始化权重和偏置
w1 = np.random.randn(input_dim, hidden_dim)
b1 = np.zeros((1, hidden_dim))
w2 = np.random.randn(hidden_dim, output_dim)
b2 = np.zeros((1, output_dim))

# 训练模型
for i in range(epochs):
    # 前向传播
    z1 = np.dot(X, w1) + b1
    a1 = sigmoid(z1)
    z2 = np.dot(a1, w2) + b2
    y_pred = z2

    # 计算损失
    loss = mse_loss(Y, y_pred)

    # 反向传播
    dy = 2 * (y_pred - Y)
    dw2 = np.dot(a1.T, dy)
    db2 = np.sum(dy, axis=0, keepdims=True)
    da1 = np.dot(dy, w2.T)
    dz1 = da1 * a1 * (1 - a1)
    dw1 = np.dot(X.T, dz1)
    db1 = np.sum(dz1, axis=0, keepdims=True)

    # 参数更新
    w2, b2 = sgd_optimizer(w2, b2, dw2, db2, learning_rate)
    w1, b1 = sgd_optimizer(w1, b1, dw1, db1, learning_rate)

    # 打印损失
    if i % 100 == 0:
        print("Epoch %d loss: %.4f" % (i, loss))

在上述代码中，sigmoid函数被用作激活函数，mse_loss函数被用作损失函数，sgd_optimizer函数被用作优化器。数据集被加载为pandas DataFrame，然后被转换为numpy数组。在训练模型时，使用随机梯度下降（SGD）更新权重和偏置。在每个epoch结束后，打印损失以跟踪进度。