用AIC（model1，model2）比较选出GAM的最优模型，写一段代码

在Python中，我们可以使用`sklearn`库中的`GridSearchCV`和`GAM`（Generalized Additive Models）来进行模型选择，通常我们会先训练两个模型`model1`和`model2`，然后通过交叉验证的方式比较它们的表现，选择最优的那个作为最终模型。这里假设我们已经有了数据集，并且`gamlss`库提供了`GAM`。

from sklearn.model_selection import GridSearchCV
import pygam

# 假设model1和model2都是GAM实例，分别初始化和设置参数网格
param_grid_model1 = {'link': ['identity', 'logistic'], 'n_splines': [50, 100]}
model1 = pygam.GAM()
grid_search1 = GridSearchCV(model1, param_grid=param_grid_model1)

param_grid_model2 = {'s(0)': [0.5, 1.0], 'interaction.depth': [2, 3]}
model2 = pygam.GAM()
grid_search2 = GridSearchCV(model2, param_grid=param_grid_model2)

# 分别拟合两个模型
grid_search1.fit(X_train, y_train)
grid_search2.fit(X_train, y_train)

# 获取每个模型的最佳参数和性能
best_params_model1 = grid_search1.best_params_
best_score_model1 = grid_search1.best_score_

best_params_model2 = grid_search2.best_params_
best_score_model2 = grid_search2.best_score_

# 比较并选择最优模型
if best_score_model1 > best_score_model2:
    optimal_model = grid_search1
    print(f"Model 1 (best params: {best_params_model1}) has the highest score.")
else:
    optimal_model = grid_search2
    print(f"Model 2 (best params: {best_params_model2}) has the highest score.")

# 使用最佳参数对整个数据集进行预测
optimal_model.fit(X_test, y_test)
y_pred = optimal_model.predict(X_test)