Non-asymptotic Properties of Generalized Mondrian Forests in Statistical Learning

TL;DR

This paper introduces a comprehensive framework for Mondrian Forests in statistical learning, providing theoretical guarantees and extending their application to various regression and classification tasks.

Contribution

It develops a general theoretical framework for Mondrian Forests, establishing risk bounds and consistency results across multiple learning tasks.

Findings

Upper bounds on regret/risk functions for estimators

Statistical consistency of the proposed methods

Applicability to diverse regression and classification problems

Abstract

Random Forests have been extensively used in regression and classification, inspiring the development of various forest-based methods. Among these, Mondrian Forests, derived from the Mondrian process, mark a significant advancement. Expanding on Mondrian Forests, this paper presents a general framework for statistical learning, encompassing a range of common learning tasks such as least squares regression, $\ell_1$ regression, quantile regression, and classification. Under mild assumptions on the loss functions, we provide upper bounds on the regret/risk functions for the estimators and demonstrate their statistical consistency.