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Title: Learning planar Ising models

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:
 [1] ; ORCiD logo [2] ; ORCiD logo [2] ;  [3]
  1. Numerica, Ft. Collins, CO (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Microsoft Research, Cambridge, MA (United States)
Publication Date:
Report Number(s):
LA-UR-16-21695
Journal ID: ISSN 1532-4435
Grant/Contract Number:
AC52-06NA25396
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
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