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Journal of Statistical Mechanics: Theory and Experiment

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Journal of Statistical Mechanics: Theory and Experiment Volume 2012 March 2012

H Chau Nguyen and Johannes Berg J. Stat. Mech. (2012) P03004 doi:10.1088/1742-5468/2012/03/P03004

Bethe–Peierls approximation and the inverse Ising problem

H Chau Nguyen and Johannes Berg

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Abstract References Cited By

We apply the Bethe–Peierls approximation to the inverse Ising problem and show how the linear response relation leads to a simple method for reconstructing couplings and fields of the Ising model. This reconstruction is exact on tree graphs, yet its computational expense is comparable to those of other mean-field methods. We compare the performance of this method to the independent-pair, naive mean-field, and Thouless–Anderson–Palmer approximations, the Sessak–Monasson expansion, and susceptibility propagation on the Cayley tree, SK model and random graph with fixed connectivity. At low temperatures, Bethe reconstruction outperforms all of these methods, while at high temperatures it is comparable to the best method available so far (the Sessak–Monasson method). The relationship between Bethe reconstruction and other mean-field methods is discussed.


Keywords

data mining (theory)

statistical inference

learning theory

network reconstruction

 

E-print Number: 1112.3501

Cited: by |

Refers: to

PACS

75.10.Hk Classical spin models

02.10.Ox Combinatorics; graph theory

05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion

MSC

05C80 Random graphs

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Subjects

Mathematical physics

Condensed matter: electrical, magnetic and optical

Statistical physics and nonlinear systems

Dates

Issue 03 (March 2012)

Received 15 December 2011, accepted for publication 10 February 2012

Published 12 March 2012

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