Analysis of a Random Forests Model

TL;DR

This paper provides a detailed analysis of the statistical properties of Breiman's random forests, demonstrating their consistency and ability to adapt to sparsity, which enhances understanding of their theoretical foundations.

Contribution

It offers the first in-depth theoretical analysis showing that random forests are consistent and adapt to sparsity, clarifying their mathematical behavior.

Findings

Random forests are consistent predictors.

They adapt to sparsity, depending only on strong features.

The convergence rate is unaffected by noise variables.

Abstract

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