Optimal structure and parameter learning of Ising models
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 informationtheoretically optimal number of samples, notably in the lowtemperature 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 DWave 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:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Skolkovo Inst. of Science and Technology, Moscow (Russia)
 Publication Date:
 Report Number(s):
 LAUR1629425
Journal ID: ISSN 23752548
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Science Advances
 Additional Journal Information:
 Journal Volume: 4; Journal Issue: 3; Journal ID: ISSN 23752548
 Publisher:
 AAAS
 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)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Mathematics
 OSTI Identifier:
 1431063
Lokhov, Andrey, Vuffray, Marc Denis, Misra, Sidhant, and Chertkov, Michael. Optimal structure and parameter learning of Ising models. United States: N. p.,
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. 2018.
"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 informationtheoretically optimal number of samples, notably in the lowtemperature 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 DWave 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 = {2018},
month = {3}
}