A Random Forest Approach for Modeling Bounded Outcomes

TL;DR

This paper introduces a novel random forest method tailored for modeling bounded outcomes within the unit interval, leveraging the beta distribution's likelihood for improved heteroscedasticity handling.

Contribution

The paper proposes a new random forest approach that explicitly incorporates the beta distribution's likelihood for better modeling of bounded outcomes.

Findings

Outperforms classical random forests on bounded data

Effectively captures heteroscedasticity in the data

Demonstrates advantages over parametric regression models

Abstract

Random forests have become an established tool for classification and regression, in particular in high-dimensional settings and in the presence of complex predictor-response relationships. For bounded outcome variables restricted to the unit interval, however, classical random forest approaches may severely suffer as they do not account for the heteroscedasticity in the data. A random forest approach is proposed for relating beta distributed outcomes to explanatory variables. The approach explicitly makes use of the likelihood function of the beta distribution for the selection of splits during the tree-building procedure. In each iteration of the tree-building algorithm one chooses the combination of explanatory variable and splitting rule that maximizes the log-likelihood function of the beta distribution with the parameter estimates derived from the nodes of the currently built tree. Several simulation studies demonstrate the properties of the method and compare its performance to classical random forest approaches as well as to parametric regression models.