OOB Errors for Random ForestsΒΆ

The RandomForestClassifier is trained using bootstrap aggregation, where each new tree is fit from a bootstrap sample of the training observations z_i = (x_i, y_i). The out-of-bag (OOB) error is the average error for each z_i calculated using predictions from the trees that do not contain z_i in their respective bootstrap sample. This allows the RandomForestClassifier to be fit and validated whilst being trained [1].

The example below demonstrates how the OOB error can be measured at the addition of each new tree during training. The resulting plot allows a practitioner to approximate a suitable value of n_estimators at which the error stabilizes.

[1]T. Hastie, R. Tibshirani and J. Friedman, “Elements of Statistical Learning Ed. 2”, p592-593, Springer, 2009.
import matplotlib.pyplot as plt

from collections import OrderedDict
from sklearn.datasets import make_classification
from sklearn.ensemble import RandomForestClassifier, ExtraTreesClassifier

# Author: Kian Ho <hui.kian.ho@gmail.com>
#         Gilles Louppe <g.louppe@gmail.com>
#         Andreas Mueller <amueller@ais.uni-bonn.de>
# License: BSD 3 Clause



# Generate a binary classification dataset.
X, y = make_classification(n_samples=500, n_features=25,
                           n_clusters_per_class=1, n_informative=15,

# NOTE: Setting the `warm_start` construction parameter to `True` disables
# support for parallelized ensembles but is necessary for tracking the OOB
# error trajectory during training.
ensemble_clfs = [
    ("RandomForestClassifier, max_features='sqrt'",
        RandomForestClassifier(warm_start=True, oob_score=True,
    ("RandomForestClassifier, max_features='log2'",
        RandomForestClassifier(warm_start=True, max_features='log2',
    ("RandomForestClassifier, max_features=None",
        RandomForestClassifier(warm_start=True, max_features=None,

# Map a classifier name to a list of (<n_estimators>, <error rate>) pairs.
error_rate = OrderedDict((label, []) for label, _ in ensemble_clfs)

# Range of `n_estimators` values to explore.
min_estimators = 15
max_estimators = 175

for label, clf in ensemble_clfs:
    for i in range(min_estimators, max_estimators + 1):
        clf.fit(X, y)

        # Record the OOB error for each `n_estimators=i` setting.
        oob_error = 1 - clf.oob_score_
        error_rate[label].append((i, oob_error))

# Generate the "OOB error rate" vs. "n_estimators" plot.
for label, clf_err in error_rate.items():
    xs, ys = zip(*clf_err)
    plt.plot(xs, ys, label=label)

plt.xlim(min_estimators, max_estimators)
plt.ylabel("OOB error rate")
plt.legend(loc="upper right")

Total running time of the script: ( 0 minutes 11.125 seconds)

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