Detecting a Path of Correlations in a Network

TL;DR

This paper addresses the challenge of detecting a correlated path within white noise by establishing theoretical bounds and proposing an effective test that nearly achieves these bounds.

Contribution

It introduces a minimax lower bound for the detection problem and proposes a test that is nearly optimal under mild conditions.

Findings

The proposed test nearly attains the minimax lower bound.

Theoretical bounds provide fundamental limits for detection.

The method is effective under mild assumptions.

Abstract

We consider the problem of detecting an anomaly in the form of a path of correlations hidden in white noise. We provide a minimax lower bound and a test that, under mild assumptions, is able to achieve the lower bound up to a multiplicative constant.