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Title: Optimal structure and parameter learning of Ising models

Abstract

Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, which is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Skolkovo Inst. of Science and Technology, Moscow (Russia)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1431063
Report Number(s):
LA-UR-16-29425
Journal ID: ISSN 2375-2548
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Science Advances
Additional Journal Information:
Journal Volume: 4; Journal Issue: 3; Journal ID: ISSN 2375-2548
Publisher:
AAAS
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats

Lokhov, Andrey, Vuffray, Marc Denis, Misra, Sidhant, and Chertkov, Michael. Optimal structure and parameter learning of Ising models. United States: N. p., 2018. Web. doi:10.1126/sciadv.1700791.
Lokhov, Andrey, Vuffray, Marc Denis, Misra, Sidhant, & Chertkov, Michael. Optimal structure and parameter learning of Ising models. United States. doi:10.1126/sciadv.1700791.
Lokhov, Andrey, Vuffray, Marc Denis, Misra, Sidhant, and Chertkov, Michael. Fri . "Optimal structure and parameter learning of Ising models". United States. doi:10.1126/sciadv.1700791. https://www.osti.gov/servlets/purl/1431063.
@article{osti_1431063,
title = {Optimal structure and parameter learning of Ising models},
author = {Lokhov, Andrey and Vuffray, Marc Denis and Misra, Sidhant and Chertkov, Michael},
abstractNote = {Reconstruction of the structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted toward developing universal reconstruction algorithms that are both computationally efficient and require the minimal amount of expensive data. Here, we introduce a new method, interaction screening, which accurately estimates model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime, which is known to be the hardest for learning. Here, the efficacy of interaction screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on real data produced by a D-Wave quantum computer. Finally, this study shows that the interaction screening method is an exact, tractable, and optimal technique that universally solves the inverse Ising problem.},
doi = {10.1126/sciadv.1700791},
journal = {Science Advances},
number = 3,
volume = 4,
place = {United States},
year = {Fri Mar 16 00:00:00 EDT 2018},
month = {Fri Mar 16 00:00:00 EDT 2018}
}

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