Enhancing Maximum Likelihood Estimation of Infection Source Localization

Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


The studies on the spreading processes over complex networks have increasingly wide applications. Sometimes this is very important to find quickly the origin of spread, e.g. the patient zero in epidemics or the origin of fake news forwarded in social network. The method of maximum likelihood estimation proposed by Pinto et al. (PTV) solves the important case of this problem in which a limited set of nodes act as observers and report times at which the spread has reached them. While the PTV algorithm has been shown to be optimal on trees there are several challenges remaining on general graphs. One important issue is the complexity \(O(N^\alpha )\) where N is the size of the network and \(\alpha \in (3,4)\) depending on the network topology and the number of observers. We address this issue with a new approach in which observers with low-quality information (i.e. with large spread encounter times) are ignored and potential sources are selected based on the likelihood gradient from high-quality observers. Our gradient maximum likelihood algorithm (GMLA) reduces this complexity to \(O(N^2log (N))\). The other issue we address here is of precision on general graphs. The original PTV approach assumes the information travels via a single, shortest path, which by this assumption is supposed to be the fastest way. We show that such assumption leads to the overestimation of propagation time in networks where multiple potential traversal paths exist. We propose a new method of source estimation based on maximum likelihood principle that takes into account the existence of multiple shortest paths. We test our modifications extensively on both synthetic and real networks and show that they successfully address the aforementioned issues and thus enhancing the PTV method of locating the source of a spread on complex networks.


Complex networks Spreading Signal detection 



The work was partially supported as RENOIR Project by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 691152 and by Ministry of Science and Higher Education (Poland) grant nos. 34/H2020/2016, 329025/PnH /2016 National Science Centre, Poland grant no. 2015/19/B/ST6/02612 and by POB Research Centre Cybersecurity and Data Science of Warsaw University of Technology within the Excellence Initiative Program - Research University (IDUB). J.A.H. was partially supported by the Russian Scientific Foundation, Agreement #17-71-30029 with co-financing of Bank Saint Petersburg. B.K.S. was partially supported by the Army Research Laboratory under Cooperative Agreement Number W911NF-09-2-0053 (the ARL Network Science CTA), by the Army Research Office grant W911NF-16-1-0524 and by the Office of Naval Research grant N00014-15-1-2640. R.P. was partially supported by the National Science Centre, Poland, agreement no. 2019/32/T/ST6/00173 and by PLGrid Infrastructure.


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Authors and Affiliations

  1. 1.Faculty of PhysicsWarsaw University of TechnologyWarsawPoland
  2. 2.Social Cognitive Networks Academic Research CenterRensselaer Polytechnic InstituteTroyUSA
  3. 3.Społeczna Akademia NaukŁódźPoland
  4. 4.ITMO UniversitySaint PetersburgRussia

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