# Reducing Subspace Models for Large-Scale Covariance Regression

arXiv: https://arxiv.org/abs/2010.00503 · HTML: https://mlsanity.com/paper/2010.00503/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

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

- [Covariance regression with random forests](https://mlsanity.com/paper/2209.08173/) (2022)

## Abstract (arXiv)

We develop an envelope model for joint mean and covariance regression in the large p, small n setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we focus on identifying covariance heterogeneity by incorporating information about mean-level differences. We use a Monte Carlo EM algorithm to identify a low-dimensional subspace which explains differences in both means and covariances as a function of covariates, and then use MCMC to estimate the posterior uncertainty conditional on the inferred low-dimensional subspace. We demonstrate the utility of our model on a motivating application on the metabolomics of aging. We also provide R code which can be used to develop and test other generalizations of the response envelope model.