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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
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Virus Propagation
• Susceptible-Infected (SI) Model [AJPH 2007]
CDC data: Visualization of the first 35 tuberculosis (TB) patients and their 1039 contacts
Diseases over contact networks
Prakash, Vreeken, Faloutsos 2012
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Outline
• Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion
Prakash, Vreeken, Faloutsos 2012
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Culprits: Problem definition
2-d grid Q: Who started it?
Prakash, Vreeken, Faloutsos 2012
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Culprits: Problem definition
Prakash, Vreeken, Faloutsos 2012
Prior work: [Lappas et al. 2010, Shah et al. 2011]
2-d grid Q: Who started it?
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Outline
• Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion
Prakash, Vreeken, Faloutsos 2012
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Culprits: Exoneration
Prakash, Vreeken, Faloutsos 2012
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Culprits: Exoneration
Prakash, Vreeken, Faloutsos 2012
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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)
Prakash, Vreeken, Faloutsos 2012
NetSleuth
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Outline
• Motivation---Introduction • Problem Definition • Intuition • MDL
– Construction – Opitimization
• Experiments • Conclusion
Prakash, Vreeken, Faloutsos 2012
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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
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Modeling using MDL
• Data: Propagation Ripples Original
Graph Infected Snapshot
Ripple R2 Ripple R1 Prakash, Vreeken, Faloutsos 2012
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Modeling using MDL
• Ripple cost
• Total MDL cost
How the ‘frontier’ advances How long is the ripple
Ripple R
Prakash, Vreeken, Faloutsos 2012
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Outline
• Motivation---Introduction • Problem Definition • Intuition • MDL
– Construction – Opitimization
• Experiments • Conclusion
Prakash, Vreeken, Faloutsos 2012
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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
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Optimizing the score
• High-quality k-seed-set – Exoneration
• Best single seed: – Smallest eigenvector of Laplacian sub-matrix – Analyze a Constrained SI epidemic
• Exonerate neighbors • Repeat
Prakash, Vreeken, Faloutsos 2012
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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
Prakash, Vreeken, Faloutsos 2012
Ripple R
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Outline
• Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion
Prakash, Vreeken, Faloutsos 2012
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Experiments
• Evaluation functions: – MDL based
– Overlap based
(JD == Jaccard distance)
Closer to 1 the better
Prakash, Vreeken, Faloutsos 2012
How far are they?
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Experiments: # of Seeds
One Seed Two Seeds
Three Seeds
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Experiments: Quality (MDL and JD)
Prakash, Vreeken, Faloutsos 2012
Ideal = 1
One Seed Two Seeds
Three Seeds
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Experiments: Quality (Jaccard Scores)
Prakash, Vreeken, Faloutsos 2012
Closer to diagonal, the better
True
Net
Sleu
th
One Seed Two Seeds
Three Seeds
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Experiments: Scalability
Prakash, Vreeken, Faloutsos 2012
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Outline
• Motivation---Introduction • Problem Definition • Intuition • MDL • Experiments • Conclusion
Prakash, Vreeken, Faloutsos 2012
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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
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B. Aditya Prakash http://www.cs.vt.edu/~badityap
Any Questions?
Prakash, Vreeken, Faloutsos 2012