Identifying interacting pairs of sites in Ising models on a countable set

TL;DR

This paper develops a method to identify interacting site pairs in infinite Ising models from finite samples, providing bounds on misidentification probabilities under certain conditions.

Contribution

It introduces a novel approach for detecting interacting pairs in infinite Ising models using finite samples, with theoretical bounds on error probabilities.

Findings

Provides an upper bound for misidentification probability

Applicable to infinite countable site sets under Dobrushin condition

Enhances understanding of interaction detection in Ising models

Abstract

This paper address the problem of identifying pairs of interacting sites from a finite sample of independent realizations of the Ising model. We consider Ising models in a infinite countable set of sites under Dobrushin uniqueness condition. The observed sample contains only the values assigned by the Ising model to a finite set of sites. Our main result is an upperbound for the probability of misidentification of the pairs of interacting sites in this finite set.