Analysis of a Random Forests Model

Random forests are a scheme proposed by Leo Breiman in the 2000's for\nbuilding a predictor ensemble with a set of decision trees that grow in\nrandomly selected subspaces of data. Despite growing interest and practical\nuse, there has been little exploration of the statistical properties of random\nforests, and little is known about the mathematical forces driving the\nalgorithm. In this paper, we offer an in-depth analysis of a random forests\nmodel suggested by Breiman in \\cite{Bre04}, which is very close to the original\nalgorithm. We show in particular that the procedure is consistent and adapts to\nsparsity, in the sense that its rate of convergence depends only on the number\nof strong features and not…