A Contrastive Divergence for Combining Variational Inference and MCMC
This work addresses a methodological bottleneck in probabilistic inference for researchers in machine learning, offering an incremental improvement over existing techniques.
The paper tackles the problem of combining Markov chain Monte Carlo (MCMC) and variational inference (VI) to improve inference by introducing the variational contrastive divergence (VCD), which replaces the standard KL divergence and is optimized efficiently, leading to better predictive performance on logistic matrix factorization and VAEs.
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).