Bayesian Group Factor Analysis

TL;DR

This paper introduces a Bayesian group factor analysis model that captures dependencies between variable groups, enabling better understanding of multi-view or multi-set data in fields like neuroimaging and systems biology.

Contribution

It proposes a novel Bayesian model with group-wise sparse factors to decompose data variation into shared and set-specific components, advancing multi-view data analysis.

Findings

Effective in neuroimaging data analysis

Successful in chemical systems biology applications

Provides interpretable factors for complex data sets

Abstract

We introduce a factor analysis model that summarizes the dependencies between observed variable groups, instead of dependencies between individual variables as standard factor analysis does. A group may correspond to one view of the same set of objects, one of many data sets tied by co-occurrence, or a set of alternative variables collected from statistics tables to measure one property of interest. We show that by assuming group-wise sparse factors, active in a subset of the sets, the variation can be decomposed into factors explaining relationships between the sets and factors explaining away set-specific variation. We formulate the assumptions in a Bayesian model which provides the factors, and apply the model to two data analysis tasks, in neuroimaging and chemical systems biology.