.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_auto_examples_model_selection_plot_grid_search_refit_callable.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_model_selection_plot_grid_search_refit_callable.py:


==================================================
Balance model complexity and cross-validated score
==================================================

This example balances model complexity and cross-validated score by
finding a decent accuracy within 1 standard deviation of the best accuracy
score while minimising the number of PCA components [1].

The figure shows the trade-off between cross-validated score and the number
of PCA components. The balanced case is when n_components=6 and accuracy=0.80,
which falls into the range within 1 standard deviation of the best accuracy
score.

[1] Hastie, T., Tibshirani, R.,, Friedman, J. (2001). Model Assessment and
Selection. The Elements of Statistical Learning (pp. 219-260). New York,
NY, USA: Springer New York Inc..




.. image:: /auto_examples/model_selection/images/sphx_glr_plot_grid_search_refit_callable_001.png
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    The best_index_ is 2
    The n_components selected is 6
    The corresponding accuracy score is 0.80




|


.. code-block:: python

    # Author: Wenhao Zhang <wenhaoz@ucla.edu>

    print(__doc__)

    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn.datasets import load_digits
    from sklearn.decomposition import PCA
    from sklearn.model_selection import GridSearchCV
    from sklearn.pipeline import Pipeline
    from sklearn.svm import LinearSVC


    def lower_bound(cv_results):
        """
        Calculate the lower bound within 1 standard deviation
        of the best `mean_test_scores`.

        Parameters
        ----------
        cv_results : dict of numpy(masked) ndarrays
            See attribute cv_results_ of `GridSearchCV`

        Returns
        -------
        float
            Lower bound within 1 standard deviation of the
            best `mean_test_score`.
        """
        best_score_idx = np.argmax(cv_results['mean_test_score'])

        return (cv_results['mean_test_score'][best_score_idx]
                - cv_results['std_test_score'][best_score_idx])


    def best_low_complexity(cv_results):
        """
        Balance model complexity with cross-validated score.

        Parameters
        ----------
        cv_results : dict of numpy(masked) ndarrays
            See attribute cv_results_ of `GridSearchCV`.

        Return
        ------
        int
            Index of a model that has the fewest PCA components
            while has its test score within 1 standard deviation of the best
            `mean_test_score`.
        """
        threshold = lower_bound(cv_results)
        candidate_idx = np.flatnonzero(cv_results['mean_test_score'] >= threshold)
        best_idx = candidate_idx[cv_results['param_reduce_dim__n_components']
                                 [candidate_idx].argmin()]
        return best_idx


    pipe = Pipeline([
            ('reduce_dim', PCA(random_state=42)),
            ('classify', LinearSVC(random_state=42)),
    ])

    param_grid = {
        'reduce_dim__n_components': [2, 4, 6, 8]
    }

    grid = GridSearchCV(pipe, cv=10, n_jobs=1, param_grid=param_grid,
                        scoring='accuracy', refit=best_low_complexity)
    digits = load_digits()
    grid.fit(digits.data, digits.target)

    n_components = grid.cv_results_['param_reduce_dim__n_components']
    test_scores = grid.cv_results_['mean_test_score']

    plt.figure()
    plt.bar(n_components, test_scores, width=1.3, color='b')

    lower = lower_bound(grid.cv_results_)
    plt.axhline(np.max(test_scores), linestyle='--', color='y',
                label='Best score')
    plt.axhline(lower, linestyle='--', color='.5', label='Best score - 1 std')

    plt.title("Balance model complexity and cross-validated score")
    plt.xlabel('Number of PCA components used')
    plt.ylabel('Digit classification accuracy')
    plt.xticks(n_components.tolist())
    plt.ylim((0, 1.0))
    plt.legend(loc='upper left')

    best_index_ = grid.best_index_

    print("The best_index_ is %d" % best_index_)
    print("The n_components selected is %d" % n_components[best_index_])
    print("The corresponding accuracy score is %.2f"
          % grid.cv_results_['mean_test_score'][best_index_])
    plt.show()

**Total running time of the script:** ( 0 minutes  16.219 seconds)


.. _sphx_glr_download_auto_examples_model_selection_plot_grid_search_refit_callable.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_grid_search_refit_callable.py <plot_grid_search_refit_callable.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_grid_search_refit_callable.ipynb <plot_grid_search_refit_callable.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_