# Covariance regression with random forests

arXiv: https://arxiv.org/abs/2209.08173 · HTML: https://mlsanity.com/paper/2209.08173/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 16 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [A Unified Framework for Random Forest Prediction Error Estimation](https://mlsanity.com/paper/1912.07435/) (2019)
- [Conditional canonical correlation estimation based on covariates with random forests](https://mlsanity.com/paper/2011.11555/) (2020)
- [Reducing Subspace Models for Large-Scale Covariance Regression](https://mlsanity.com/paper/2010.00503/) (2020)
- [RFpredInterval: An R Package for Prediction Intervals with Random Forests and Boosted Forests](https://mlsanity.com/paper/2106.08217/) (2021)

## Built on by (most cited first, 1 of 1)

- [High-Dimensional Dynamic Covariance Models with Random Forests](https://mlsanity.com/paper/2505.12444/) (2025)

## Abstract (arXiv)

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.