Rumor source detection for rumor spreading on random increasing
        trees

Fuchs, Michael; Yu, Pei-Duo

doi:10.1214/ecp.v20-3743

Cited by 19 publications

(10 citation statements)

References 10 publications

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“…They consequently defined a notion of rumor centrality, which was shown to be equivalent to maximum likelihood estimation in the case of regular trees. Follow-up papers [9,11,22] include generalizations to recursive trees and scenarios where only incomplete information is provided about the subgraph of infected nodes.…”

Section: Introductionmentioning

confidence: 99%

Confidence Sets for the Source of a Diffusion in Regular Trees

Khim

Loh

2017

IEEE Trans. Netw. Sci. Eng.

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We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size independent of the number of infected nodes. Our estimators are motivated by analogous results in the literature concerning identification of the root node in preferential attachment and uniform attachment trees. At the core of our proofs is a probabilistic analysis of Pólya urns corresponding to the number of uninfected neighbors in specific subtrees of the infection tree. We also provide an example illustrating the shortcomings of source estimation techniques in settings where the underlying graph is asymmetric.

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Section: Introductionmentioning

confidence: 99%

Confidence Sets for the Source of a Diffusion in Regular Trees

Khim

Loh

2017

IEEE Trans. Netw. Sci. Eng.

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“…These types of dynamics on networks are popular models e.g. for the spread of biological epidemics in structured populations (Moore and Newman, 2000;Pastor-Satorras and Vespignani, 2001;Ganesh et al, 2015), malware in computer networks (Shah and Zaman, 2010), and rumours in social networks (Fuchs and Yu, 2015;Shah and Zaman, 2016), and are also sometimes referred to as contact processes. In addition, we impose a rate γ > 0 at which a new infection enters the network, infecting one uniformly sampled node.…”

Section: The Susceptible-infected-susceptible Networkmentioning

confidence: 99%

“…We are interested in inferring the initial location of the observed large infection, which may no longer be infected itself. Point estimators for similar inference problems have been studied in (Shah and Zaman, 2010;Fuchs and Yu, 2015;Shah and Zaman, 2016).…”

Section: The Susceptible-infected-susceptible Networkmentioning

confidence: 99%

Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo

2017

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We present a sequential Monte Carlo algorithm for Markov chain trajectories with proposals constructed in reverse time, which is advantageous when paths are conditioned to end in a rare set. The reverse time proposal distribution is constructed by approximating the ratio of Green's functions in Nagasawa's formula. Conditioning arguments can be used to interpret these ratios as low-dimensional conditional sampling distributions of some coordinates of the process given the others. Hence the difficulty in designing SMC proposals in high dimension is greatly reduced. We illustrate our method on estimating an overflow probability in a queueing model, the probability that a diffusion follows a narrowing corridor, and the initial location of an infection in an epidemic model on a network.

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“…A network centrality called the rumor centrality was introduced in [7] to solve optimally special instances of the problem when the graph topology of the online social networks is assumed to be degree-regular tree with countably infinite number of vertices and assuming a SI (susceptible-infectious) spreading model. This problem was subsequently extended to various problem settings, e.g., extension in [8] to random increasing trees, extension in [9] to probabilistic sampling of the rumor graph, extension in [10] to star graph, extension in [11], [12] to the scenario of multiple sources, extension in [13] to multiple observations. The authors in [14] proposed a Markov chain Monte Carlo based algorithms, and the authors in [15] proposed message-passing algorithms based on probabilistic analysis of graph boundaries.…”

Section: Introductionmentioning

confidence: 99%

Epidemic Source Detection in Contact Tracing Networks: Epidemic Centrality in Graphs and Message-Passing Algorithms

Yu,

Tan,

2022

Preprint

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We study the epidemic source detection problem in contact tracing networks modeled as a graph-constrained maximum likelihood estimation problem using the susceptible-infected model in epidemiology. Based on a snapshot observation of the infection subgraph, we first study finite degree regular graphs and regular graphs with cycles separately, thereby establishing a mathematical equivalence in maximal likelihood ratio between the case of finite acyclic graphs and that of cyclic graphs. In particular, we show that the optimal solution of the maximum likelihood estimator can be refined to distances on graphs based on a novel statistical distance centrality that captures the optimality of the nonconvex problem. An efficient contact tracing algorithm is then proposed to solve the general case of finite degree-regular graphs with multiple cycles. Our performance evaluation on a variety of graphs shows that our algorithms outperform the existing state-of-the-art heuristics using contact tracing data from the SARS-CoV 2003 and COVID-19 pandemics by correctly identifying the superspreaders on some of the largest superspreading infection clusters in Singapore and Taiwan.

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Rumor source detection for rumor spreading on random increasing trees

Cited by 19 publications

References 10 publications

Confidence Sets for the Source of a Diffusion in Regular Trees

Confidence Sets for the Source of a Diffusion in Regular Trees

Inference and rare event simulation for stopped Markov processes via reverse-time sequential Monte Carlo

Epidemic Source Detection in Contact Tracing Networks: Epidemic Centrality in Graphs and Message-Passing Algorithms

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