Sequential Estimation of Network Cascades

12/09/2019

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by   Anirudh Sridhar, et al.

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We consider the problem of locating the source of a network cascade, given a noisy time-series of network data. We assume that at time zero, the cascade starts with one unknown vertex and spreads deterministically at each time step. The goal is to find a sequential estimation procedure for the source that outputs an estimate for the cascade source as fast as possible, subject to a bound on the estimation error. For general graphs that satisfy a symmetry property, we show that matrix sequential probability ratio tests (MSPRTs) 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.