Testing ising models
Name
1.9781611975031.130.pdf
Description
Published version
Size
631.9 KB
Format
Adobe PDF
Checksum (MD5)
a3f97ac2f4574278cf5ca7db95467b8a
Author(s)
Daskalakis, C
Dikkala, N
Kamath, G
Date Issued
January 1, 2018
Journal
Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Daskalakis, C, Dikkala, N and Kamath, G. 2018. "Testing ising models." Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.
Version
Final published version
Abstract
© Copyright 2018 by SIAM. Given samples from an unknown multivariate distribution p, is it possible to distinguish whether p is the product of its marginals versus p being far from every product distribution? Similarly, is it possible to distinguish whether p equals a given distribution q versus p and q being far from each other? These problems of testing independence and goodness-of-fit have received enormous attention in statistics, information theory, and theoretical computer science, with sample-optimal algorithms known in several interesting regimes of parameters [BFF+01, Pan08, VV17, ADK15, DK16]. Unfortunately, it has also been understood that these problems become intractable in large dimensions, necessitating exponential sample complexity. Motivated by the exponential lower bounds for general distributions as well as the ubiquity of Markov Random Fields (MRFs) in the modeling of high-dimensional distributions, we initiate the study of distribution testing on structured multivariate distributions, and in particular the prototypical example of MRFs: the Ising Model. We demonstrate that, in this structured setting, we can avoid the curse of dimensionality, obtaining sample and time efficient testers for independence and goodness-of-fit. One of the key technical challenges we face along the way is bounding the variance of functions of the Ising model.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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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/10.1137/1.9781611975031.130
