Adaptive partition Factor Analysis

TL;DR

This paper introduces a novel Bayesian approach to multi-study factor analysis with adaptive shrinkage priors, enabling more flexible modeling of shared and study-specific latent factors, with demonstrated superior performance and practical applications.

Contribution

It extends existing multi-study factor analysis by developing new shrinkage priors for latent factors, allowing for more adaptable modeling of shared and study-specific effects.

Findings

Proposed method performs competitively across various scenarios.

Provides richer insights into latent structures.

Demonstrated effectiveness on biological datasets.

Abstract

Factor Analysis has traditionally been utilized across diverse disciplines to extrapolate latent traits that influence the behavior of multivariate observed variables. Historically, the focus has been on analyzing data from a single study, neglecting the potential study-specific variations present in data from multiple studies. Multi-study factor analysis has emerged as a recent methodological advancement that addresses this gap by distinguishing between latent traits shared across studies and study-specific components arising from artifactual or population-specific sources of variation. In this paper, we extend the current methodologies by introducing novel shrinkage priors for the latent factors, thereby accommodating a broader spectrum of scenarios -- from the absence of study-specific latent factors to models in which factors pertain only to small subgroups nested within or shared between the studies. For the proposed construction we provide conditions for identifiability of factor loadings and guidelines to perform straightforward posterior computation via Gibbs sampling. Through comprehensive simulation studies, we demonstrate that our proposed method exhibits competing performance across a variety of scenarios compared to existing methods, yet providing richer insights. The practical benefits of our approach are further illustrated through applications to bird species co-occurrence data and ovarian cancer gene expression data.