Download Influence and Correlation in Social Networks

Influence and Correlation in
Social Networks
Priyanka Garg
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.
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.
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.
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.
Testing for Influence
• Shuffle Test:
– Chronological property
User
A
B
C
User
A
B
C
Time
1
2
3
Time
2
3
1
• Edge-Reversal Test:
– Asymmetry property
C
A
C
A
B
B
Shuffle test on Flickr data
Edge-reversal test on Flickr data
Tagging correlation can not be attributed
to the social influence!
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”.
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.
Distinguishing Influence from
Homophily
Exaggerated Homophily Amongst Early
Adopters
Challenges
• All attributes of users can’t be observed. The latent homophily
can’t be distinguished from influence.
X(i) = attributes of node i.
A(i,j) = 1 if i & j are friends
Y(i,t) = Action of i at time t.
• Feedback effects between similarity and Social Influence in
Online Communities. (KDD’08)
References
• S. Aral, L. Muhnik, A. Sundararajan. Distinguishing influencebased contagion from homophily-driven diffusion in dynamic
networks. http://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