A Contrastive Divergence for Combining Variational Inference and MCMC

Francisco Ruiz, Michalis Titsias
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5537-5545, 2019.

Abstract

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).

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-ruiz19a, title = {A Contrastive Divergence for Combining Variational Inference and {MCMC}}, author = {Ruiz, Francisco and Titsias, Michalis}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {5537--5545}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/ruiz19a/ruiz19a.pdf}, url = {https://proceedings.mlr.press/v97/ruiz19a.html}, abstract = {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).} }
Endnote
%0 Conference Paper %T A Contrastive Divergence for Combining Variational Inference and MCMC %A Francisco Ruiz %A Michalis Titsias %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-ruiz19a %I PMLR %P 5537--5545 %U https://proceedings.mlr.press/v97/ruiz19a.html %V 97 %X 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).
APA
Ruiz, F. & Titsias, M.. (2019). A Contrastive Divergence for Combining Variational Inference and MCMC. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5537-5545 Available from https://proceedings.mlr.press/v97/ruiz19a.html.

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