Belief propagation with multipoint correlations and its application to Inverse problem

TL;DR

This paper introduces explicit formulas for the Bethe approximation incorporating multipoint correlations, leading to a new iterative algorithm that improves accuracy in spin systems and has potential applications in inverse problems.

Contribution

It provides explicit formulas for the Bethe approximation with multipoint correlations and proposes an improved iterative algorithm for better accuracy in spin systems.

Findings

The new algorithm yields more accurate critical point locations.

Formulas include magnetization and correlations in magnetic fields.

Potential application to inverse Ising models.

Abstract

We give explicit formulas of the Bethe approximation with multipoint correlations for systems with magnetic field. The obtained formulas include the closed form of the magnetization and the correlations between adjacent degrees of freedom. On the basis of our results, we propose a new iterative algorithm of the improved Bethe approximation. We confirm that the proposed technique is available for the random spin systems and indeed gives more accurate locations of the critical points. We discuss the possibility of the application of our method to the Inverse Ising model by use of these equations.