.. _sphx_glr_auto_examples_ensemble_plot_gradient_boosting_regularization.py:


================================
Gradient Boosting regularization
================================

Illustration of the effect of different regularization strategies
for Gradient Boosting. The example is taken from Hastie et al 2009.

The loss function used is binomial deviance. Regularization via
shrinkage (``learning_rate < 1.0``) improves performance considerably.
In combination with shrinkage, stochastic gradient boosting
(``subsample < 1.0``) can produce more accurate models by reducing the
variance via bagging.
Subsampling without shrinkage usually does poorly.
Another strategy to reduce the variance is by subsampling the features
analogous to the random splits in Random Forests
(via the ``max_features`` parameter).

.. [1] T. Hastie, R. Tibshirani and J. Friedman, "Elements of Statistical
    Learning Ed. 2", Springer, 2009.



.. image:: /auto_examples/ensemble/images/sphx_glr_plot_gradient_boosting_regularization_001.png
    :align: center





.. code-block:: python

    print(__doc__)

    # Author: Peter Prettenhofer <peter.prettenhofer@gmail.com>
    #
    # License: BSD 3 clause

    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn import ensemble
    from sklearn import datasets


    X, y = datasets.make_hastie_10_2(n_samples=12000, random_state=1)
    X = X.astype(np.float32)

    # map labels from {-1, 1} to {0, 1}
    labels, y = np.unique(y, return_inverse=True)

    X_train, X_test = X[:2000], X[2000:]
    y_train, y_test = y[:2000], y[2000:]

    original_params = {'n_estimators': 1000, 'max_leaf_nodes': 4, 'max_depth': None, 'random_state': 2,
                       'min_samples_split': 5}

    plt.figure()

    for label, color, setting in [('No shrinkage', 'orange',
                                   {'learning_rate': 1.0, 'subsample': 1.0}),
                                  ('learning_rate=0.1', 'turquoise',
                                   {'learning_rate': 0.1, 'subsample': 1.0}),
                                  ('subsample=0.5', 'blue',
                                   {'learning_rate': 1.0, 'subsample': 0.5}),
                                  ('learning_rate=0.1, subsample=0.5', 'gray',
                                   {'learning_rate': 0.1, 'subsample': 0.5}),
                                  ('learning_rate=0.1, max_features=2', 'magenta',
                                   {'learning_rate': 0.1, 'max_features': 2})]:
        params = dict(original_params)
        params.update(setting)

        clf = ensemble.GradientBoostingClassifier(**params)
        clf.fit(X_train, y_train)

        # compute test set deviance
        test_deviance = np.zeros((params['n_estimators'],), dtype=np.float64)

        for i, y_pred in enumerate(clf.staged_decision_function(X_test)):
            # clf.loss_ assumes that y_test[i] in {0, 1}
            test_deviance[i] = clf.loss_(y_test, y_pred)

        plt.plot((np.arange(test_deviance.shape[0]) + 1)[::5], test_deviance[::5],
                '-', color=color, label=label)

    plt.legend(loc='upper left')
    plt.xlabel('Boosting Iterations')
    plt.ylabel('Test Set Deviance')

    plt.show()

**Total running time of the script:**
(0 minutes 12.004 seconds)



.. container:: sphx-glr-download

    **Download Python source code:** :download:`plot_gradient_boosting_regularization.py <plot_gradient_boosting_regularization.py>`


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_gradient_boosting_regularization.ipynb <plot_gradient_boosting_regularization.ipynb>`