Probabilistic Relational Models for Link Prediction Problem
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This document discusses probabilistic relational models for link prediction. It introduces probabilistic relational networks, including relational Bayesian networks (RBNs) and relational Markov networks (RMNs). RBNs define a joint probability distribution over attributes and relations. RMNs focus on symmetric interactions using clique templates. Both approaches can be used for link prediction by modeling factors that affect relations between entities, such as attributes, structural properties, and complex patterns.
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References
[1] Getoor, Lise. Introduction to statistical relational learning. MIT press,
2007.
[2] Pfeffer, Avrom J., and Daphne Koller. Probabilistic reasoning for
complex systems. Stanford: Stanford University, 2000.
[3] Koller, Daphne, and Avi Pfeffer. "Probabilistic frame-based
systems."AAAI/IAAI. 1998.
[4] Taskar, Ben, Pieter Abbeel, and Daphne Koller. "Discriminative
probabilistic models for relational data." Proceedings of the Eighteenth
conference on Uncertainty in artificial intelligence. Morgan Kaufmann
Publishers Inc., 2002.
[5] Taskar, Ben, et al. "Link prediction in relational data." Advances in
neural information processing systems. 2003.](https://image.slidesharecdn.com/8ae438f5-a158-48da-9815-e5db8b040ba7-160513075256/85/Probabilistic-Relational-Models-for-Link-Prediction-Problem-23-320.jpg)
Probabilistic Relational Models for Link Prediction Problem
- 1. Probabilistic Relational Models for Link Prediction Problem By: Sina Sajadmanesh Advisor: Dr. Hamid Reza Rabiee
- 2. 2 DMLLink Prediction DMLDMLLink Prediction2 Outline Introduction Probabilistic Relational Models Directed vs. Undirected Networks Relational Bayesian Networks Relational Markov Networks
- 3. 3 DMLLink Prediction DMLDMLLink Prediction3 Introduction Probabilistic Relational Models Combines probabilistic graphical models with entity-relationship models Defines a joint probability distribution over attributes of entities and relations A method for describing probabilistic relationships among attributes of entities and related entities
- 4. 4 DMLLink Prediction DML4 Introduction Probabilistic Relational Network Directed Graphical Model • Relational Bayesian Network (RBN) • Focus on causal interactions Undirected Graphical Model • Relational Markov Network (RMN) • Focus on symmetric interactions
- 5. 5 DMLLink Prediction DMLDMLLink Prediction5 Outline Introduction Relational Bayesian Networks Relational Schema Probabilistic Model Relational Skeleton Attribute Uncertainty Semantics Link Prediction Relational Markov Networks
- 6. 6 DMLLink Prediction DMLDMLLink Prediction6 Relational Bayesian Networks
- 7. 7 DMLLink Prediction DMLDMLLink Prediction7 Relational Bayesian Networks Relational Schema Author Good Writer Author of Has Review Review Paper Quality Accepted Mood Length Smart
- 8. 8 DMLLink Prediction DMLDMLLink Prediction8 Relational Bayesian Networks Probabilistic Model Length Mood Author Good Writer Paper Quality Accepted Review Smart
- 9. 9 DMLLink Prediction DMLDMLLink Prediction9 Relational Bayesian Networks Relational Skeleton Fixed relational skeleton σ: set of objects in each class relations between them Author A1 Paper P1 Author: A1 Review: R1 Review R2 Review R1 Author A2 Paper P2 Author: A1 Review: R2 Paper P3 Author: A2 Review: R2 Review R2
- 10. 10 DMLLink Prediction DMLDMLLink Prediction10 Relational Bayesian Networks Attribute Uncertainty RBN defines distribution over instantiations of attributes
- 11. 11 DMLLink Prediction DMLDMLLink Prediction11 Relational Bayesian Networks Aggregate Dependencies Review R1 Length Mood Review R2 Length Mood Review R3 Length Mood Paper P1 Accepted Quality
- 12. 12 DMLLink Prediction DMLDMLLink Prediction12 Relational Bayesian Networks Aggregate Dependencies sum, min, max, avg, mode, count Review R1 Length Mood Review R2 Length Mood Review R3 Length Mood Paper P1 Accepted Quality mode 3.07.0 4.06.0 8.02.0 9.01.0 , , , , , tt ft tf ff P(A | Q, M)MQ
- 13. 13 DMLLink Prediction DMLDMLLink Prediction13 Relational Bayesian Networks Semantics Probability distribution over instantiation I Author Paper Review Author A1 Paper P2 Paper P1 Review R3 Review R2 Review R1 Author A2 Paper P3 𝑃 𝐼 𝜎, 𝑆, 𝜃 = 𝑥∈𝜎 𝑥.𝐴 𝑃 𝑥. 𝐴 𝑝𝑎𝑟𝑒𝑛𝑡𝑠(𝑥. 𝐴))
- 14. 14 DMLLink Prediction DMLDMLLink Prediction14 Relational Bayesian Networks Link Prediction ? ? ?
- 15. 15 DMLLink Prediction DMLDMLLink Prediction15 Relational Bayesian Networks Link Prediction Cites Paper Topic Words Paper Topic Words Exists Citer.Topic Cited.Topic 0.995 0.005Theory Theory False True AITheory 0.999 0.001 AIAI 0.993 0.008 AI Theory 0.997 0.003
- 16. 16 DMLLink Prediction DMLDMLLink Prediction16 Relational Bayesian Networks Link Prediction Paper#2 Topic Paper#3Topic WordN Paper#1 Word1 Topic ... ... ... Author #1 Area Inst #1-#2 Author #2 Area Inst Exists #2-#3 Exists #2-#1 Exists #3-#1 Exists #1-#3 Exists WordN Word1 WordN Word1 Exists #3-#2
- 17. 17 DMLLink Prediction DMLDMLLink Prediction17 Outline Introduction Relational Bayesian Networks Relational Markov Networks Advantages of Undirected Models Markov instead of Bayesian network Relational Clique Templates Formal Definition Link Prediction
- 18. 18 DMLLink Prediction DMLDMLLink Prediction18 Relational Markov Networks Advantages of Undirected Models Cycles are not a problem Easy to learn discriminatively Symmetric, non-causal interactions Handles patterns involving multiple entities • Triangle patterns • Transitive patterns Devised for collective classification
- 19. 19 DMLLink Prediction DMLDMLLink Prediction19 Relational Markov Networks Markov instead of Bayesian network Author2 Paper2 TopicArea Venue Paper1 Topic Author1 SubArea Area 1.8 AI TH TH 0.3 1.5 0.2 AIAI TH AI TH T2T1 (T1,T2) Template potential
- 20. 20 DMLLink Prediction DMLDMLLink Prediction20 Relational Markov Networks Relational Clique Templates Specify tuples of variables in the network instantiation using relational query language Components: • F a set of entity variables (FROM) • W condition about the attributes (WHERE) • S subset of attributes (SELECT) Query results to cliques SELECT p1.topic, p2.topic FROM Paper p1, Paper p2, Cite c WHERE c.citer=p1.key AND c.cited=p2.key
- 21. 21 DMLLink Prediction DMLDMLLink Prediction21 Relational Markov Networks Formal Definition Set of clique templates C Set of potential functions Ф • Φ 𝑐 𝑉𝑐 = exp{𝑤𝑐 𝑓𝑐(𝑉𝑐)} Defines a conditional distribution over labels of an instantiation 𝑃 𝐼 Ф, 𝐶 = 1 𝑍 𝐶 𝑐∈𝐶(𝐼) Φ 𝑐 𝐼. 𝑣𝑐
- 22. 22 DMLLink Prediction DMLDMLLink Prediction22 Relational Markov Networks Link Prediction Factors affecting the relations of different entities Entity’s attributes: • Properties, Labels Entity’s structural properties: • Similarity, Transitivity More complex patterns can be captured using cliques that represents dependencies and correlations
- 23. 23 DMLLink Prediction DMLDMLLink Prediction23 References [1] Getoor, Lise. Introduction to statistical relational learning. MIT press, 2007. [2] Pfeffer, Avrom J., and Daphne Koller. Probabilistic reasoning for complex systems. Stanford: Stanford University, 2000. [3] Koller, Daphne, and Avi Pfeffer. "Probabilistic frame-based systems."AAAI/IAAI. 1998. [4] Taskar, Ben, Pieter Abbeel, and Daphne Koller. "Discriminative probabilistic models for relational data." Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence. Morgan Kaufmann Publishers Inc., 2002. [5] Taskar, Ben, et al. "Link prediction in relational data." Advances in neural information processing systems. 2003.
- 24. Q&A
Editor's Notes
- #7: hello