Why does not GridSearchCV give best score ? - Scikit Learn

Question

I have a dataset with 158 rows and 10 columns. I try to build multiple linear regression model and try to predict future value.

I used GridSearchCV for tunning parameters.

Here is my GridSearchCV and Regression function :

def GridSearch(data):
    X_train, X_test, y_train, y_test = cross_validation.train_test_split(data, ground_truth_data, test_size=0.3, random_state = 0)
    
    parameters = {'fit_intercept':[True,False], 'normalize':[True,False], 'copy_X':[True, False]}
    
    model = linear_model.LinearRegression()
    
    grid = GridSearchCV(model,parameters)
    
    grid.fit(X_train, y_train)
    predictions = grid.predict(X_test)
    
    print "Grid best score: ", grid.best_score_
    print "Grid score function: ", grid.score(X_test,y_test)

Output of this code is :

Grid best score: 0.720298870251

Grid score function: 0.888263112299

My question is what is the difference between best_score_ and score function ?

How the score function can be better than the best_score function ?

Thanks in advance.

Answer 1

The best_score_ is the best score from the cross-validation. That is, the model is fit on part of the training data, and the score is computed by predicting the rest of the training data. This is because you passed X_train and y_train to fit; the fit process thus does not know anything about your test set, only your training set.

The score method of the model object scores the model on the data you give it. You passed X_test and y_test, so this call computes the score of the fit (i.e., tuned) model on the test set.

In short, the two scores are calculated on different data sets, so it shouldn't be surprising that they are different.