On Multilevel Monte Carlo Unbiased Gradient Estimation for Deep Latent Variable Models

Yuyang Shi, Rob Cornish
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3925-3933, 2021.

Abstract

Standard variational schemes for training deep latent variable models rely on biased gradient estimates of the target objective. Techniques based on the Evidence Lower Bound (ELBO), and tighter variants obtained via importance sampling, produce biased gradient estimates of the true log-likelihood. The family of Reweighted Wake-Sleep (RWS) methods further relies on a biased estimator of the inference objective, which biases training of the encoder also. In this work, we show how Multilevel Monte Carlo (MLMC) can provide a natural framework for debiasing these methods with two different estimators. We prove rigorously that this approach yields unbiased gradient estimators with finite variance under reasonable conditions. Furthermore, we investigate methods that can reduce variance and ensure finite variance in practice. Finally, we show empirically that the proposed unbiased estimators outperform IWAE and other debiasing method on a variety of applications at the same expected cost.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-shi21d, title = { On Multilevel Monte Carlo Unbiased Gradient Estimation for Deep Latent Variable Models }, author = {Shi, Yuyang and Cornish, Rob}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3925--3933}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/shi21d/shi21d.pdf}, url = {https://proceedings.mlr.press/v130/shi21d.html}, abstract = { Standard variational schemes for training deep latent variable models rely on biased gradient estimates of the target objective. Techniques based on the Evidence Lower Bound (ELBO), and tighter variants obtained via importance sampling, produce biased gradient estimates of the true log-likelihood. The family of Reweighted Wake-Sleep (RWS) methods further relies on a biased estimator of the inference objective, which biases training of the encoder also. In this work, we show how Multilevel Monte Carlo (MLMC) can provide a natural framework for debiasing these methods with two different estimators. We prove rigorously that this approach yields unbiased gradient estimators with finite variance under reasonable conditions. Furthermore, we investigate methods that can reduce variance and ensure finite variance in practice. Finally, we show empirically that the proposed unbiased estimators outperform IWAE and other debiasing method on a variety of applications at the same expected cost. } }
Endnote
%0 Conference Paper %T On Multilevel Monte Carlo Unbiased Gradient Estimation for Deep Latent Variable Models %A Yuyang Shi %A Rob Cornish %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-shi21d %I PMLR %P 3925--3933 %U https://proceedings.mlr.press/v130/shi21d.html %V 130 %X Standard variational schemes for training deep latent variable models rely on biased gradient estimates of the target objective. Techniques based on the Evidence Lower Bound (ELBO), and tighter variants obtained via importance sampling, produce biased gradient estimates of the true log-likelihood. The family of Reweighted Wake-Sleep (RWS) methods further relies on a biased estimator of the inference objective, which biases training of the encoder also. In this work, we show how Multilevel Monte Carlo (MLMC) can provide a natural framework for debiasing these methods with two different estimators. We prove rigorously that this approach yields unbiased gradient estimators with finite variance under reasonable conditions. Furthermore, we investigate methods that can reduce variance and ensure finite variance in practice. Finally, we show empirically that the proposed unbiased estimators outperform IWAE and other debiasing method on a variety of applications at the same expected cost.
APA
Shi, Y. & Cornish, R.. (2021). On Multilevel Monte Carlo Unbiased Gradient Estimation for Deep Latent Variable Models . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3925-3933 Available from https://proceedings.mlr.press/v130/shi21d.html.

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