Sequential Estimation of Network Cascades

TL;DR

This paper develops an adaptive sequential testing method to quickly and accurately locate the source of a network cascade using noisy data, with proven asymptotic optimality on certain graph structures.

Contribution

It introduces a family of MSPRT procedures for source localization in networks, demonstrating their asymptotic optimality and applicability to various graph types.

Findings

MSPRTs are asymptotically optimal for regular trees.

The methods perform well in simulations.

The approach applies to general graph classes.

Abstract

We consider the problem of locating the source of a network cascade, given a noisy time-series of network data. Initially, the cascade starts with one unknown, affected vertex and spreads deterministically at each time step. The goal is to find an adaptive procedure that outputs an estimate for the source as fast as possible, subject to a bound on the estimation error. For a general class of graphs, we describe a family of matrix sequential probability ratio tests (MSPRTs) that are first-order asymptotically optimal up to a constant factor as the estimation error tends to zero. We apply our results to lattices and regular trees, and show that MSPRTs are asymptotically optimal for regular trees. We support our theoretical results with simulations.