Rapid Posterior Exploration in Bayesian Non-negative Matrix Factorization

TL;DR

This paper introduces a rapid posterior exploration method for Bayesian Non-negative Matrix Factorization using RRTs, improving coverage of the posterior distribution and inference quality over traditional methods.

Contribution

It presents a novel RRT-based approach integrated with nonparametric variational inference for faster, more comprehensive Bayesian NMF posterior exploration.

Findings

Greater posterior coverage achieved

Higher ELBO values compared to standard methods

Effective on both real and synthetic data

Abstract

Non-negative Matrix Factorization (NMF) is a popular tool for data exploration. Bayesian NMF promises to also characterize uncertainty in the factorization. Unfortunately, current inference approaches such as MCMC mix slowly and tend to get stuck on single modes. We introduce a novel approach using rapidly-exploring random trees (RRTs) to asymptotically cover regions of high posterior density. These are placed in a principled Bayesian framework via an online extension to nonparametric variational inference. On experiments on real and synthetic data, we obtain greater coverage of the posterior and higher ELBO values than standard NMF inference approaches.