Reducing Subspace Models for Large-Scale Covariance Regression
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.00503
- arXiv:
- arXiv:2010.00503
- Bibcode:
- 2020arXiv201000503F
- Keywords:
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- Statistics - Methodology