用python实现BP神经网络算法，并输出多个评价指标：R2，RMSE，MSE，MAPE和MAE

在Python中，我们可以使用`scikit-learn`库中的`LinearRegression`模型（对于简单的线性回归）或更专业的`sklearn.neural_networks.MLPRegressor`（多层感知器，用于非线性预测）来实现基础的BP（Backpropagation）神经网络。然而，如果你想要自定义BP神经网络，你可以选择使用`Keras`或`PyTorch`这样的深度学习框架。

以下是一个简单的例子，演示如何使用`MLPRegressor`实现一个基本的BP神经网络并计算所需的评价指标：

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_error, mean_absolute_percentage_error
import numpy as np

# 假设我们有数据集X和y
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# 数据预处理
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# 创建神经网络模型
from sklearn.neural_network import MLPRegressor
nn_model = MLPRegressor(hidden_layer_sizes=(100,), activation='relu', solver='adam', max_iter=500)

# 训练模型
nn_model.fit(X_train, y_train)

# 预测
y_pred = nn_model.predict(X_test)

# 计算评价指标
r2 = r2_score(y_test, y_pred)
rmse = np.sqrt(mean_squared_error(y_test, y_pred))
mse = mean_squared_error(y_test, y_pred)
mape = mean_absolute_percentage_error(y_test, y_pred)
mae = mean_absolute_error(y_test, y_pred)

print(f"R2 Score: {r2}")
print(f"RMSE: {rmse}")
print(f"MSE: {mse}")
print(f"MAPE: {mape}")
print(f"MAE: {mae}")

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