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Diffusion archeology for diffusion progression history reconstruction

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Abstract

Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed, while it is occurring—perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel Prize Collecting Dominating Set Vertex cover relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.

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Notes

  1. http://www.cs.cmu.edu/~ckingsf/software/dhrec.

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Acknowledgments

We thank anonymous reviewers for their very useful comments and suggestions. This work has been partially funded by the US National Science Foundation (CCF-1256087, CCF-1319998) and US National Institutes of Health (R21HG006913 and R01HG007104). C.K. received support as an Alfred P. Sloan Research Fellow.

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Authors and Affiliations

  1. Machine Learning Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Emre Sefer

  2. Computational Biology Department, Carnegie Mellon University, Pittsburgh, PA, USA

    Carl Kingsford

Authors
  1. Emre Sefer
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  2. Carl Kingsford
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Corresponding author

Correspondence to Emre Sefer.

Additional information

A preliminary version of this paper appeared in ICDM 2014 [29].

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Sefer, E., Kingsford, C. Diffusion archeology for diffusion progression history reconstruction. Knowl Inf Syst 49, 403–427 (2016). https://doi.org/10.1007/s10115-015-0904-x

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