Exact mean field inference in asymmetric kinetic Ising systems

TL;DR

This paper presents an exact mean field approach for asymmetric kinetic Ising models that accurately computes local magnetizations and correlations, and efficiently solves inverse problems even in strongly coupled or finite-range systems.

Contribution

It introduces an exact mean field method applicable to single instances of asymmetric kinetic Ising models, extending previous weak-coupling approaches to strong coupling and finite-range cases.

Findings

Exact local magnetizations and correlations for asymmetric SK model

Efficient inverse problem solution for time-dependent couplings and fields

Applicable to finite-range and diluted asymmetric spin glasses

Abstract

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.