Amortized Rejection Sampling in Universal Probabilistic Programming
Saeid Naderiparizi, Adam Scibior, Andreas Munk, Mehrdad Ghadiri, Atilim Gunes Baydin, Bradley J. Gram-Hansen, Christian A. Schroeder De Witt, Robert Zinkov
Abstract
Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method’s correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework.
BibTeX
@InProceedings{pmlr-v151-naderiparizi22a,
title = { Amortized Rejection Sampling in Universal Probabilistic Programming },
author = {Naderiparizi, Saeid and Scibior, Adam and Munk, Andreas and Ghadiri, Mehrdad and Gunes Baydin, Atilim and Gram-Hansen, Bradley J. and Schroeder De Witt, Christian A. and Zinkov, Robert and Torr, Philip and Rainforth, Tom and Whye Teh, Yee and Wood, Frank},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {8392--8412},
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/naderiparizi22a/naderiparizi22a.pdf},
url = {https://proceedings.mlr.press/v151/naderiparizi22a.html},
abstract = { Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method’s correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework. }
}