  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.
