Quickest Inference of Susceptible-Infected Cascades in Sparse Networks

TL;DR

This paper introduces a rapid adaptive method for estimating the source and spread of susceptible-infected cascades in large, sparse networks using noisy diagnostic data, achieving near-instantaneous full spread estimation.

Contribution

It presents a novel adaptive procedure that estimates cascade source and full spread quickly, outperforming existing methods in sparse network settings.

Findings

Estimates cascade source with high accuracy in sub-polynomial time.

Successfully recovers full cascade spread before a polynomial log(n) affected nodes.

Simulation results confirm the method's effectiveness in realistic scenarios.

Abstract

We consider the task of estimating a network cascade as fast as possible. The cascade is assumed to spread according to a general Susceptible-Infected process with heterogeneous transmission rates from an unknown source in the network. While the propagation is not directly observable, noisy information about its spread can be gathered through multiple rounds of error-prone diagnostic testing. We propose a novel adaptive procedure which quickly outputs an estimate for the cascade source and the full spread under this observation model. Remarkably, under mild conditions on the network topology, our procedure is able to estimate the full spread of the cascade in an $n$-vertex network, before $\mathrm{poly log}(n)$ vertices are affected by the cascade. We complement our theoretical analysis with simulation results illustrating the effectiveness of our methods.