Truncated variational sampling for ‘Black Box’ optimization of generative models

Abstract

We investigate the optimization of two probabilistic generative models with binary latent variables using a novel variational EM approach. The approach distinguishes itself from previous variational approaches by using latent states as variational parameters. Here we use efficient and general purpose sampling procedures to vary the latent states, and investigate the “black box” applicability of the resulting optimization approach. For general purpose applicability, samples are drawn from approximate marginal distributions as well as from the prior distribution of the considered generative model. As such, sampling is defined in a generic form with no analytical derivations required. As a proof of concept, we then apply the novel procedure (A) to Binary Sparse Coding (a model with continuous observables), and (B) to basic Sigmoid Belief Networks (which are models with binary observables). Numerical experiments verify that the investigated approach efficiently as well as effectively increases a variational free energy objective without requiring any additional analytical steps.