Markov Chain Monte Carlo and Variational Inference: Bridging the Gap

Tim Salimans, Diederik Kingma, Max Welling
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1218-1226, 2015.

Abstract

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-salimans15, title = {Markov Chain Monte Carlo and Variational Inference: Bridging the Gap}, author = {Salimans, Tim and Kingma, Diederik and Welling, Max}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1218--1226}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/salimans15.pdf}, url = {https://proceedings.mlr.press/v37/salimans15.html}, abstract = {Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results.} }
Endnote
%0 Conference Paper %T Markov Chain Monte Carlo and Variational Inference: Bridging the Gap %A Tim Salimans %A Diederik Kingma %A Max Welling %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-salimans15 %I PMLR %P 1218--1226 %U https://proceedings.mlr.press/v37/salimans15.html %V 37 %X Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results.
RIS
TY - CPAPER TI - Markov Chain Monte Carlo and Variational Inference: Bridging the Gap AU - Tim Salimans AU - Diederik Kingma AU - Max Welling BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-salimans15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1218 EP - 1226 L1 - http://proceedings.mlr.press/v37/salimans15.pdf UR - https://proceedings.mlr.press/v37/salimans15.html AB - Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of variational inference and Monte Carlo methods where we incorporate one or more steps of MCMC into our variational approximation. By doing so we obtain a rich class of inference algorithms bridging the gap between variational methods and MCMC, and offering the best of both worlds: fast posterior approximation through the maximization of an explicit objective, with the option of trading off additional computation for additional accuracy. We describe the theoretical foundations that make this possible and show some promising first results. ER -
APA
Salimans, T., Kingma, D. & Welling, M.. (2015). Markov Chain Monte Carlo and Variational Inference: Bridging the Gap. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1218-1226 Available from https://proceedings.mlr.press/v37/salimans15.html.

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