Total Variation Distance Meets Probabilistic Inference

Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S. Meel, Dimitrios Myrisiotis, A. Pavan, N. V. Vinodchandran
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:3776-3794, 2024.

Abstract

In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance to probabilistic inference over directed graphical models. This reduction leads to a fully polynomial randomized approximation scheme (FPRAS) for estimating TV distances between same-structure distributions over any class of Bayes nets for which there is an efficient probabilistic inference algorithm. In particular, it leads to an FPRAS for estimating TV distances between distributions that are defined over a common Bayes net of small treewidth. Prior to this work, such approximation schemes only existed for estimating TV distances between product distributions. Our approach employs a new notion of partial couplings of high-dimensional distributions, which might be of independent interest.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-bhattacharyya24a, title = {Total Variation Distance Meets Probabilistic Inference}, author = {Bhattacharyya, Arnab and Gayen, Sutanu and Meel, Kuldeep S. and Myrisiotis, Dimitrios and Pavan, A. and Vinodchandran, N. V.}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {3776--3794}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/bhattacharyya24a/bhattacharyya24a.pdf}, url = {https://proceedings.mlr.press/v235/bhattacharyya24a.html}, abstract = {In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance to probabilistic inference over directed graphical models. This reduction leads to a fully polynomial randomized approximation scheme (FPRAS) for estimating TV distances between same-structure distributions over any class of Bayes nets for which there is an efficient probabilistic inference algorithm. In particular, it leads to an FPRAS for estimating TV distances between distributions that are defined over a common Bayes net of small treewidth. Prior to this work, such approximation schemes only existed for estimating TV distances between product distributions. Our approach employs a new notion of partial couplings of high-dimensional distributions, which might be of independent interest.} }
Endnote
%0 Conference Paper %T Total Variation Distance Meets Probabilistic Inference %A Arnab Bhattacharyya %A Sutanu Gayen %A Kuldeep S. Meel %A Dimitrios Myrisiotis %A A. Pavan %A N. V. Vinodchandran %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-bhattacharyya24a %I PMLR %P 3776--3794 %U https://proceedings.mlr.press/v235/bhattacharyya24a.html %V 235 %X In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance to probabilistic inference over directed graphical models. This reduction leads to a fully polynomial randomized approximation scheme (FPRAS) for estimating TV distances between same-structure distributions over any class of Bayes nets for which there is an efficient probabilistic inference algorithm. In particular, it leads to an FPRAS for estimating TV distances between distributions that are defined over a common Bayes net of small treewidth. Prior to this work, such approximation schemes only existed for estimating TV distances between product distributions. Our approach employs a new notion of partial couplings of high-dimensional distributions, which might be of independent interest.
APA
Bhattacharyya, A., Gayen, S., Meel, K.S., Myrisiotis, D., Pavan, A. & Vinodchandran, N.V.. (2024). Total Variation Distance Meets Probabilistic Inference. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:3776-3794 Available from https://proceedings.mlr.press/v235/bhattacharyya24a.html.

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