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S tatistical R elational L earning: A Quick Intro

S tatistical R elational L earning: A Quick Intro. Lise Getoor University of Maryland, College Park. acknowledgements. Synthesis of ideas of many individuals who have participated in various SRL workshops :

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S tatistical R elational L earning: A Quick Intro

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  1. Statistical Relational Learning: A Quick Intro Lise Getoor University of Maryland, College Park

  2. acknowledgements • Synthesis of ideas of many individuals who have participated in various SRL workshops : • Hendrik Blockeel, Mark Craven, James Cussens, Bruce D’Ambrosio, Luc De Raedt, Tom Dietterich, Pedro Domingos, Saso Dzeroski, Peter Flach, Rob Holte, Manfred Jaeger, David Jensen, Kristian Kersting, Daphne Koller, Heikki Mannila, Tom Mitchell, Ray Mooney, Stephen Muggleton, Kevin Murphy, Jen Neville, David Page, Avi Pfeffer, Claudia Perlich, David Poole, Foster Provost, Dan Roth, Stuart Russell, Taisuke Sato, Jude Shavlik, Ben Taskar, Lyle Ungar and many others… • and students: • Indrajit Bhattacharya, Mustafa Bilgic, Rezarta Islamaj, Louis Licamele, Qing Lu, Galileo Namata, Vivek Sehgal, Prithviraj Sen

  3. Why SRL? • Traditional statistical machine learning approaches assume: • A random sample of homogeneous objects from single relation • Traditional ILP/relational learning approaches assume: • No noise or uncertainty in data • Real world data sets: • Multi-relational, heterogeneous and semi-structured • Noisy and uncertain • Statistical Relational Learning: • newly emerging research area at the intersection of research in social network and link analysis, hypertext and web mining, graph mining, relational learning and inductive logic programming • Sample Domains: • web data, bibliographic data, epidemiological data, communication data, customer networks, collaborative filtering, trust networks, biological data, sensor networks, natural language, vision

  4. SRL Approaches • Directed Approaches • Bayesian Network Tutorial • Rule-based Directed Models • Frame-based Directed Models • Undirected Approaches • Markov Network Tutorial • Frame-based Undirected Models • Rule-based Undirected Models

  5. Probabilistic Relational Models • PRMs w/ Attribute Uncertainty • Inference in PRMs • Learning in PRMs • PRMs w/ Structural Uncertainty • PRMs w/ Class Hierarchies • Representation & Inference • [Koller & Pfeffer 98, Pfeffer, Koller, Milch &Takusagawa 99, Pfeffer 00] • Learning, Structural Uncertainty & Class Hierarchies • [Friedman et al. 99, Getoor, Friedman, Koller & Taskar 01 & 02, Getoor 01]

  6. Relational Schema Author Review Good Writer Mood Smart Length Paper Quality Accepted Has Review Author of • Describes the types of objects and relations in the database

  7. Probabilistic Relational Model Review Author Smart Mood Good Writer Length Paper Quality Accepted

  8. Paper.Accepted | æ ö ÷ ç Paper.Quality, P ÷ ç ÷ ç Paper.Review.Mood è ø Probabilistic Relational Model Review Author Smart Mood Good Writer Length Paper Quality Accepted

  9. Probabilistic Relational Model Review Author Smart Mood Good Writer Length Paper P(A | Q, M) Q , M f , f 0 . 1 0 . 9 Quality f , t 0 . 2 0 . 8 Accepted t , f 0 . 6 0 . 4 t , t 0 . 7 0 . 3

  10. Primary Keys Foreign Keys Relational Skeleton Paper P1 Author: A1 Review: R1 Review R1 Author A1 Paper P2 Author: A1 Review: R2 Review R2 Author A2 Review R2 Paper P3 Author: A2 Review: R2 Fixed relational skeleton : • set of objects in each class • relations between them

  11. Smart Smart Mood Mood Mood Good Writer Good Writer Length Length Length Quality Quality Quality Accepted Accepted Accepted PRM w/ Attribute Uncertainty Paper P1 Author: A1 Review: R1 Author A1 Review R1 Paper P2 Author: A1 Review: R2 Author A2 Review R2 Paper P3 Author: A2 Review: R2 Review R3 PRM defines distribution over instantiations of attributes

  12. Low Pissy r2.Mood r3.Mood P(A | Q, M) Q , M P2.Quality P3.Quality f , f 0 . 1 0 . 9 f , t 0 . 2 0 . 8 P(A | Q, M) Q , M t , f 0 . 6 0 . 4 f , f 0 . 1 0 . 9 t , t 0 . 7 0 . 3 f , t 0 . 2 0 . 8 t , f 0 . 6 0 . 4 t , t 0 . 7 0 . 3 A Portion of the BN P2.Accepted P3.Accepted

  13. High Low Pissy Pissy r2.Mood r3.Mood P2.Quality P3.Quality A Portion of the BN P(A | Q, M) Q , M f , f 0 . 1 0 . 9 f , t 0 . 2 0 . 8 P2.Accepted t , f 0 . 6 0 . 4 t , t 0 . 7 0 . 3 P3.Accepted

  14. Review R2 Review R3 Review R1 Mood Mood Mood Length Length Length Paper P1 Quality Accepted PRM: Aggregate Dependencies Paper Review Mood Quality Length Accepted

  15. Review R3 Review R1 Review R2 Mood Mood Mood Length Length Length Paper P1 Quality Accepted PRM: Aggregate Dependencies Paper Review Mood Quality Length Accepted P(A | Q, M) Q , M f , f 0 . 1 0 . 9 f , t 0 . 2 0 . 8 t , f 0 . 6 0 . 4 t , t 0 . 7 0 . 3 mode sum, min, max, avg, mode, count

  16. Objects Attributes PRM with AU Semantics Author • Review • R1 Author A1 Paper Paper P1 • Review • R2 Author A2 Review Paper P2 • Review • R3 Paper P3 PRM + relational skeleton = probability distribution over completions I:

  17. Probabilistic Relational Models • PRMs w/ Attribute Uncertainty • Inference in PRMs • Learning in PRMs • PRMs w/ Structural Uncertainty • PRMs w/ Class Hierarchies

  18. Kinds of structural uncertainty • How many objects does an object relate to? • how many Authors does Paper1 have? • Which object is an object related to? • does Paper1 cite Paper2 or Paper3? • Which class does an object belong to? • is Paper1a JournalArticleor aConferencePaper? • Does an object actually exist? • Are two objects identical?

  19. Structural Uncertainty • Motivation: PRM with AU only well-defined when the skeleton structure is known • May be uncertain about relational structure itself • Construct probabilistic models of relational structure that capture structural uncertainty • Mechanisms: • Reference uncertainty • Existence uncertainty • Number uncertainty • Type uncertainty • Identity uncertainty

  20. ? ? ? Existence Uncertainty Document Collection Document Collection

  21. PRM w/ Exists Uncertainty Paper Paper Topic Topic Cites Words Words Exists Dependency model for existence of relationship

  22. Theory Theory 0.995 0005 Theory AI 0.999 0001 AI Theory 0.997 0003 AI AI 0.993 0008 Exists Uncertainty Example Paper Paper Topic Topic Cites Words Words Exists False True Cited.Topic Citer.Topic

  23. ??? Paper P2 Topic Theory Paper P2 Topic Theory Paper P5 Topic AI Paper P5 Topic AI Paper P4 Topic Theory Paper P4 Topic Theory Paper P3 Topic AI Paper P3 Topic AI Paper P1 Topic ??? Paper P1 Topic ??? object skeleton  PRM-EU + objectskeleton   probability distribution over full instantiations I PRMs w/ EU Semantics Paper Paper Topic Topic Cites Words Words Exists PRM EU

  24. But…what about Probabilistic DBs? • Similarities: • Representation, e.g. • PRMs can model attribute correlations compactly (or) • PRMs can model tuple uncertainty by introducing exists random variable for each uncertain tuple (maybe) • PRMs can model join dependencies compactly • Differences: • ML emphasis on generalization and compact modeling • DB emphasis on loss-less data storage • Commonality: • Need for efficient query processing

  25. Conclusion • Statistical Relational Learning • Supports multi-relational, heterogeneous domains • Supports noisy, uncertain, non-IID data • aka, real-world data! • Different approaches: • rule-based vs. frame-based • directed vs. undirected • Many common issues: • Need for collective classification and consolidation • Need for aggregation and combining rules • Need to handle labeled and unlabeled data • Need to handle structural uncertainty • etc. • Great opportunity for combining machine learning for hierarchical statistical models with probabilistic databases which can efficiently store, query, update models

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