Massively parallel reweighted wake-sleep

Thomas Heap, Gavin Leech, Laurence Aitchison
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:870-878, 2023.

Abstract

Reweighted wake-sleep (RWS) is a machine learning method for performing Bayesian inference in a very general class of models. RWS draws $K$ samples from an underlying approximate posterior, then uses importance weighting to provide a better estimate of the true posterior. RWS then updates its approximate posterior towards the importance-weighted estimate of the true posterior. However, recent work [Chattergee and Diaconis, 2018] indicates that the number of samples required for effective importance weighting is exponential in the number of latent variables. Attaining such a large number of importance samples is intractable in all but the smallest models. Here, we develop massively parallel RWS, which circumvents this issue by drawing $K$ samples of all $n$ latent variables, and individually reasoning about all $K^n$ possible combinations of samples. While reasoning about $K^n$ combinations might seem intractable, the required computations can be performed in polynomial time by exploiting conditional independencies in the generative model. We show considerable improvements over standard “global” RWS, which draws $K$ samples from the full joint.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-heap23a, title = {Massively parallel reweighted wake-sleep}, author = {Heap, Thomas and Leech, Gavin and Aitchison, Laurence}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {870--878}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/heap23a/heap23a.pdf}, url = {https://proceedings.mlr.press/v216/heap23a.html}, abstract = {Reweighted wake-sleep (RWS) is a machine learning method for performing Bayesian inference in a very general class of models. RWS draws $K$ samples from an underlying approximate posterior, then uses importance weighting to provide a better estimate of the true posterior. RWS then updates its approximate posterior towards the importance-weighted estimate of the true posterior. However, recent work [Chattergee and Diaconis, 2018] indicates that the number of samples required for effective importance weighting is exponential in the number of latent variables. Attaining such a large number of importance samples is intractable in all but the smallest models. Here, we develop massively parallel RWS, which circumvents this issue by drawing $K$ samples of all $n$ latent variables, and individually reasoning about all $K^n$ possible combinations of samples. While reasoning about $K^n$ combinations might seem intractable, the required computations can be performed in polynomial time by exploiting conditional independencies in the generative model. We show considerable improvements over standard “global” RWS, which draws $K$ samples from the full joint.} }
Endnote
%0 Conference Paper %T Massively parallel reweighted wake-sleep %A Thomas Heap %A Gavin Leech %A Laurence Aitchison %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-heap23a %I PMLR %P 870--878 %U https://proceedings.mlr.press/v216/heap23a.html %V 216 %X Reweighted wake-sleep (RWS) is a machine learning method for performing Bayesian inference in a very general class of models. RWS draws $K$ samples from an underlying approximate posterior, then uses importance weighting to provide a better estimate of the true posterior. RWS then updates its approximate posterior towards the importance-weighted estimate of the true posterior. However, recent work [Chattergee and Diaconis, 2018] indicates that the number of samples required for effective importance weighting is exponential in the number of latent variables. Attaining such a large number of importance samples is intractable in all but the smallest models. Here, we develop massively parallel RWS, which circumvents this issue by drawing $K$ samples of all $n$ latent variables, and individually reasoning about all $K^n$ possible combinations of samples. While reasoning about $K^n$ combinations might seem intractable, the required computations can be performed in polynomial time by exploiting conditional independencies in the generative model. We show considerable improvements over standard “global” RWS, which draws $K$ samples from the full joint.
APA
Heap, T., Leech, G. & Aitchison, L.. (2023). Massively parallel reweighted wake-sleep. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:870-878 Available from https://proceedings.mlr.press/v216/heap23a.html.

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