A Contrastive Divergence for Combining Variational Inference and MCMC

by   Francisco J. R. Ruiz, et al.

We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To make inference tractable, we introduce the variational contrastive divergence (VCD), a new divergence that replaces the standard Kullback-Leibler (KL) divergence used in VI. The VCD captures a notion of discrepancy between the initial variational distribution and its improved version (obtained after running the MCMC steps), and it converges asymptotically to the symmetrized KL divergence between the variational distribution and the posterior of interest. The VCD objective can be optimized efficiently with respect to the variational parameters via stochastic optimization. We show experimentally that optimizing the VCD leads to better predictive performance on two latent variable models: logistic matrix factorization and variational autoencoders (VAEs).


page 1

page 2

page 3

page 4


A Divergence Bound for Hybrids of MCMC and Variational Inference and an Application to Langevin Dynamics and SGVI

Two popular classes of methods for approximate inference are Markov chai...

Markovian Score Climbing: Variational Inference with KL(p||q)

Modern variational inference (VI) uses stochastic gradients to avoid int...

Why (and When and How) Contrastive Divergence Works

Contrastive divergence (CD) is a promising method of inference in high d...

Posterior inference unchained with EL_2O

Statistical inference of analytically non-tractable posteriors is a diff...

An Easy to Interpret Diagnostic for Approximate Inference: Symmetric Divergence Over Simulations

It is important to estimate the errors of probabilistic inference algori...

Variational Inference for Additive Main and Multiplicative Interaction Effects Models

In plant breeding the presence of a genotype by environment (GxE) intera...

Langevin Autoencoders for Learning Deep Latent Variable Models

Markov chain Monte Carlo (MCMC), such as Langevin dynamics, is valid for...

Please sign up or login with your details

Forgot password? Click here to reset