Beta Process Non-negative Matrix Factorization with Stochastic Structured Mean-Field Variational Inference
This is an incremental improvement for researchers in nonparametric Bayesian methods, addressing a specific inference bottleneck in NMF models.
The paper tackles the challenge of performing variational inference for beta process non-negative matrix factorization (NMF) with Poisson likelihood, which lacks conjugacy, by developing a stochastic structured mean-field variational inference algorithm. The results show that the algorithm can reasonably recover hidden data structures on synthetic and real examples.
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.