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 talk, 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.
Travail joint avec L. Devroye (Université McGill de Montréal) et G. Lugosi (Université Pompeu Fabra de Barcelone).