Beta Process Non-negative Matrix Factorization with Stochastic Structured Mean-Field Variational Inference

Abstract: Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with Poisson likelihood. Unlike the linear Gaussian model, which is well-studied in the nonparametric Bayesian literature, NMF model with beta process prior does not enjoy the conjugacy. We leverage the recently developed stochastic structured mean-field variational inference to relax the conjugacy constraint and restore the dependencies among the latent variables in the approximating variational distribution. Preliminary results on both synthetic and real examples demonstrate that the proposed inference algorithm can reasonably recover the hidden structure of the data.