# High-Dimensional Dynamic Covariance Models with Random Forests

arXiv: https://arxiv.org/abs/2505.12444 · HTML: https://mlsanity.com/paper/2505.12444/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 18 May 2025.

## Builds on (most cited first, 8 of 8)

- [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)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Local Linear Forests](https://mlsanity.com/paper/1807.11408/) (2018)
- [Dynamic Linear Discriminant Analysis in High Dimensional Space](https://mlsanity.com/paper/1708.00205/) (2017)
- [A Nonconvex Framework for Structured Dynamic Covariance Recovery](https://mlsanity.com/paper/2011.05601/) (2020)
- [A Dynamic Structure for High Dimensional Covariance Matrices and its Application in Portfolio Allocation](https://mlsanity.com/paper/1506.01407/) (2015)
- [Covariance regression with random forests](https://mlsanity.com/paper/2209.08173/) (2022)

## Abstract (arXiv)

This paper introduces a novel nonparametric method for estimating high-dimensional dynamic covariance matrices with multiple conditioning covariates, leveraging random forests and supported by robust theoretical guarantees. Unlike traditional static methods, our dynamic nonparametric covariance models effectively capture distributional heterogeneity. Furthermore, unlike kernel-smoothing methods, which are restricted to a single conditioning covariate, our approach accommodates multiple covariates in a fully nonparametric framework. To the best of our knowledge, this is the first method to use random forests for estimating high-dimensional dynamic covariance matrices. In high-dimensional settings, we establish uniform consistency theory, providing nonasymptotic error rates and model selection properties, even when the response dimension grows sub-exponentially with the sample size. These results hold uniformly across a range of conditioning variables. The method's effectiveness is demonstrated through simulations and a stock dataset analysis, highlighting its ability to model complex dynamics in high-dimensional scenarios.