如何对不同程度的多项式使用GridSearchCV？

我想做的是遍历一些适合不同阶次多项式的OLS，以查看哪个阶次在预测mpg给定值horsepower时表现更好（同时使用LOOCV和KFold）。我编写了代码，但无法弄清楚如何使用将该PolynomialFeatures函数应用于每次迭代GridSearchCv，因此最终写成这样：

import pandas as pd
import matplotlib.pyplot as plt
from sklearn.model_selection import LeaveOneOut, KFold
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error



df = pd.read_csv('http://web.stanford.edu/~oleg2/hse/auto/Auto.csv')[['horsepower','mpg']].dropna()

pows = range(1,11)
first, second, mse = [], [], 0     # 'first' is data for the first plot and 'second' is for the second one

for p in pows:
  mse = 0
  for train_index, test_index in LeaveOneOut().split(df):
      x_train, x_test = df.horsepower.iloc[train_index], df.horsepower.iloc[test_index]
      y_train, y_test = df.mpg.iloc[train_index], df.mpg.iloc[test_index]
      polynomial_features = PolynomialFeatures(degree = p)
      x = polynomial_features.fit_transform(x_train.values.reshape(-1,1))   #getting the polynomial
      ft = LinearRegression().fit(x,y_train)
      x1 = polynomial_features.fit_transform(x_test.values.reshape(-1,1))   #getting the polynomial
      mse += mean_squared_error(y_test, ft.predict(x1))
  first.append(mse/len(df))
    
for p in pows: 
    temp = []   
    for i in range(9):      # this is to plot a few graphs for comparison
        mse = 0
        for train_index, test_index in KFold(10, True).split(df):
            x_train, x_test = df.horsepower.iloc[train_index], df.horsepower.iloc[test_index]
            y_train, y_test = df.mpg.iloc[train_index], df.mpg.iloc[test_index]
            polynomial_features = PolynomialFeatures(degree = p)
            x = polynomial_features.fit_transform(x_train.values.reshape(-1,1))   #getting the polynomial
            ft = LinearRegression().fit(x,y_train)
            x1 = polynomial_features.fit_transform(x_test.values.reshape(-1,1))   #getting the polynomial
            mse += mean_squared_error(y_test, ft.predict(x1))
        temp.append(mse/10)
    second.append(temp)      


f, pt = plt.subplots(1,2,figsize=(12,5.1))
f.tight_layout(pad=5.0)
pt[0].set_ylim([14,30])
pt[1].set_ylim([14,30])
pt[0].plot(pows, first, color='darkblue', linewidth=1)
pt[0].scatter(pows, first, color='darkblue')
pt[1].plot(pows, second)
pt[0].set_title("LOOCV", fontsize=15)
pt[1].set_title("10-fold CV", fontsize=15)
pt[0].set_xlabel('Degree of Polynomial', fontsize=15)
pt[1].set_xlabel('Degree of Polynomial', fontsize=15)
pt[0].set_ylabel('Mean Squared Error', fontsize=15)
pt[1].set_ylabel('Mean Squared Error', fontsize=15)
plt.show()

它产生：

这可以正常工作，您可以在计算机上运行它以进行测试。这确实符合我的要求，但似乎确实过多。我GridSearchCv实际上是在寻求有关如何使用或其他方法来改进它的建议。我尝试将PolynomialFeatures用作传递给LinearRegression()，但无法x即时更改。一个工作示例将不胜感激。