Reducing Subspace Models for Large-Scale Covariance Regression

Alexander Franks

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arXiv · 2010.00503

Reducing Subspace Models for Large-Scale Covariance Regression

Alexander Franks

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Abstract

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.

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Alexander Franks. 2020-10-01. Reducing Subspace Models for Large-Scale Covariance Regression. https://arxiv.org/abs/2010.00503

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