Forêts aléatoires

Abstract

Random forests are a learning algorithm proposed by Breiman (2001)which combines several randomized decision trees and aggregates theirpredictions by averaging. Despite its wide usage and outstanding prac-tical performance, little is known about the mathematical propertiesof the procedure. This disparity between theory and practice orig-inates in the difficulty to simultaneously analyze both the random-ization process and the highly data-dependent tree structure. In thepresent paper, we take a step forward in forest exploration by prov-ing a consistency result for Breiman's (2001) original algorithm in thecontext of additive regression models. Our analysis also sheds an in-teresting light on how random forests can nicely adapt to sparsity inhigh-dimensional settings.