Structure Learning of Antiferromagnetic Ising Models
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Shah_Structure learning.pdf
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Author(s)
Bresler, Guy
Gamarnik, David
Shah, Devavrat
Date Issued
2014
Journal
Advances in Neural Information Processing Systems (NIPS)
Publisher
Neural Information Processing Systems Foundation
Citation
Bresler, Guy, David Gamarnik, and Devavrat Shah. "Structure Learning of Antiferromagnetic Ising Models." Advances in Neural Information Processing Systems 27 (NIPS 2014).
Version
Author's final manuscript
Abstract
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. Our first result is an unconditional computational lower bound of Ω(p[superscript d/2]) for learning general graphical models on p nodes of maximum degree d, for the class of statistical algorithms recently introduced by Feldman et al. The construction is related to the notoriously difficult learning parities with noise problem in computational learning theory. Our lower bound shows that the [~ over O](p[superscript d+2]) runtime required by Bresler, Mossel, and Sly's exhaustive-search algorithm cannot be significantly improved without restricting the class of models. Aside from structural assumptions on the graph such as it being a tree, hypertree, tree-like, etc., most recent papers on structure learning assume that the model has the correlation decay property. Indeed, focusing on ferromagnetic Ising models, Bento and Montanari showed that all known low-complexity algorithms fail to learn simple graphs when the interaction strength exceeds a number related to the correlation decay threshold. Our second set of results gives a class of repelling (antiferromagnetic) models that have the \emph{opposite} behavior: very strong repelling allows efficient learning in time [~ over O](p[superscript 2]). We provide an algorithm whose performance interpolates between [~ over O](p[superscript 2]) and [~ over O](p[superscript d+2]) depending on the strength of the repulsion.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Sloan School of Management
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DOI of Published Version
https://papers.nips.cc/paper/5319-structure-learning-of-antiferromagnetic-ising-models
