python实现BP神经网络回归预测模型

好的，下面是基于Python实现BP神经网络回归预测模型的步骤：

1. 导入相关库和数据

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

data = pd.read_csv('data.csv')
X = data.iloc[:, :-1].values
y = data.iloc[:, -1].values

2. 数据预处理

sc = StandardScaler()
X = sc.fit_transform(X)

3. 分割数据为训练集和测试集

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)

4. 初始化神经网络参数

input_nodes = X_train.shape[1] # 输入层节点个数
hidden_nodes = 5 # 隐藏层节点个数
output_nodes = 1 # 输出层节点个数
learning_rate = 0.1 # 学习率
epochs = 1000 # 迭代次数

# 初始化权重
weights_input_hidden = np.random.normal(0.0, pow(hidden_nodes, -0.5), (hidden_nodes, input_nodes))
weights_hidden_output = np.random.normal(0.0, pow(output_nodes, -0.5), (output_nodes, hidden_nodes))

5. 定义激活函数和误差函数

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

# 定义误差函数MSE
def MSE(y, y_hat):
    return np.mean(np.square(y - y_hat))

6. 训练神经网络

for epoch in range(epochs):
    # 前向传播
    hidden_inputs = np.dot(weights_input_hidden, X_train.T)
    hidden_outputs = sigmoid(hidden_inputs)
    final_inputs = np.dot(weights_hidden_output, hidden_outputs)
    final_outputs = final_inputs
    
    # 计算误差
    error = MSE(y_train, final_outputs)
    
    # 反向传播
    output_errors = y_train.reshape(-1, 1) - final_outputs
    hidden_errors = np.dot(weights_hidden_output.T, output_errors) * hidden_outputs * (1 - hidden_outputs)
    
    # 更新权重
    weights_hidden_output += learning_rate * np.dot(output_errors, hidden_outputs.T)
    weights_input_hidden += learning_rate * np.dot(hidden_errors, X_train)

7. 测试神经网络

# 前向传播
hidden_inputs = np.dot(weights_input_hidden, X_test.T)
hidden_outputs = sigmoid(hidden_inputs)
final_inputs = np.dot(weights_hidden_output, hidden_outputs)
final_outputs = final_inputs

# 计算误差
error = MSE(y_test, final_outputs)
print("测试集误差：", error)

以上就是基于Python实现BP神经网络回归预测模型的步骤。