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Gradient Boosting regularization#

Illustration of the effect of different regularization strategies for Gradient Boosting. The example is taken from Hastie et al 2009 [1].

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).

plot gradient boosting regularization

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
importmatplotlib.pyplotasplt
importnumpyasnp
fromsklearnimport datasets, ensemble
fromsklearn.metricsimport log_loss
fromsklearn.model_selectionimport train_test_split
X, y = datasets.make_hastie_10_2 (n_samples=4000, random_state=1)
# map labels from {-1, 1} to {0, 1}
labels, y = np.unique (y, return_inverse=True)
X_train, X_test, y_train, y_test = train_test_split (X, y, test_size=0.8, random_state=0)
original_params = {
 "n_estimators": 400,
 "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=0.2", "turquoise", {"learning_rate": 0.2, "subsample": 1.0}),
 ("subsample=0.5", "blue", {"learning_rate": 1.0, "subsample": 0.5}),
 (
 "learning_rate=0.2, subsample=0.5",
 "gray",
 {"learning_rate": 0.2, "subsample": 0.5},
 ),
 (
 "learning_rate=0.2, max_features=2",
 "magenta",
 {"learning_rate": 0.2, "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_proba in enumerate(clf.staged_predict_proba(X_test)):
 test_deviance[i] = 2 * log_loss (y_test, y_proba[:, 1])
 plt.plot (
 (np.arange (test_deviance.shape[0]) + 1)[::5],
 test_deviance[::5],
 "-",
 color=color,
 label=label,
 )
plt.legend (loc="upper right")
plt.xlabel ("Boosting Iterations")
plt.ylabel ("Test Set Deviance")
plt.show ()