Approximate Counting, the Lovász Local Lemma, and Inference in Graphical Models
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3268930.pdf
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420.48 KB
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Adobe PDF
Checksum (MD5)
f6103c73f52d23ed25c626f86fd67e2c
Author(s)
Moitra, Ankur
Date Issued
2019
Journal
Journal of the ACM
Publisher
Association for Computing Machinery (ACM)
Version
Final published version
Abstract
© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. In this article, we introduce a new approach to approximate counting in bounded degree systems with higher-order constraints. Our main result is an algorithm to approximately count the number of solutions to a CNF formula Φ when the width is logarithmic in the maximum degree. This closes an exponential gap between the known upper and lower bounds. Moreover, our algorithm extends straightforwardly to approximate sampling, which shows that under Lovász Local Lemma-like conditions it is not only possible to find a satisfying assignment, it is also possible to generate one approximately uniformly at random from the set of all satisfying assignments. Our approach is a significant departure from earlier techniques in approximate counting, and is based on a framework to bootstrap an oracle for computing marginal probabilities on individual variables. Finally, we give an application of our results to show that it is algorithmically possible to sample from the posterior distribution in an interesting class of graphical models.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Statistics and Data Science Center (Massachusetts Institute of Technology)
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1145/3268930
