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

Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a mean-field variational inference algorithm for beta process non-negative matrix factorization (NMF) model. Unlike the linear Gaussian model, which is well-studied in the nonparametric Bayesian literature, NMF model does not enjoy the conjugacy. We leverage the recently developed stochastic structured mean-field variational inference to restore the dependencies between 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.