Rapid Posterior Exploration in Bayesian Non-negative Matrix Factorization
This work addresses uncertainty characterization in NMF for data exploration, offering an incremental improvement over existing inference techniques.
The paper tackled the problem of slow mixing and mode trapping in Bayesian Non-negative Matrix Factorization by introducing a novel approach using rapidly-exploring random trees (RRTs) integrated with nonparametric variational inference, resulting in greater posterior coverage and higher ELBO values compared to standard methods.
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.