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

TL;DR

This paper empirically evaluates stochastic variational algorithms for beta process factor analysis, revealing that modeling intra-local variable dependence enhances performance, with findings consistent with prior results in LDA but with important differences.

Contribution

It extends the understanding of stochastic variational inference from LDA to sparse latent factor models, highlighting the importance of modeling intra-local dependencies.

Findings

Gibbs sampling within SVI effectively maintains posterior dependencies.

Modeling intra-local variable dependence improves BPFA performance.

Results are consistent with LDA but show key differences in posterior dependencies.

Abstract

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.