An Empirical Study of Stochastic Variational Algorithms for the Beta Bernoulli Process
This work addresses scaling Bayesian inference for sparse latent factor models, which is incremental as it extends existing SVI methods to a new domain.
The study investigated whether insights from stochastic variational inference (SVI) in topic models apply to sparse latent factor models like beta process factor analysis (BPFA), finding that while Gibbs sampling within SVI is effective, different posterior dependencies are crucial for BPFA, with approximations modeling intra-local variable dependence performing best.
Stochastic variational inference (SVI) is emerging as the most promising candidate for scaling 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 several 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, specifically beta process factor analysis (BPFA). We demonstrate that the big picture is consistent: using Gibbs sampling within SVI to maintain certain posterior dependencies is extremely effective. 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.