Learning planar ising models

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

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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. We demonstrate our method in simulations and for two applications: Modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalJournal of Machine Learning Research
Volume17
StatePublished - Dec 1 2016
Externally publishedYes

Keywords

  • Graphical models
  • Ising models

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

Fingerprint

Dive into the research topics of 'Learning planar ising models'. Together they form a unique fingerprint.

Cite this