Expandable Factor Analysis

TL;DR

Expandable factor analysis offers a scalable Bayesian approach for estimating sparse, low-rank factor models with unknown number of factors, demonstrating improved accuracy and applicability to large biological datasets.

Contribution

It introduces a continuous shrinkage prior and an estimation algorithm that adaptively determines the number of factors, enhancing scalability and accuracy in high-dimensional settings.

Findings

Outperforms competitors in false discovery and true positive rates

Effective in large-scale gene expression data analysis

Provides a data-driven method for selecting hyperparameters

Abstract

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable inference in factor models when the number of factors is unknown. The method relies on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low-rank and sparse loadings matrix. The structure of the prior leads to an estimation algorithm that accommodates uncertainty in the number of factors. We propose an information criterion to select the hyperparameters of the prior. Expandable factor analysis has better false discovery rates and true positive rates than its competitors across diverse simulations. We apply the proposed approach to a gene expression study of aging in mice, illustrating superior results relative to four competing methods.