Bayesian Combinatorial Multi-Study Factor Analysis

TL;DR

Tetris is a Bayesian method that extends multi-study factor analysis to identify latent factors shared by any combination of studies, improving dimension reduction and covariance estimation in high-dimensional data.

Contribution

It introduces a novel Bayesian approach using an Indian Buffet Process to model partially shared latent factors across multiple studies.

Findings

Successfully identifies shared and study-specific factors in simulations

Enhances covariance estimation accuracy

Reveals gene expression patterns in breast cancer datasets

Abstract

Analyzing multiple studies allows leveraging data from a range of sources and populations, but until recently, there have been limited methodologies to approach the joint unsupervised analysis of multiple high-dimensional studies. A recent method, Bayesian Multi-Study Factor Analysis (BMSFA), identifies latent factors common to all studies, as well as latent factors specific to individual studies. However, BMSFA does not allow for partially shared factors, i.e. latent factors shared by more than one but less than all studies. We extend BMSFA by introducing a new method, Tetris, for Bayesian combinatorial multi-study factor analysis, which identifies latent factors that can be shared by any combination of studies. We model the subsets of studies that share latent factors with an Indian Buffet Process. We test our method with an extensive range of simulations, and showcase its utility not only in dimension reduction but also in covariance estimation. Finally, we apply Tetris to high-dimensional gene expression datasets to identify patterns in breast cancer gene expression, both within and across known classes defined by germline mutations.