Learning planar Ising models

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; Netrapalli, Praneeth

Title: Learning planar Ising models

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Abstract

Inference and learning of graphical models are both well-studied 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 geo-chemical depth trends from Mars rover data.

Authors:

Johnson, Jason K. ^[1];

^[2];

^[2]; Netrapalli, Praneeth ^[3]

Numerica, Ft. Collins, CO (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Microsoft Research, Cambridge, MA (United States)

Publication Date:: Thu Dec 01 00:00:00 EST 2016

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1342860

Report Number(s):: LA-UR-16-21695
Journal ID: ISSN 1532-4435

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Machine Learning Research

Additional Journal Information:: Journal Volume: 17; Journal Issue: 215; Journal ID: ISSN 1532-4435

Publisher:: JMLR

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; computer science; planetary sciences; Ising models; graphical models

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                    Johnson, Jason K., Oyen, Diane Adele, Chertkov, Michael, and Netrapalli, Praneeth. Learning planar Ising models.  United States: N. p., 2016. 
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                    Johnson, Jason K., Oyen, Diane Adele, Chertkov, Michael, & Netrapalli, Praneeth. Learning planar Ising models.  United States.

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                    Johnson, Jason K., Oyen, Diane Adele, Chertkov, Michael, and Netrapalli, Praneeth. Thu .  
"Learning planar Ising models".  United States.  https://www.osti.gov/servlets/purl/1342860.

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@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 well-studied 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 geo-chemical depth trends from Mars rover data.},

  doi          = {},

  journal      = {Journal of Machine Learning Research},

  number       = 215,

  volume       = 17,

  place        = {United States},

  year         = {Thu Dec 01 00:00:00 EST 2016},

  month        = {Thu Dec 01 00:00:00 EST 2016}

}

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