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Information Spread and Information Maximization in Social Networks
Xie Yiran
5.28
Spreading Through Networks
Application: viral marketing
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Purchase decisions are increasingly influencedby opinions of friends in Social Media
How frequently do you sharerecommendations online?
Viral/Word-of-Mouth Marketing
Idea: exploit social influence for marketing
Basic assumption: word-of-mouth effect◦ Actions, opinions, buying behaviors, innovations,
etc. propagate in a social network
Target users who are likely to produceword-of-mouth diffusion
◦ Additional reach, clicks, conversions,brand awareness
◦ Target the influencers27
Social networks & marketing
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Identifying influencers: start-ups
Klout◦ Measure of overall influence online (mostly Twitter, now FB and LinkedIn)◦ Score = function of true reach, amplification probability and network influence◦ Claims score to be highly correlated to clicks, comments and retweets
Peer Index◦ Identifies/Scores authorities on the social web by topic
SocialMatica◦ Ranks 32M people by vertical/topic, claims to take into account quality of authored
content
Influencer50◦ Clients: IBM, Microsoft, SAP, Oracle and a long list of tech companies
+ Svnetwork, Bluecalypso, CrowdBooster, Sproutsocial, TwentyFeet,EmpireAvenue, Twitaholic , and many others …
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Finding the influencers …
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“He’s not a ‘Super Influencer’,he’s a very naughty boy!”
Homophily or Influence?Homophily: tendency to stay together with
people similar to you
“Birds of a feather flock together”
E.g. I’m overweight I date overweight girls
Influence: force that a person A exerts on aperson B that changes the behavior/opinion of B
Influence is a causal process
E.g. my girlfriend gains weight I gain weight too36
Viral marketing &The Influence Maximization Problem
Problem statement:◦ find a seed-set of influential people such thatby targeting them we maximize the spreadof viral propagations
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Word-of-mouth (viral) marketing is believed to be a promisingmarketing strategy.
Increasing popularity of online social networks may enable largescale viral marketing
2
xphone is good
xphone is good
xphone is good
Word-of-mouth (WoM) effect in socialnetworks xphone is good
xphone is good
xphone is good
xphone is good
Diffusion/Propagation Modelsand the Influence Maximization
(IM) Problem
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• Node v– fv (s) : threshold function for v
– θv : threshold for v
• Reward function : r(A(S))– A(S) : final set of active nodes– Influence spread:
T-1 T
• Use greedy algorithm framework
• Use Monte Carlo simulations to estimate 𝜎 𝑆
Influence spread is submodular in both IC a𝜎 𝑆nd LT models
Scalable Influence Maximization
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Theory versus Practice
...the trouble about arguments is,they ain't nothing but theories,after all, and theories don't provenothing, they only give you a placeto rest on, a spell, when you aretuckered out butting around andaround trying to find out somethingthere ain't no way to find out...There's another trouble abouttheories: there's always a hole inthem somewheres, sure, if youlook close enough.
- “Tom Sawyer Abroad”, Mark Twain
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·
Learning Influence Models
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Where do the numbers come from?
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Learning influence modelsWhere do influence probabilities come from?
◦◦◦◦
Real world social networks don’t have probabilities!Can we learn the probabilities from action logs?Sometimes we don’t even know the social networkCan we learn the social network , too?
Does influence probability change over time?◦ Yes! How can we take time into account?◦ Can we predict the time at which user is most likely
to perform an action?
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Where do the weights come from?
Influence Maximization – Gen 0:academic collaboration networks (real)with weights assigned arbitrarily usingsome models:◦ Trivalency: weights chosen uniformly at
random from {0.1, 0.01, 0.001}.0.1
0.001
0.010.001
0.01 0.01
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P1. Social network not given
Observe activation times, assumeprobability of a successful activationdecays (e.g., exponentially) with time
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Actual network Learned network
,,,,
[Gomez-Rodriguez, Leskovec, & Krause KDD 2010]
P2. Social network given
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Several models of influence probability◦ in the context of General Threshold model + time◦ consistent with IC and LT models
With or without explicit attribution
Models able to predict whether a user will perform an action ornot: predict the time at which she will perform it
Introduce metrics of user and action influenceability◦ high values genuine influence
Develop efficient algorithms to learn the parameters of themodels; minimize the number of scans over the propagation log
Incrementally property
[[Goyal, Bonchi, and L. WSDM2010 ]
Comparison of Static, CT and DTmodels
Time-conscious models better than the static model◦ CT and DT models perform equally well
Static and DT models are far more efficient compared toCT models because of their incremental nature
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Predicting Time – Distribution ofError
Operating Point is chosen corresponding to◦ TPR: 82.5%, FPR: 17.5%.
Most of the time, error in the prediction is verysmall
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