Approximate counting, the Lovasz local lemma, and inference in graphical models
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1610.04317.pdf
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Author(s)
Moitra, Ankur
Date Issued
June 2017
Journal
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017
Publisher
Association for Computing Machinery (ACM)
Citation
Moitra, Ankur. “Approximate Counting, the Lovasz Local Lemma, and Inference in Graphical Models.” Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017 (2017).
Version
Original manuscript
Abstract
In this paper we introduce a new approach for approximately 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 Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1145/3055399.3055428
