A particle-based variational approach to Bayesian Non-negative Matrix Factorization

TL;DR

This paper introduces a particle-based variational method for Bayesian Non-negative Matrix Factorization that improves approximation quality, handles multimodality effectively, and is computationally efficient compared to existing approaches.

Contribution

It proposes a novel particle-based variational approach for Bayesian NMF that enhances posterior approximation, addresses multimodality, and simplifies model inspection.

Findings

Better posterior approximations achieved faster than baselines.

Effectively captures multimodal posterior distributions.

Demonstrates practical advantages on real datasets.

Abstract

Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to provide a principled understanding of the non-identifiability inherent in NMF-- an issue ideally addressed by a Bayesian approach. Despite their suitability, current Bayesian NMF approaches have failed to gain popularity in an applied setting; they sacrifice flexibility in modeling for tractable computation, tend to get stuck in local modes, and require many thousands of samples for meaningful uncertainty estimates. We address these issues through a particle-based variational approach to Bayesian NMF that only requires the joint likelihood to be differentiable for tractability, uses a novel initialization technique to identify multiple modes in the posterior, and allows domain experts to inspect a `small' set of factorizations that faithfully represent the posterior. We introduce and employ a class of likelihood and prior distributions for NMF that formulate a Bayesian model using popular non-Bayesian NMF objectives. On several real datasets, we obtain better particle approximations to the Bayesian NMF posterior in less time than baselines and demonstrate the significant role that multimodality plays in NMF-related tasks.