1. Influence and Correlation in Social Networks Priyanka Garg

2. Behavioral correlation Human behaviors tend to cluster in network space and in time. Recent studies show behavioral clustering in – Example: Obesity is contagious! Several alternative explanations besides peer influence could also explain these patterns.

3. Sources of correlation Social influence: One person performing an action can cause her contacts to do the same. – Example: A bought an IPhone after B told him it’s cool Homophily: We tend to choose friends who like the same things and behave in the same ways that we do. – Example: Two marathon runners are more likely to become friends. Confounding factors: External influence from elements in the environment. – Example: Co-workers have same health benefit plans and hence they tend to have similar fitness.

4. What we want? Separate correlation from causation. – A notoriously difficult problem. Why? – Different marketing strategies – Cases I (Influence is prominent) Peer-to-peer marketing strategy that creates incentives for adopters to spread positive word-of-mouth (WOM). – Cases II (Homophily is prominent) Traditional market segmentation strategy based on observable characteristics of consumers.

5. Idea # 1 (KDD’08) If influence does not play a role, the activation time of a user should be independent of the activation time of his friends. Influence model: each agent becomes active in each time step independently with probability p(a), where a is the # of active friends. Coefficient α measures social correlation.

6. Testing for Influence Shuffle Test: – Chronological property Edge-Reversal Test: – Asymmetry property UserABC Time123 UserABC Time231 A B C A B C

7. Shuffle test on Flickr data

8. Edge-reversal test on Flickr data Tagging correlation can not be attributed to the social influence!

9. Yahoo! Go dataset (PNAS’09) Homophily can also explain temporal clustering. If friends are more similar, they are more likely to have similar desires to be “early adopter”.

10. A dynamic matched sampling procedure Match nodes conditionally on the their attribute X. Define a propensity score for each node Treated node. Node having X friends who have already adopted Go. Match each “treated” node to closest “untreated” node. For every time unit, calculate the fraction of number of “treated” and number of “untreated” nodes. Gives a comparison of the adoption rates of those with friends who have adopted and those without.

11. Distinguishing Influence from Homophily

12. Exaggerated Homophily Amongst Early Adopters

13. Challenges All attributes of users can’t be observed. The latent homophily can’t be distinguished from influence. Feedback effects between similarity and Social Influence in Online Communities. (KDD’08) X(i) = attributes of node i. A(i,j) = 1 if i & j are friends Y(i,t) = Action of i at time t.

14. References S. Aral, L. Muhnik, A. Sundararajan. Distinguishing influence- based contagion from homophily-driven diffusion in dynamic networks. http://roybal.iq.harvard.edu/pdf/mersih2/aral.pdfhttp://roybal.iq.harvard.edu/pdf/mersih2/aral.pdf A. Anagnostopoulos, R. Kumar, M. Mahdian. Influence and Correlation in Social Networks. KDD’08 C. R. Shalizi and Andrew C. Thomas. Homophily, Contagion, Confounding: Pick Any Three. Sociological methods and research’ 2011. http://cscs.umich.edu/~crshalizi/weblog/656.html http://cscs.umich.edu/~crshalizi/weblog/656.html