Collapsed Variational Inference for Nonparametric Bayesian Group Factor Analysis

TL;DR

This paper introduces a fast collapsed variational inference algorithm for nonparametric Bayesian group factor analysis, enabling scalable analysis of large datasets by efficiently inferring shared and group-specific structures.

Contribution

The paper develops a novel collapsed variational inference method for NGFA that marginalizes group-specific parameters, improving computational efficiency over existing sampling-based methods.

Findings

Outperforms state-of-the-art GFA methods on synthetic data

Demonstrates effectiveness on real-world neuroimaging data

Enables scalable analysis of large datasets

Abstract

Group factor analysis (GFA) methods have been widely used to infer the common structure and the group-specific signals from multiple related datasets in various fields including systems biology and neuroimaging. To date, most available GFA models require Gibbs sampling or slice sampling to perform inference, which prevents the practical application of GFA to large-scale data. In this paper we present an efficient collapsed variational inference (CVI) algorithm for the nonparametric Bayesian group factor analysis (NGFA) model built upon an hierarchical beta Bernoulli process. Our CVI algorithm proceeds by marginalizing out the group-specific beta process parameters, and then approximating the true posterior in the collapsed space using mean field methods. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our CVI algorithm for the NGFA compared with state-of-the-art GFA methods.