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1 RANDOM FORESTS Department of Statistics(1随机森林部门的统计数据)
1
RANDOM FORESTS
Leo Breiman
Statistics Department
University of California
Berkeley, CA 94720
January 2001
Abstract
Random forests are a combination of tree predictors
such that each tree depends on the values of a random
vector sampled independently and with the same
distribution for all trees in the forest. The
generalization error for forests converges a.s. to a limit
as the number of trees in the forest becomes large.
The generalization error of a forest of tree classifiers
depends on the strength of the individual trees in the
forest and the correlation between them. Using a
random selection of features to split each node yields
error rates that compare favorably to Adaboost
(Freund and Schapire[1996]), but are more robust with
respect to noise. Internal estimates monitor error,
strength, and correlation and these are used to show
the response to increasing the number of features used
in the splitting. Internal estimates are also used to
measure variable importance. These ideas are also
applicable to regression.
2
1. Random Forests
1.1 Introduction
Significant improvements in classification accuracy have resulted from growing
an ensemble of trees and letting them vote for the most popular class. In order
to grow these ensembles, often random vectors are generated that govern the
growth of each tree in the ensemble. An early example is bagging (Breiman
[1996]), where to grow eac
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