.. _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 # # 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 ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_gradient_boosting_regularization.ipynb `