Markov Logic Networks: Exploring their Application to Social Network Analysis Parag Singla Dept. of Computer Science and Engineering Indian Institute of.

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Presentation transcript:

Markov Logic Networks: Exploring their Application to Social Network Analysis Parag Singla Dept. of Computer Science and Engineering Indian Institute of Technology, Delhi Joint work with people at University of Washington and IIT Delhi

Overview Motivation Markov logic Application to Social Network Analysis Opportunities/Challenges

Social Network and Smoking Behavior SmokingCancer

Social Network and Smoking Behavior Smoking leads toCancer

Social Network and Smoking Behavior Smoking leads toCancer Friendship Similar Smoking Habits

Social Network and Smoking Behavior Smoking leads toCancer Friendship leads to Similar Smoking Habits

Examples Web search Information extraction Natural language processing Perception Medical diagnosis Computational biology Social networks Ubiquitous computing Etc.

Examples

Motivation Real World Entities and Relationships Uncertain Behavior

Motivation Markov Logic = First Order Logic + Markov Networks Real World Entities and Relationships Uncertain Behavior

Overview Motivation Markov logic Application to Social Network Analysis Future Directions

Markov Logic [Richardson and Domingos 06] A logical KB : A set of hard constraints How can we make them soft constraints Give each formula a weight (Higher weight  Stronger constraint)

Example: Friends & Smokers

Two constants: Anil (A) and Bunty (B)

Example: Friends & Smokers Cancer(A) Smokes(A)Smokes(B) Cancer(B) Two constants: Anil (A) and Bunty (B)

Example: Friends & Smokers Cancer(A) Smokes(A)Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Two constants: Anil (A) and Bunty (B)

Example: Friends & Smokers Cancer(A) Smokes(A)Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Two constants: Anil (A) and Bunty (B)

Example: Friends & Smokers Cancer(A) Smokes(A)Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Two constants: Anil (A) and Bunty (B)

Example: Friends & Smokers Cancer(A) Smokes(A)Friends(A,A) Friends(B,A) Smokes(B) Friends(A,B) Cancer(B) Friends(B,B) Two constants: Anil (A) and Bunty (B) State of the World  {0,1} Assignment to the nodes

Probability Distribution Weight of formula iNo. of true groundings of formula i in x

Computing Probabilities: Marginal Inference Cancer(A) Smokes(A)? Friends(A,A) Friends(B,A) Smokes(B)? Friends(A,B) Cancer(B)? Friends(B,B) What is the probability Smokes(B) = 1?

Inference: Belief Propagation Variables Clauses Smokes(Anil) Smokes(Anil)  Friends(Anil, Bunty)  Smokes(Bunty)

Belief Propagation Variables Clauses

Lifted Belief Propagation [Singla and Domingos, 2008]   ,  : Functions of edge counts Variables Clauses

Learning Parameters [Lowd and Domingos 07]

Smokes Smokes(Anil) Smokes(Bunty) Closed World Assumption: Anything not in the database is assumed false. Three constants: Anil, Bunty, Priya Cancer Cancer(Anil) Cancer(Bunty) Friends Friends(Anil, Bunty) Friends(Bunty, Anil) Friends(Anil, Priya) Friends(Priya, Anil)

Overview Motivation Markov logic Application to Social Network Analysis Observations/Challenges

Large Social Network Analysis

Twitter Datasets [Ruhela et al. ANTS 2011] SNAP Twitter7:196 Million Tweets 9.8 Million Users Kaist:1.4 Billion Social Relations Twitter:7.4 Million User Locations Yahoo! PlaceFinder :4 Million user location mapped to Latitude-Longitude OpenCalais:Semantic categorization of 114 Million Tweets into 4135 different topics

Who “Tweets” on what? Sachin is my favorite batsman! He’s going to do get the century! Century of Centuries! Wow! Go Sachin go! Cricket tonight!

Who “Tweets” on what? Sachin is my favorite batsman! He’s going to do get the century! Century of Centuries! Wow! Go Sachin go! I am going to watch the match today! Cricket tonight!

Who “Tweets” on what? Sachin is my favorite batsman! He’s going to do get the century! Century of Centuries! Wow! Go Sachin go! I am going to watch the match today! Cricket tonight! Attribution Problem

Features: Own Past Behavior tweets(uid,topic,+t) => tweet_T(uid,topic) Anil T = 51 t = 1…50 Time

Features: Followers’ Past Behavior tweets(uid1,topic,+t) ^ follows(uid2,uid1) => tweets_T(uid2,topic) Anil Bunty Priya Anil T = 51t = 1…50 Time

Features: Followers’ Current Behavior Anil Bunty Priya Anil T = 51t = 1…50 Time Bunty Priya tweets_T(uid1,topic) ^ follows(uid2,uid1) => tweets_T(uid2,topic)

Overview Motivation Markov logic Application to Social Network Analysis Challenges/Opportunities

Scaling up – extremely large-sized networks Lifted Belief Propagation Cluster “approximately similar” nodes Micro/Macro Properties Can we abstract out micro details? Learning Time varying data Incremental (online) learning

Other Research Directions Lifted Inference - Graph-Cut, SAT Learning with partial observability Video Activity Recognition