Information Spread and Information Maximization in Social Networks

Xie Yiran

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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

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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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