Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

Note

Go to the end to download the full example code or to run this example in your browser via Binder

# Custom refit strategy of a grid search with cross-validation

This examples shows how a classifier is optimized by cross-validation, which is done using the `GridSearchCV` object on a development set that comprises only half of the available labeled data.

The performance of the selected hyper-parameters and trained model is then measured on a dedicated evaluation set that was not used during the model selection step.

More details on tools available for model selection can be found in the sections on Cross-validation: evaluating estimator performance and Tuning the hyper-parameters of an estimator.

## The dataset

We will work with the `digits` dataset. The goal is to classify handwritten digits images. We transform the problem into a binary classification for easier understanding: the goal is to identify whether a digit is `8` or not.

    from sklearn import datasets

    digits = datasets.load_digits()

In order to train a classifier on images, we need to flatten them into vectors. Each image of 8 by 8 pixels needs to be transformed to a vector of 64 pixels. Thus, we will get a final data array of shape `(n_images, n_pixels)`.

    n_samples = len(digits.images)
    X = digits.images.reshape((n_samples, -1))
    y = digits.target == 8
    print(
        f"The number of images is {X.shape[0]} and each image contains {X.shape[1]} pixels"
    )

    The number of images is 1797 and each image contains 64 pixels

As presented in the introduction, the data will be split into a training and a testing set of equal size.

    from sklearn.model_selection import train_test_split

    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=0)

## Define our grid-search strategy

We will select a classifier by searching the best hyper-parameters on folds of the training set. To do this, we need to define the scores to select the best candidate.

    scores = ["precision", "recall"]

We can also define a function to be passed to the `refit` parameter of the `GridSearchCV` instance. It will implement the custom strategy to select the best candidate from the `cv_results_` attribute of the `GridSearchCV`. Once the candidate is selected, it is automatically refitted by the `GridSearchCV` instance.

Here, the strategy is to short-list the models which are the best in terms of precision and recall. From the selected models, we finally select the fastest model at predicting. Notice that these custom choices are completely arbitrary.

    import pandas as pd

    def print_dataframe(filtered_cv_results):
        """Pretty print for filtered dataframe"""
        for mean_precision, std_precision, mean_recall, std_recall, params in zip(
            filtered_cv_results["mean_test_precision"],
            filtered_cv_results["std_test_precision"],
            filtered_cv_results["mean_test_recall"],
            filtered_cv_results["std_test_recall"],
            filtered_cv_results["params"],
        ):
            print(
                f"precision: {mean_precision:0.3f} (±{std_precision:0.03f}),"
                f" recall: {mean_recall:0.3f} (±{std_recall:0.03f}),"
                f" for {params}"
            )
        print()

    def refit_strategy(cv_results):
        """Define the strategy to select the best estimator.

        The strategy defined here is to filter-out all results below a precision threshold
        of 0.98, rank the remaining by recall and keep all models with one standard
        deviation of the best by recall. Once these models are selected, we can select the
        fastest model to predict.

        Parameters
        ----------
        cv_results : dict of numpy (masked) ndarrays
            CV results as returned by the `GridSearchCV`.

        Returns
        -------
        best_index : int
            The index of the best estimator as it appears in `cv_results`.
        """
        # print the info about the grid-search for the different scores
        precision_threshold = 0.98

        cv_results_ = pd.DataFrame(cv_results)
        print("All grid-search results:")
        print_dataframe(cv_results_)

        # Filter-out all results below the threshold
        high_precision_cv_results = cv_results_[
            cv_results_["mean_test_precision"] > precision_threshold
        ]

        print(f"Models with a precision higher than {precision_threshold}:")
        print_dataframe(high_precision_cv_results)

        high_precision_cv_results = high_precision_cv_results[
            [
                "mean_score_time",
                "mean_test_recall",
                "std_test_recall",
                "mean_test_precision",
                "std_test_precision",
                "rank_test_recall",
                "rank_test_precision",
                "params",
            ]
        ]

        # Select the most performant models in terms of recall
        # (within 1 sigma from the best)
        best_recall_std = high_precision_cv_results["mean_test_recall"].std()
        best_recall = high_precision_cv_results["mean_test_recall"].max()
        best_recall_threshold = best_recall - best_recall_std

        high_recall_cv_results = high_precision_cv_results[
            high_precision_cv_results["mean_test_recall"] > best_recall_threshold
        ]
        print(
            "Out of the previously selected high precision models, we keep all the\n"
            "the models within one standard deviation of the highest recall model:"
        )
        print_dataframe(high_recall_cv_results)

        # From the best candidates, select the fastest model to predict
        fastest_top_recall_high_precision_index = high_recall_cv_results[
            "mean_score_time"
        ].idxmin()

        print(
            "\nThe selected final model is the fastest to predict out of the previously\n"
            "selected subset of best models based on precision and recall.\n"
            "Its scoring time is:\n\n"
            f"{high_recall_cv_results.loc[fastest_top_recall_high_precision_index]}"
        )

        return fastest_top_recall_high_precision_index

## Tuning hyper-parameters

Once we defined our strategy to select the best model, we define the values of the hyper-parameters and create the grid-search instance:

    from sklearn.model_selection import GridSearchCV
    from sklearn.svm import SVC

    tuned_parameters = [
        {"kernel": ["rbf"], "gamma": [1e-3, 1e-4], "C": [1, 10, 100, 1000]},
        {"kernel": ["linear"], "C": [1, 10, 100, 1000]},
    ]

    grid_search = GridSearchCV(
        SVC(), tuned_parameters, scoring=scores, refit=refit_strategy
    )
    grid_search.fit(X_train, y_train)

    All grid-search results:
    precision: 1.000 (±0.000), recall: 0.854 (±0.063), for {'C': 1, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.257 (±0.061), for {'C': 1, 'gamma': 0.0001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 10, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 0.968 (±0.039), recall: 0.780 (±0.083), for {'C': 10, 'gamma': 0.0001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 100, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 0.905 (±0.058), recall: 0.889 (±0.074), for {'C': 100, 'gamma': 0.0001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 1000, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 0.904 (±0.058), recall: 0.890 (±0.073), for {'C': 1000, 'gamma': 0.0001, 'kernel': 'rbf'}
    precision: 0.695 (±0.073), recall: 0.743 (±0.065), for {'C': 1, 'kernel': 'linear'}
    precision: 0.643 (±0.066), recall: 0.757 (±0.066), for {'C': 10, 'kernel': 'linear'}
    precision: 0.611 (±0.028), recall: 0.744 (±0.044), for {'C': 100, 'kernel': 'linear'}
    precision: 0.618 (±0.039), recall: 0.744 (±0.044), for {'C': 1000, 'kernel': 'linear'}

    Models with a precision higher than 0.98:
    precision: 1.000 (±0.000), recall: 0.854 (±0.063), for {'C': 1, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.257 (±0.061), for {'C': 1, 'gamma': 0.0001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 10, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 100, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 1000, 'gamma': 0.001, 'kernel': 'rbf'}

    Out of the previously selected high precision models, we keep all the
    the models within one standard deviation of the highest recall model:
    precision: 1.000 (±0.000), recall: 0.854 (±0.063), for {'C': 1, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 10, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 100, 'gamma': 0.001, 'kernel': 'rbf'}
    precision: 1.000 (±0.000), recall: 0.877 (±0.069), for {'C': 1000, 'gamma': 0.001, 'kernel': 'rbf'}

    The selected final model is the fastest to predict out of the previously
    selected subset of best models based on precision and recall.
    Its scoring time is:

    mean_score_time                                           0.003416
    mean_test_recall                                          0.877206
    std_test_recall                                           0.069196
    mean_test_precision                                            1.0
    std_test_precision                                             0.0
    rank_test_recall                                                 3
    rank_test_precision                                              1
    params                 {'C': 100, 'gamma': 0.001, 'kernel': 'rbf'}
    Name: 4, dtype: object

    GridSearchCV(estimator=SVC(),
                 param_grid=[{'C': [1, 10, 100, 1000], 'gamma': [0.001, 0.0001],
                              'kernel': ['rbf']},
                             {'C': [1, 10, 100, 1000], 'kernel': ['linear']}],
                 refit=<function refit_strategy at 0x7fca80cc5080>,
                 scoring=['precision', 'recall'])

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
GridSearchCV

    GridSearchCV(estimator=SVC(),
                 param_grid=[{'C': [1, 10, 100, 1000], 'gamma': [0.001, 0.0001],
                              'kernel': ['rbf']},
                             {'C': [1, 10, 100, 1000], 'kernel': ['linear']}],
                 refit=<function refit_strategy at 0x7fca80cc5080>,
                 scoring=['precision', 'recall'])

estimator: SVC

    SVC()

SVC

    SVC()

The parameters selected by the grid-search with our custom strategy are:

    grid_search.best_params_

    {'C': 100, 'gamma': 0.001, 'kernel': 'rbf'}

Finally, we evaluate the fine-tuned model on the left-out evaluation set: the `grid_search` object has automatically been refit on the full training set with the parameters selected by our custom refit strategy.

We can use the classification report to compute standard classification metrics on the left-out set:

    from sklearn.metrics import classification_report

    y_pred = grid_search.predict(X_test)
    print(classification_report(y_test, y_pred))

                  precision    recall  f1-score   support

           False       0.99      1.00      0.99       807
            True       1.00      0.87      0.93        92

        accuracy                           0.99       899
       macro avg       0.99      0.93      0.96       899
    weighted avg       0.99      0.99      0.99       899

Note

The problem is too easy: the hyperparameter plateau is too flat and the output model is the same for precision and recall with ties in quality.

Total running time of the script: (0 minutes 7.434 seconds)

Gallery generated by Sphinx-Gallery