Unbiased gradient estimation for variational auto-encoders using coupled Markov chains

Francisco J. R. Ruiz, Michalis K. Titsias, Taylan Cemgil, Arnaud Doucet
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:707-717, 2021.

Abstract

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model’s likelihood. Fitting its parameters via maximum likelihood (ML) is challenging since the computation of the marginal likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a ML training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We obtain the estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and with finite variance. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-ruiz21a, title = {Unbiased gradient estimation for variational auto-encoders using coupled {M}arkov chains}, author = {Ruiz, Francisco J. R. and Titsias, Michalis K. and Cemgil, Taylan and Doucet, Arnaud}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {707--717}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/ruiz21a/ruiz21a.pdf}, url = {https://proceedings.mlr.press/v161/ruiz21a.html}, abstract = {The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model’s likelihood. Fitting its parameters via maximum likelihood (ML) is challenging since the computation of the marginal likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a ML training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We obtain the estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and with finite variance. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.} }
Endnote
%0 Conference Paper %T Unbiased gradient estimation for variational auto-encoders using coupled Markov chains %A Francisco J. R. Ruiz %A Michalis K. Titsias %A Taylan Cemgil %A Arnaud Doucet %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-ruiz21a %I PMLR %P 707--717 %U https://proceedings.mlr.press/v161/ruiz21a.html %V 161 %X The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model’s likelihood. Fitting its parameters via maximum likelihood (ML) is challenging since the computation of the marginal likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a ML training scheme for VAEs by introducing unbiased estimators of the log-likelihood gradient. We obtain the estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and with finite variance. We show experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance.
APA
Ruiz, F.J.R., Titsias, M.K., Cemgil, T. & Doucet, A.. (2021). Unbiased gradient estimation for variational auto-encoders using coupled Markov chains. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:707-717 Available from https://proceedings.mlr.press/v161/ruiz21a.html.

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