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Spotting Culprits in Epidemics: How many and Which ones?

Spotting Culprits in Epidemics: How many and Which ones?. B. Aditya Prakash Virginia Tech Jilles Vreeken University of Antwerp Christos Faloutsos Carnegie Mellon University. IEEE ICDM Brussels December 11, 2012. Contagions. Social collaboration Information Diffusion Viral Marketing

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Spotting Culprits in Epidemics: How many and Which ones?

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  1. Spotting Culprits in Epidemics: How many and Which ones? B. Aditya Prakash Virginia Tech JillesVreekenUniversity of Antwerp Christos FaloutsosCarnegie Mellon University IEEE ICDM Brussels December 11, 2012

  2. Contagions • Social collaboration • Information Diffusion • Viral Marketing • Epidemiology and Public Health • Cyber Security • Human mobility • Games and Virtual Worlds • Ecology • Localized effects: riots…

  3. Virus Propagation • Susceptible-Infected (SI) Model [AJPH 2007] β CDC data: Visualization of the first 35 tuberculosis (TB) patients and their 1039 contacts Diseases over contact networks Prakash, Vreeken, Faloutsos 2012

  4. Outline • Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion Prakash, Vreeken, Faloutsos 2012

  5. Culprits: Problem definition 2-d grid Q: Who started it? Prakash, Vreeken, Faloutsos 2012

  6. Culprits: Problem definition 2-d grid Q: Who started it? Prior work: [Lappas et al. 2010, Shah et al. 2011] Prakash, Vreeken, Faloutsos 2012

  7. Outline • Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion Prakash, Vreeken, Faloutsos 2012

  8. Culprits: Exoneration Prakash, Vreeken, Faloutsos 2012

  9. Culprits: Exoneration Prakash, Vreeken, Faloutsos 2012

  10. Who are the culprits • Two-part solution • use MDL for number of seeds • for a given number: • exoneration = centrality + penalty • Running time = • linear! (in edges and nodes) NetSleuth Prakash, Vreeken, Faloutsos 2012

  11. Outline • Motivation---Introduction • Problem Definition • Intuition • MDL • Construction • Opitimization • Experiments • Conclusion Prakash, Vreeken, Faloutsos 2012

  12. Modeling using MDL • Minimum Description Length Principle == Induction by compression • Related to Bayesian approaches • MDL = Model + Data • Model • Scoring the seed-set Number of possible |S|-sized sets En-coding integer |S| Prakash, Vreeken, Faloutsos 2012

  13. Modeling using MDL • Data: Propagation Ripples Infected Snapshot Original Graph Ripple R1 Ripple R2 Prakash, Vreeken, Faloutsos 2012

  14. Modeling using MDL • Ripple cost • Total MDL cost Ripple R How the ‘frontier’ advances How long is the ripple Prakash, Vreeken, Faloutsos 2012

  15. Outline • Motivation---Introduction • Problem Definition • Intuition • MDL • Construction • Opitimization • Experiments • Conclusion Prakash, Vreeken, Faloutsos 2012

  16. How to optimize the score? • Two-step process • Given k, quickly identify high-quality set • Given these nodes, optimize the ripple R Prakash, Vreeken, Faloutsos 2012

  17. Optimizing the score • High-quality k-seed-set • Exoneration • Best single seed: • Smallest eigenvector of Laplaciansub-matrix • Analyze a Constrained SI epidemic • Exonerate neighbors • Repeat Prakash, Vreeken, Faloutsos 2012

  18. Optimizing the score • Optimizing R • Get the MLE ripple! • Finally use MDL score to tell us the best set • NetSleuth: Linear running time in nodes and edges Ripple R Prakash, Vreeken, Faloutsos 2012

  19. Outline • Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion Prakash, Vreeken, Faloutsos 2012

  20. Experiments • Evaluation functions: • MDL based • Overlap based (JD == Jaccard distance) How far are they? Closer to 1 the better Prakash, Vreeken, Faloutsos 2012

  21. Experiments: # of Seeds One Seed Two Seeds Three Seeds

  22. Experiments: Quality (MDL and JD) One Seed Two Seeds Ideal = 1 Three Seeds Prakash, Vreeken, Faloutsos 2012

  23. Experiments: Quality (Jaccard Scores) One Seed Two Seeds NetSleuth Closer to diagonal, the better True Three Seeds Prakash, Vreeken, Faloutsos 2012

  24. Experiments: Scalability Prakash, Vreeken, Faloutsos 2012

  25. Outline • Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion Prakash, Vreeken, Faloutsos 2012

  26. Conclusion • Given:Graph and Infections • Find: Best ‘Culprits’ • Two-part solution • use MDL for number of seeds • for a given number: exoneration = centrality + penalty • NetSleuth: • Linear running time in nodes and edges Prakash, Vreeken, Faloutsos 2012

  27. Any Questions? B. AdityaPrakash http://www.cs.vt.edu/~badityap Prakash, Vreeken, Faloutsos 2012

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