Small-correlation expansions for the inverse Ising problem

被引：103

作者：

Sessak, Vitor ^{[1
]}

Monasson, Remi ^{[1
]}

机构：

[1] Ecole Normale Super, Phys Theor Lab, F-75231 Paris 05, France

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2009年 / 42卷 / 05期

关键词：

MEAN-FIELD THEORY; SOLVABLE MODEL;

D O I：

10.1088/1751-8113/42/5/055001

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a systematic small-correlation expansion to solve the inverse Ising problem and find a set of couplings and fields corresponding to a given set of correlations and magnetizations. Couplings are calculated up to the third order in the correlations for generic magnetizations and to the seventh order in the case of zero magnetizations; in addition, we show how to sum some useful classes of diagrams exactly. The resulting expansion outperforms existing algorithms on the Sherrington-Kirkpatrick spin-glass model.

引用

页数：17

共 16 条

[1]

[Anonymous], 2013, THEORY SIMPLE LIQUID

[2]

[Anonymous], 2003, Information Theory, Inference, and Learning Algorithms

[3]

COCCO S, 2008, UNPUB

[4]

DEDOMINICIS C, 1964, J MATH PHYS, V5, P31, DOI 10.1063/1.1704064

[5]

Georges A, 2004, AIP CONF PROC, V715, P3, DOI 10.1063/1.1800733

[6] HOW TO EXPAND AROUND MEAN-FIELD THEORY USING HIGH-TEMPERATURE EXPANSIONS [J].

GEORGES, A ;

YEDIDIA, JS .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (09) :2173-2192

[7]

MARINARI E, 1998, SPIN GLASSES RANDOM

[8]

MEZARD M, 2007, TAUC C COMPL NEUR NE

[9] CONVERGENCE CONDITION OF THE TAP EQUATION FOR THE INFINITE-RANGED ISING SPIN-GLASS MODEL [J].

PLEFKA, T .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1982, 15 (06) :1971-1978

[10] Weak pairwise correlations imply strongly correlated network states in a neural population [J].

Schneidman, E ;

Berry, MJ ;

Segev, R ;

Bialek, W .

NATURE, 2006, 440 (7087) :1007-1012

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