Double Control Variates for Gradient Estimation in Discrete Latent Variable Models

Michalis Titsias, Jiaxin Shi
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6134-6151, 2022.

Abstract

Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach adds no extra computational cost compared to standard training with the REINFORCE leave-one-out estimator. We apply our method to challenging high-dimensional toy examples and for training variational autoencoders with binary latent variables. We show that our estimator can have lower variance compared to other state-of-the-art estimators.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-titsias22a, title = { Double Control Variates for Gradient Estimation in Discrete Latent Variable Models }, author = {Titsias, Michalis and Shi, Jiaxin}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6134--6151}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/titsias22a/titsias22a.pdf}, url = {https://proceedings.mlr.press/v151/titsias22a.html}, abstract = { Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach adds no extra computational cost compared to standard training with the REINFORCE leave-one-out estimator. We apply our method to challenging high-dimensional toy examples and for training variational autoencoders with binary latent variables. We show that our estimator can have lower variance compared to other state-of-the-art estimators. } }
Endnote
%0 Conference Paper %T Double Control Variates for Gradient Estimation in Discrete Latent Variable Models %A Michalis Titsias %A Jiaxin Shi %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-titsias22a %I PMLR %P 6134--6151 %U https://proceedings.mlr.press/v151/titsias22a.html %V 151 %X Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach adds no extra computational cost compared to standard training with the REINFORCE leave-one-out estimator. We apply our method to challenging high-dimensional toy examples and for training variational autoencoders with binary latent variables. We show that our estimator can have lower variance compared to other state-of-the-art estimators.
APA
Titsias, M. & Shi, J.. (2022). Double Control Variates for Gradient Estimation in Discrete Latent Variable Models . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6134-6151 Available from https://proceedings.mlr.press/v151/titsias22a.html.

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