Sharp Signal Detection Under Ferromagnetic Ising Models

TL;DR

This paper investigates how dependence affects the detection of structured signals in ferromagnetic Ising models, providing sharp detection thresholds across various models and demonstrating robustness to dependence strength.

Contribution

It offers precise detection thresholds for different ferromagnetic Ising models and shows how to perform detection without detailed knowledge of dependence strength.

Findings

Sharp detection constants for lattice and mean-field Ising models

Detection thresholds relate closely to dependence structure

Method robust to varying dependence strength

Abstract

In this paper we study the effect of dependence on detecting a class of structured signals in Ferromagnetic Ising models. Natural examples of our class include Ising Models on lattices, and Mean-Field type Ising Models such as dense Erd\H{o}s-R\'{e}nyi, and dense random regular graphs. Our results not only provide sharp constants of detection in each of these cases and thereby pinpoint the precise relationship of the detection problem with the underlying dependence, but also demonstrate how to be agnostic over the strength of dependence present in the respective models.