1. Bo Zong, Yinghui Wu, Ambuj K. Singh, Xifeng Yan 1 Inferring the Underlying Structure of Information Cascades 12-12-2012@ICDM12

2. Information cascades in social networks 2  Information propagation in social networks  Cascade: a subgraph tracking propagation trace (a) Facebook shared link (b) Twitter retweet But missing structure: a)Privacy policies b) Crawling noise. (a) A social graph Importance of Cascades a)Viral marketing b)Recommendation c)Information Security (b) A cascade

3. An example: cascade structure inference 3  We can fully observe a social graph, but the cascade structure is partially observed. #iPhone5 Alice, 1pmBob, 1:50pm David Cooper, 3pmEd Frank Alice, 1pm Bob, 1:50pm Cooper, 3pm David Frank Alice, 1pm Bob, 1:50pm Cooper, 3pm David 1. Which one? 2. How difficult? 3. Algorithms? 4. Accuracy?

4. Roadmap 4  Introduction  Preliminary  Problem definition  Our solutions  Experimental results  Conclusions

5. Preliminary 5  Diffusion graph, G = (V, E)  Independent Cascade Model  Diffusion function, f : E  [0,1]  Partial observation, X X={ (A, 0), (B, 1), (C, 3) } AB D CE F 1 2 0 1 3 0.3 0.5 0.7 0.8 0.7 0.8 0.6 0.3 0.4 0.9 0.8 G

6. Problem definition 6 Minimum Perfect Consistent Tree (PCT)  Input  diffusion graph G  source s  partial observation X  Output  cascade T: a tree in G   (v, t)  X, s reaches v by exactly t edges  minimize:  Variants  Weighted, PCT w  Non-weighted, PCT min A 0 B 1 C 3 D F T 0.7 0.8 0.7 0.9 0.046 0.7 0.3 0.8 0.5 0.8 0.7 0.6 0.8 0.9 0.3 0.4 A 0B 1 D C 3Ed F G X={ (A, 0), (B, 1), (C, 2) } 0.8

7. Problem definition (cont.) 7 Minimum Bounded Consistent Tree (BCT)  Input  diffusion graph G  source s  partial observation X  Output  cascade T: a tree in G   (v, t)  X, s reaches v by  t edges  minimize:  Variants  Weighted, BCT w  Non-weighted, BCT min A 0 B 1 C 3 David T 0.7 0.8 0.155 0.7 0.3 0.8 0.5 0.8 0.7 0.6 0.8 0.9 0.3 0.4 A 0B 1 D C 3Ed F G X={ (A, 0), (B, 1), (C, 2) } 0.8

8. Perfect consistent tree (PCT) 8  Complexity of PCT w and PCT min  NP-complete  APX-hard  Heuristic: bottom-up search  Perfect consistent SP tree  Reduce to Steiner tree  Approximable in for PCT w  Approximable in for PCT min …… …… titi … t max t1t1 S t i+1 … … … … Shortest Path

9. Bounded consistent tree (BCT) 9  Complexity of BCT w and BCT min  NP-complete  Approximable in for BCT w  Approximable in for BCT min  Approximating BCT w and BCT min  (v, t)  X, connect v to s with the shortest path

10. Datasets 10  Enron email  G: 86,808 nodes and 660,642 edges  260 cascades (depth  3, #nodes  8)  Twitter hashtag retweets  G:  17M nodes,  1,400M edges,  70M Retweets  321 cascades (depth  4, #nodes  10)  Synthetic cascades on Facebook  G:  3M nodes,  28M edges  Diffusion functions are learned.

11. Metrics 11  Partial observation  define uncertainty  randomly remove nodes from T and add them into X until  is reached.  Performance metric  precision: rate of #correct estimates to # estimates  recall: rate of # correct estimates to # missing nodes

12. Effectiveness on Perfect Consistent Tree 12

13. Effectiveness on Bounded Consistent Tree 13

14. Scalability on PCT and BCT 14

15. Conclusions 15  Defined the cascade structure inference problem  perfect and bounded consistent trees;  metrics for quality of consistent trees  Investigated the cascade structure inference problem  Analyzed the problem complexity  Proposed approximations and heuristics  Experimental results verify the effectiveness and efficiency of our solutions

16. Thanks 16  Questions?