Covariance regression with random forests

TL;DR

This paper introduces CovRegRF, a novel random forest-based method for estimating conditional covariance matrices of multivariate responses, with a significance test for covariate effects, validated through simulations and real data.

Contribution

The paper presents a new covariance regression method using random forests with a specialized splitting rule and a significance test, advancing multivariate analysis techniques.

Findings

Accurate covariance matrix estimation demonstrated in simulations

Type-1 error rate is well controlled in significance testing

Effective application to thyroid disease data

Abstract

Capturing the conditional covariances or correlations among the elements of a multivariate response vector based on covariates is important to various fields including neuroscience, epidemiology and biomedicine. We propose a new method called Covariance Regression with Random Forests (CovRegRF) to estimate the covariance matrix of a multivariate response given a set of covariates, using a random forest framework. Random forest trees are built with a splitting rule specially designed to maximize the difference between the sample covariance matrix estimates of the child nodes. We also propose a significance test for the partial effect of a subset of covariates. We evaluate the performance of the proposed method and significance test through a simulation study which shows that the proposed method provides accurate covariance matrix estimates and that the Type-1 error is well controlled. An application of the proposed method to thyroid disease data is also presented. CovRegRF is implemented in a freely available R package on CRAN.