What is the meaning of 'mean_test_score' in cv_result?

Question

Hello I'm doing a GridSearchCV and I'm printing the result with the .cv_results_ function from scikit learn.

My problem is that when I'm evaluating by hand the mean on all the test score splits I obtain a different number compared to what it is written in 'mean_test_score'. Which is different from the standard np.mean()?

I attach here the code with the result:

n_estimators = [100]
max_depth = [3]
learning_rate = [0.1]

param_grid = dict(max_depth=max_depth, n_estimators=n_estimators, learning_rate=learning_rate)

gkf = GroupKFold(n_splits=7)


grid_search = GridSearchCV(model, param_grid, scoring=score_auc, cv=gkf)
grid_result = grid_search.fit(X, Y, groups=patients)

grid_result.cv_results_

The result of this operation is:

{'mean_fit_time': array([ 8.92773601]),
 'mean_score_time': array([ 0.04288721]),
 'mean_test_score': array([ 0.83490629]),
 'mean_train_score': array([ 0.95167036]),
 'param_learning_rate': masked_array(data = [0.1],
              mask = [False],
        fill_value = ?),
 'param_max_depth': masked_array(data = [3],
              mask = [False],
        fill_value = ?),
 'param_n_estimators': masked_array(data = [100],
              mask = [False],
        fill_value = ?),
 'params': ({'learning_rate': 0.1, 'max_depth': 3, 'n_estimators': 100},),
 'rank_test_score': array([1]),
 'split0_test_score': array([ 0.74821666]),
 'split0_train_score': array([ 0.97564995]),
 'split1_test_score': array([ 0.80089016]),
 'split1_train_score': array([ 0.95361201]),
 'split2_test_score': array([ 0.92876979]),
 'split2_train_score': array([ 0.93935856]),
 'split3_test_score': array([ 0.95540287]),
 'split3_train_score': array([ 0.94718634]),
 'split4_test_score': array([ 0.89083901]),
 'split4_train_score': array([ 0.94787374]),
 'split5_test_score': array([ 0.90926355]),
 'split5_train_score': array([ 0.94829775]),
 'split6_test_score': array([ 0.82520379]),
 'split6_train_score': array([ 0.94971417]),
 'std_fit_time': array([ 1.79167576]),
 'std_score_time': array([ 0.02970254]),
 'std_test_score': array([ 0.0809713]),
 'std_train_score': array([ 0.0105566])}

As you can see, doing the np.mean of all the test_score it gives you a value approximately of 0.8655122606479532 while the 'mean_test_score' is 0.83490629

Thanks for you help, Leonardo.

Answer 1

I will post this as a new answer since its so much code:

The test and train scores of the folds are: (taken from the results you posted in your question)

test_scores = [0.74821666,0.80089016,0.92876979,0.95540287,0.89083901,0.90926355,0.82520379]
train_scores = [0.97564995,0.95361201,0.93935856,0.94718634,0.94787374,0.94829775,0.94971417]

The amount of training samples in those folds are: (taken from the output of print([(len(train), len(test)) for train, test in gkf.split(X, groups=patients)]))

train_len = [41835, 56229, 56581, 58759, 60893, 60919, 62056]
test_len = [24377, 9983, 9631, 7453, 5319, 5293, 4156]

Then the test- and train-means with the amount of training samples per fold as weight is:

train_avg = np.average(train_scores, weights=train_len)
-> 0.95064898361714389
test_avg = np.average(test_scores, weights=test_len)
-> 0.83490628649308296

So this is exactly the value sklearn gives you. It is also the correct mean accuracy of your classification. The mean of the folds is incorrect in that it depends on the somewhat arbitrary splits/folds you chose.

So in concusion, both explanations were indeed identical and correct.

Answer 2

If you see the original code of GridSearchCV in their github repository, they dont use np.mean() instead they use np.average() with weights. Hence the difference. Here's their code:

n_splits = 3
test_sample_counts = np.array(test_sample_counts[:n_splits],
                                    dtype=np.int)
weights = test_sample_counts if self.iid else None
means = np.average(test_scores, axis=1, weights=weights)
stds = np.sqrt(np.average((test_scores - means[:, np.newaxis]) 
                               axis=1, weights=weights))

 cv_results = dict()
 for split_i in range(n_splits):
        cv_results["split%d_test_score" % split_i] = test_scores[:,
                                                              split_i]
 cv_results["mean_test_score"] = means        
 cv_results["std_test_score"] = stds

In case you want to know more about the difference between them take a look Difference between np.mean() and np.average()

Answer 3

I suppose the reason for the different means are different weighting factors in the mean calculation.

The mean_test_score that sklearn returns is the mean calculated on all samples where each sample has the same weight.

If you calculate the mean by taking the mean of the folds (splits), then you only get the same results if the folds are all of equal size. If they are not, then all samples of larger folds will automatically have a smaller impact on the mean of the folds than smaller folds, and the other way around.

Small numeric example:

mean([2,3,5,8,9]) = 5.4 # mean over all samples ('mean_test_score')

mean([2,3,5]) = 3.333 # mean of fold 1
mean([8,9]) = 8.5 # mean of fold 2

mean(3.333, 8.5) = 5.91 # mean of means of folds

5.4 != 5.91