@InProceedings{berenbrink_676,
    title = {Inference of a rumor's source in the independent cascade model},
    author = {Berenbrink, Petra and Hahn-Klimroth, Max and Kaaser, Dominik and Krieg, Lena and Rau, Malin},
    abstract = {We consider the so-called Independent Cascade Model for rumor spreading or epidemic processes popularized by Kempe et al.\ (2003).
        In this model, a node of a network is the source of a rumor -- it is informed.
        In discrete time steps, each informed node ``infects'' each of its uninformed neighbors with probability p.
        While many facets of this process are studied in the literature, less is known about the inference problem: given a number of infected nodes in a network, can we learn the source of the rumor?
        In the context of epidemiology this problem is often referred to as patient zero problem.
        It belongs to a broader class of problems where the goal is to infer parameters of the underlying spreading model.
        In this work we present a maximum likelihood estimator for the rumor's source, given a snapshot of the process in terms of a set of active nodes X after t steps. Our results show that, for acyclic graphs,  the likelihood estimator undergoes a phase transition as a function of $t$. We provide a rigorous analysis for two prominent classes of acyclic network, namely d-regular trees and Galton-Watson trees, and verify empirically that our heuristics work well in various general networks. }
}

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