Machine learning for Dynamic Social Network Analysis Applications

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Machine learning for Dynamic Social Network Analysis Applications: Models Manuel Gomez Rodriguez Max Planck

Machine learning for Dynamic Social Network Analysis Applications: Models Manuel Gomez Rodriguez Max Planck Institute for Software Systems UC 3 M, MAY 2017

Outline of the Seminar REPRESENTATION: TEMPORAL POINT PROCESSES 1. Intensity function 2. Basic building

Outline of the Seminar REPRESENTATION: TEMPORAL POINT PROCESSES 1. Intensity function 2. Basic building blocks 3. Superposition 4. Marks and SDEs with jumps APPLICATIONS: MODELS 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition This lecture APPLICATIONS: CONTROL 1. Influence maximization 2. Activity shaping 3. When-to-post Slides/references: learning. mpi-sws. org/uc 3 m-seminar 2

Applications: Models 1. Idea adoption 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition

Applications: Models 1. Idea adoption 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition 3

Idea adoption: an example S means D Christine D follows S Bob 3. 00

Idea adoption: an example S means D Christine D follows S Bob 3. 00 pm 3. 25 pm Beth 3. 27 pm Joe David 4. 15 pm Friggeri et al. , 2014 They can have an impact in the off-line world 4

Idea adoption representation We represent an idea adoptions using terminating temporal point processes: N

Idea adoption representation We represent an idea adoptions using terminating temporal point processes: N 1(t) Idea adoption: N 2(t) N 3(t) User Idea Time N 4(t) N 5(t) 5

Idea adoption intensity Source (given, not modeled) Follow-ups (modeled) N 1(t) N 2(t) N

Idea adoption intensity Source (given, not modeled) Follow-ups (modeled) N 1(t) N 2(t) N 3(t) N 4(t) N 5(t) Memory Adopt idea only Previous once Influence from messages by user v on user u 6 [Gomez-Rodriguez et al. , ICML 2011]

Model inference from multiple adoptions Conditional intensities Maximum likelihood approach to find model parameters!

Model inference from multiple adoptions Conditional intensities Maximum likelihood approach to find model parameters! Idea adoption log-likelihood Sum up log-likelihoods of multiple ideas! Theorem. For any choice of parametric memory, the maximum likelihood problem is convex in B. 7 [Gomez-Rodriguez et al. , ICML 2011]

Topic-sensitive rates Topic-modulated influence: LDA weight for topic l 8 [Du et al. ,

Topic-sensitive rates Topic-modulated influence: LDA weight for topic l 8 [Du et al. , AISTATS 2013]

Dynamic influence In some cases, influence change over time: #greece retweets Propagation over networks

Dynamic influence In some cases, influence change over time: #greece retweets Propagation over networks 0 with variable influence T 9 [Gomez-Rodriguez et al. , WSDM 2013]

Memetracker [Leskovec et al. , KDD ’ 09] 10

Memetracker [Leskovec et al. , KDD ’ 09] 10

Insights I: real world events 11 Youtube video: http: //youtu. be/h. Bea. Sf. RCU

Insights I: real world events 11 Youtube video: http: //youtu. be/h. Bea. Sf. RCU 4 c

Insights II: dynamic clusters 12 Youtube video: http: //youtu. be/h. Bea. Sf. RCU 4

Insights II: dynamic clusters 12 Youtube video: http: //youtu. be/h. Bea. Sf. RCU 4 c

Recurrent events: beyond cascades Up to this point, we have assumed we can map

Recurrent events: beyond cascades Up to this point, we have assumed we can map each event to a cascade In general, especially in social networks: Difficult to distinguish cascades in event data Most cascades are single nodes (or forests) no likes no comments no shares 13

Recurrent events representation We represent messages using nonterminating temporal point processes: N 1(t) Recurrent

Recurrent events representation We represent messages using nonterminating temporal point processes: N 1(t) Recurrent event: N 2(t) N 3(t) User Time N 4(t) N 5(t) [Farajtabar et al. , NIPS 2014]

Recurrent events intensity N 1(t) N 2(t) N 3(t) N 4(t) N 5(t) User’s

Recurrent events intensity N 1(t) N 2(t) N 3(t) N 4(t) N 5(t) User’s Messages on her Previous intensity own initiative Influence from messages by user v on user u Hawkes process Cascade sources! Memory 15 [De et al. , NIPS 2016]

Applications: Models 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition

Applications: Models 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition 16

Opinion dynamics: an example S means D Christine D follows S Bob Beth is

Opinion dynamics: an example S means D Christine D follows S Bob Beth is influential Joe David Expressed opinions 17

Message representation We represent messages using marked temporal point processes: NA(t) NB(t) NC (t)

Message representation We represent messages using marked temporal point processes: NA(t) NB(t) NC (t) Message: User Sentiment (mark) Time 18 Noisy observation of latent opinion [De et al. , NIPS 2016]

Message intensity NA(t) NB(t) NC (t) User’s Messages on her Previous intensity own initiative

Message intensity NA(t) NB(t) NC (t) User’s Messages on her Previous intensity own initiative Influence from messages by user v on user u Hawkes process Memory 19 [De et al. , NIPS 2016]

Sentiment distribution Latent opinion Sentiment: Continuous (based on sentiment analysis): It depends on the

Sentiment distribution Latent opinion Sentiment: Continuous (based on sentiment analysis): It depends on the recorded data Discrete (based on upvotes/downvotes): 20 [De et al. , NIPS 2016]

Stochastic process for (latent) opinions Memory User’s latent opinion x. Alice(t) influence from user

Stochastic process for (latent) opinions Memory User’s latent opinion x. Alice(t) influence from user v on user u User’s initial opinion <0, disagree Bob m(t) Christine >0, agree Alice a. Christine, Alicem 2 αAlice Previous sentiment by user v a. Bob, Alicem 1 m 3 m 2 21 [De et al. , NIPS 2016]

Opinion model as Jump SDEs Proposition. The tuple (x*(t), λ*(t), N(t)) is a Markov

Opinion model as Jump SDEs Proposition. The tuple (x*(t), λ*(t), N(t)) is a Markov process, whose dynamics are defined by the following marked jumped stochastic differential equations (SDEs) Latent opinions Message intensities ! k r o Netw Informational influence Expressed opinions Temporal influence ! k r o Netw 22 [De et al. , NIPS 2016]

Model inference from opinion data Events likelihood Message sentiments (marks) Message times Theorem. The

Model inference from opinion data Events likelihood Message sentiments (marks) Message times Theorem. The maximum likelihood problem is convex in the model parameters. Markov property Sums and integrals in linear time! 23 [De et al. , NIPS 2016]

Opinion forecasting The Avengers: Age of Ultron, 05/2015 The forecasted opinion becomes less accurate

Opinion forecasting The Avengers: Age of Ultron, 05/2015 The forecasted opinion becomes less accurate as T 24 increases, as one may expect. [De et al. , NIPS 2016]

Applications: Models 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition

Applications: Models 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition 25

Information reliability: an example Learning from the crowd (‘crowdlearning’) has become very popular: Users

Information reliability: an example Learning from the crowd (‘crowdlearning’) has become very popular: Users learn from the knowledge other users contribute Refutations Knowledge is reviewed by users, who can verify or refute it verifications and depend on the source trustworthiness ✗ 26

Information reliability: key, simple idea A source is trustworthy if: Its contributions are verified

Information reliability: key, simple idea A source is trustworthy if: Its contributions are verified more frequently and/or Over time, each document has ✗ Its contributions are a different level of refuted more rarely inherent unrealibility Challenge At a time t, a document may be disputed Verifications: rarer Refutations: more frequent 27 [Tabibian et al. , WWW 2017]

Representation: temporal point processes Statement additions NA(t) (one process per document) NR 1(t) NR

Representation: temporal point processes Statement additions NA(t) (one process per document) NR 1(t) NR 3(t) NR 2(t) Statement refutations (one process per statement) NR 2(t) source Statement: ✗ refutation time e = (s, t, τ) 28 addition time [Tabibian et al. , WWW 2017]

Intensity of statement additions Statement additions NA(t) (one process per article) Intensity or rate

Intensity of statement additions Statement additions NA(t) (one process per article) Intensity or rate (Statements per time unit) Article unreliability Effect of past refutations (Mixture of Gaussians) Temporal evolution of the intrinsic reliability of the article (topic dependent; topic weight wd) Refuted statements trigger the arrival of new statements to replace them 29 [Tabibian et al. , WWW 2017]

Intensity of statement refutations Statement additions NA(t) (one process per article) NR 1(t) Statement

Intensity of statement refutations Statement additions NA(t) (one process per article) NR 1(t) Statement refutations NR 3(t) NR 2(t) (one process per statement) Refutations happen only once Intensity or rate (Statements per time unit) ✗ NR 2(t) Source trustworthiness Article unreliability (topic dependent; topic weight w ) (Mixture of Gaussians) Shared across statements of an article! d The higher the parameter , the quickest an article gets refuted 30 [Tabibian et al. , WWW 2017]

Model inference from event data Conditional intensities Events likelihood Theorem. The maximum likelihood problem

Model inference from event data Conditional intensities Events likelihood Theorem. The maximum likelihood problem is convex in the model parameters. 31 [Tabibian et al. , WWW 2017]

Wikipedia article reliability Democratic nomination US elections Barack Obama’s Wikipedia Article (Arrival of information

Wikipedia article reliability Democratic nomination US elections Barack Obama’s Wikipedia Article (Arrival of information vs intrinsic unreliability) 32 [Tabibian et al. , WWW 2017]

Source trustworthiness Politics bbc. co. uk breitbart. com Probability of refutation within 6 months

Source trustworthiness Politics bbc. co. uk breitbart. com Probability of refutation within 6 months in a stable Wikipedia article 33 [Tabibian et al. , WWW 2017]

Applications: Models 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Learning patterns

Applications: Models 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Learning patterns 34

Learning patterns: An example 1 st year computer science student Introduction to programming Discrete

Learning patterns: An example 1 st year computer science student Introduction to programming Discrete math Project presentation For/do-while loops Define Set theory functions Powerpoint Graph Theory Class vs. Keynote inheritance Export Geometrypptx to pdf t If … else How to write switch Logic Private functions PP templates Class destructor Plot library 35

Learning patterns: content + dynamics 1 st year computer science student Introduction to programming

Learning patterns: content + dynamics 1 st year computer science student Introduction to programming Discrete math Project presentation t Content + Dynamics = Learning pattern programming + semester math + semester presentation + week 36

People share same learning patterns Introduction to programming Discrete math Project presentation How can

People share same learning patterns Introduction to programming Discrete math Project presentation How can we identify the learning pattern each event belongs to? t 37

Learning events representation We represent the learning events using marked temporal point processes: Task

Learning events representation We represent the learning events using marked temporal point processes: Task Learning event: Content Time Learning pattern (hidden) 38 [Mavroforakis et al. , WWW 2017]

Learning pattern intensity Task Intensity or rate (events / hour) Memory Learning pattern popularity

Learning pattern intensity Task Intensity or rate (events / hour) Memory Learning pattern popularity Hawkes process New task rate Task 39 New task Follow-up [Mavroforakis et al. , WWW 2017]

User learning events intensity Users adopt more than one learning pattern: A user’s eventspatterns

User learning events intensity Users adopt more than one learning pattern: A user’s eventspatterns as a multidimensional Hawkes: # oflearning is infinite. Efficient model Learning pattern inference using Time e h t Sequential Montecarlo! tails in low! Content De nce be e r e f re 40 [Mavroforakis et al. , WWW 2017]

Learning pattern (I): Version Control Content Intensity Intensities Version control tasks tend to be

Learning pattern (I): Version Control Content Intensity Intensities Version control tasks tend to be specific, quickly solved after performing few questions 41 [Mavroforakis et al. , WWW 2017]

Learning pattern (II): Machine learning Content Intensities Machine learning tasks tend to be more

Learning pattern (II): Machine learning Content Intensities Machine learning tasks tend to be more complex and require asking more questions 42 [Mavroforakis et al. , WWW 2017]

Types of users Intensity Explorers Intensity Loyals Ov in l er 10 ess pat

Types of users Intensity Explorers Intensity Loyals Ov in l er 10 ess pat tha te n a rns yea r 2 le arn ove ing p r 4 att yea ern rs s 43 [Mavroforakis et al. , WWW 2017]

REPRESENTATION: TEMPORAL POINT PROCESSES 1. Intensity function 2. Basic building blocks 3. Superposition 4.

REPRESENTATION: TEMPORAL POINT PROCESSES 1. Intensity function 2. Basic building blocks 3. Superposition 4. Marks and SDEs with jumps APPLICATIONS: MODELS 1. Information propagation 2. Opinion dynamics 3. Information reliability 4. Knowledge acquisition APPLICATIONS: CONTROL 1. Influence maximization 2. Activity shaping 3. When-to-post Slides/references: learning. mpi-sws. org/sydney-seminar This lecture Next lecture 44