An Empirical Study of Stochastic Variational Algorithms for the Beta Bernoulli Process

Stochastic variational inference (SVI) is emerg-ing as the most promising candidate for scal-ing inference in Bayesian probabilistic models to large datasets. However, the performance of these methods has been assessed primarily in the context of Bayesian topic models, particularly latent Dirichlet allocation (LDA). Deriving sev-eral new algorithms, and using synthetic, image and genomic datasets, we investigate whether the understanding gleaned from LDA applies in the setting of sparse latent factor models, specifi-cally beta process factor analysis (BPFA). We demonstrate that the big picture is consistent: us-ing Gibbs sampling within SVI to maintain cer-tain posterior dependencies is extremely effec-tive. However, we find that different posterior dependencies are important in BPFA relative to LDA. Particularly, approximations able to model intra-local variable dependence perform best. 1