Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis

TL;DR

This paper introduces SUFA, a Bayesian subspace factor analysis model that effectively distinguishes shared and condition-specific covariance structures across multiple high-dimensional datasets, with proven identifiability and efficient computation.

Contribution

The paper proposes SUFA models that ensure identifiability of shared and specific covariance components and develop scalable Bayesian inference algorithms for multi-source data integration.

Findings

Successfully separates shared and condition-specific covariance structures.

Provides scalable, fully integrated Bayesian inference algorithms.

Demonstrates effectiveness on gene expression datasets in immunology.

Abstract

Factor analysis provides a canonical framework for imposing lower-dimensional structure such as sparse covariance in high-dimensional data. High-dimensional data on the same set of variables are often collected under different conditions, for instance in reproducing studies across research groups. In such cases, it is natural to seek to learn the shared versus condition-specific structure. Existing hierarchical extensions of factor analysis have been proposed, but face practical issues including identifiability problems. To address these shortcomings, we propose a class of SUbspace Factor Analysis (SUFA) models, which characterize variation across groups at the level of a lower-dimensional subspace. We prove that the proposed class of SUFA models lead to identifiability of the shared versus group-specific components of the covariance, and study their posterior contraction properties. Taking a Bayesian approach, these contributions are developed alongside efficient posterior computation algorithms. Our sampler fully integrates out latent variables, is easily parallelizable and has complexity that does not depend on sample size. We illustrate the methods through application to integration of multiple gene expression datasets relevant to immunology.