# Shared Subspace Models for Multi-Group Covariance Estimation

arXiv: https://arxiv.org/abs/1607.03045 · HTML: https://mlsanity.com/paper/1607.03045/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2016.

## Built on by (most cited first, 2 of 2)

- [Joint estimation of high-dimensional spiked covariance matrices via a partially shared subspace](https://mlsanity.com/paper/2607.08123/) (2026)
- [K-Tensors: Clustering Positive Semi-Definite Matrices](https://mlsanity.com/paper/2306.06534/) (2023)

## Abstract (arXiv)

We develop a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting. This is done by assuming a spiked covariance model for each group and sharing information about the space spanned by the group-level eigenvectors. We use an empirical Bayes method to identify a low-dimensional subspace which explains variation across all groups and use an MCMC algorithm to estimate the posterior uncertainty of eigenvectors and eigenvalues on this subspace. The implementation and utility of our model is illustrated with analyses of high-dimensional multivariate gene expression.