Doubly Semi-Implicit Variational Inference

Dmitry Molchanov, Valery Kharitonov, Artem Sobolev, Dmitry Vetrov
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2593-2602, 2019.

Abstract

We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-the-art prior for variational autoencoders, which improves its performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-molchanov19a, title = {Doubly Semi-Implicit Variational Inference}, author = {Molchanov, Dmitry and Kharitonov, Valery and Sobolev, Artem and Vetrov, Dmitry}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2593--2602}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/molchanov19a/molchanov19a.pdf}, url = {https://proceedings.mlr.press/v89/molchanov19a.html}, abstract = {We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-the-art prior for variational autoencoders, which improves its performance.} }
Endnote
%0 Conference Paper %T Doubly Semi-Implicit Variational Inference %A Dmitry Molchanov %A Valery Kharitonov %A Artem Sobolev %A Dmitry Vetrov %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-molchanov19a %I PMLR %P 2593--2602 %U https://proceedings.mlr.press/v89/molchanov19a.html %V 89 %X We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference in models where the prior and the posterior can be expressed as an intractable infinite mixture of some analytic density with a highly flexible implicit mixing distribution. We provide a sandwich bound on the evidence lower bound (ELBO) objective that can be made arbitrarily tight. Unlike discriminator-based and kernel-based approaches to implicit variational inference, DSIVI optimizes a proper lower bound on ELBO that is asymptotically exact. We evaluate DSIVI on a set of problems that benefit from implicit priors. In particular, we show that DSIVI gives rise to a simple modification of VampPrior, the current state-of-the-art prior for variational autoencoders, which improves its performance.
APA
Molchanov, D., Kharitonov, V., Sobolev, A. & Vetrov, D.. (2019). Doubly Semi-Implicit Variational Inference. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2593-2602 Available from https://proceedings.mlr.press/v89/molchanov19a.html.

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