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news 2025/6/20 15:46:12

作业：手动构造类似的数据集（如cosx数据），观察不同的机器学习模型的差异

模型比较

1. 线性回归

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error# 线性回归
lr = LinearRegression()
lr.fit(X_train, y_train)
y_pred = lr.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print(f"Linear Regression MSE: {mse:.4f}")

2. 随机森林

from sklearn.ensemble import RandomForestRegressorrf = RandomForestRegressor(n_estimators=100, random_state=42)
rf.fit(X_train, y_train)
y_pred = rf.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
print(f"Random Forest MSE: {mse:.4f}")

3. 支持向量回归(SVR)

from sklearn.svm import SVR
from sklearn.preprocessing import StandardScaler# 标准化数据
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)svr = SVR(kernel='rbf', C=100, gamma=0.1, epsilon=0.1)
svr.fit(X_train_scaled, y_train)
y_pred = svr.predict(X_test_scaled)
mse = mean_squared_error(y_test, y_pred)
print(f"SVR MSE: {mse:.4f}")

4. 简单RNN

from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import SimpleRNN, Dense# 重塑数据为RNN需要的形状 [样本数, 时间步数, 特征数]
X_train_rnn = X_train.reshape((X_train.shape[0], X_train.shape[1], 1))
X_test_rnn = X_test.reshape((X_test.shape[0], X_test.shape[1], 1))# 构建RNN模型
model = Sequential([SimpleRNN(50, activation='tanh', input_shape=(X_train_rnn.shape[1], 1)),Dense(1)
])
model.compile(optimizer='adam', loss='mse')# 训练模型
history = model.fit(X_train_rnn, y_train, epochs=50, batch_size=32, validation_data=(X_test_rnn, y_test), verbose=0)y_pred = model.predict(X_test_rnn)
mse = mean_squared_error(y_test, y_pred)
print(f"Simple RNN MSE: {mse:.4f}")

5. LSTM

from tensorflow.keras.layers import LSTM# 构建LSTM模型
model = Sequential([LSTM(50, activation='tanh', input_shape=(X_train_rnn.shape[1], 1)),Dense(1)
])
model.compile(optimizer='adam', loss='mse')# 训练模型
history = model.fit(X_train_rnn, y_train, epochs=50, batch_size=32, validation_data=(X_test_rnn, y_test), verbose=0)y_pred = model.predict(X_test_rnn)
mse = mean_squared_error(y_test, y_pred)
print(f"LSTM MSE: {mse:.4f}")

可视化比较

import matplotlib.pyplot as plt# 绘制预测结果对比
plt.figure(figsize=(12, 6))
plt.plot(y_test[:100], label='True')
plt.plot(lr.predict(X_test)[:100], label='Linear Regression')
plt.plot(rf.predict(X_test)[:100], label='Random Forest')
plt.plot(svr.predict(X_test_scaled)[:100], label='SVR')
plt.plot(model.predict(X_test_rnn)[:100], label='LSTM')
plt.legend()
plt.title('Comparison of Model Predictions')
plt.show()