Consistency of Random Forests and Other Averaging Classifiers

Gérard Biau; Luc Devroye; Gábor Lugosi

In the last years of his life, Leo Breiman promoted random forests for use in classification. He suggested using averaging as a means of obtaining good discrimination rules. The base classifiers used for averaging are simple and randomized, often based on random samples from the data. He left a few questions unanswered regarding the consistency of such rules. In this paper, we give a number of theorems that establish the universal consistency of averaging rules. We also show that some popular classifiers, including one suggested by Breiman, are not universally consistent.

Consistency of Random Forests and Other Averaging Classifiers

Abstract