Learning planar Ising models
Inference and learning of graphical models are both wellstudied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geochemical depth trends from Mars rover data.
 Authors:

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 Numerica, Ft. Collins, CO (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Microsoft Research, Cambridge, MA (United States)
 Publication Date:
 Report Number(s):
 LAUR1621695
Journal ID: ISSN 15324435
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Machine Learning Research
 Additional Journal Information:
 Journal Volume: 17; Journal Issue: 215; Journal ID: ISSN 15324435
 Publisher:
 JMLR
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; computer science; planetary sciences; Ising models; graphical models
 OSTI Identifier:
 1342860
Johnson, Jason K., Oyen, Diane Adele, Chertkov, Michael, and Netrapalli, Praneeth. Learning planar Ising models. United States: N. p.,
Web.
Johnson, Jason K., Oyen, Diane Adele, Chertkov, Michael, & Netrapalli, Praneeth. Learning planar Ising models. United States.
Johnson, Jason K., Oyen, Diane Adele, Chertkov, Michael, and Netrapalli, Praneeth. 2016.
"Learning planar Ising models". United States.
doi:. https://www.osti.gov/servlets/purl/1342860.
@article{osti_1342860,
title = {Learning planar Ising models},
author = {Johnson, Jason K. and Oyen, Diane Adele and Chertkov, Michael and Netrapalli, Praneeth},
abstractNote = {Inference and learning of graphical models are both wellstudied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geochemical depth trends from Mars rover data.},
doi = {},
journal = {Journal of Machine Learning Research},
number = 215,
volume = 17,
place = {United States},
year = {2016},
month = {12}
}