Improved convergence rates for some kernel random forest algorithms

TL;DR

This paper improves the theoretical convergence rates of certain kernel-based random forest algorithms, specifically centered and uniform KeRF, and explores their associated reproducing kernel Hilbert spaces.

Contribution

It provides new convergence rate bounds for centered and uniform KeRF algorithms and analyzes their underlying reproducing kernel Hilbert spaces.

Findings

Improved convergence rates for centered KeRF.

Enhanced convergence bounds for uniform KeRF.

Analysis of the reproducing kernel Hilbert space associated with centered KeRF.

Abstract

Random forests are notable learning algorithms first introduced by Breinman in 2001, they are widely used for classification and regression tasks and their mathematical properties are under ongoing research. We consider a specific class of random forest algorithms related to kernel methods, the so-called KeRF (Kernel Random Forests.) In particular, we investigate thoroughly two explicit algorithms, designed independently of the data set, the centered KeRF and the uniform KeRF. In the present article, we provide an improvement in the rate of convergence for both algorithms and we explore the related reproducing kernel Hilbert space defined by the explicit kernel of the centered random forest.