1. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 1 Jeff A. Bilmes University of Washington Department of Electrical Engineering EE512 Spring, 2006 Graphical Models Jeff A. Bilmes Lecture 2 Slides March 30 th, 2006

2. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 2 d-separation, 3 canonical BNs, Bayes ball Undirected Models Start computing probabilities Outline of Today’s Lecture

3. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 3 Books and Sources for Today Jordan: Chapters 1 and 2 Derin 1989 (Markov Random Fields) Lauritzen, 1986. Any graph theory text.

4. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 4 L1: Tues, 3/28: Overview, GMs, Intro BNs. L2: Thur, 3/30: semantics of BNs + UGMs L3: Tues, 4/4 L4: Thur, 4/6 L5: Tue, 4/11 L6: Thur, 4/13 L7: Tues, 4/18 L8: Thur, 4/20 L9: Tue, 4/25 L10: Thur, 4/27 L11: Tues, 5/2 L12: Thur, 5/4 L13: Tues, 5/9 L14: Thur, 5/11 L15: Tue, 5/16 L16: Thur, 5/18 L17: Tues, 5/23 L18: Thur, 5/25 L19: Tue, 5/30 L20: Thur, 6/1: final presentations Class Road Map

5. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 5 Makeup Time Constraints

6. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 6 READING: Chapter 1,2 in Jordan’s book (pick up book from basement of communications copy center). Syllabus handout If you have not signed up before: –List handout: name, department, and email –List handout: regular makeup slot, and discussion section Reminder: course web page: http://ssli.ee.washington.edu/ee512 http://ssli.ee.washington.edu/ee512 TA discussions and office hours: –Office hours: Thursdays 3:30-4:30, Sieg Ground Floor Tutorial Center –Discussion Sections: Fridays 9:30-10:30, Sieg Ground Floor Tutorial Center Lecture Room Announcements

7. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 7 Bayesian Networks & CI

8. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 8 Bayesian Networks & CI

9. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 9 Bayesian Networks & CI

10. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 10 Pictorial d-separation: blocked/unblocked paths Blocked Paths Unblocked Paths

11. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 11 Three 3-node examples of BNs and their conditional independence statements. V1V1 V2V2 V3V3 V1V1 V2V2 V3V3 V1V1 V2V2 V3V3 Three Canonical Cases

12. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 12 Case 1 Markov Chain

13. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 13 Case 2 Still a Markov Chain

14. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 14 Case 3 NOT a Markov Chain

15. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 15 SUVs Greenhouse Gasses Global Warming Lung Cancer Smoking Bad Breath GeneticsCancerSmoking Examples of the three cases

16. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 16 Bayes Ball

17. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 17 Ex: What are some conditional independences? D. Poole M. Jordan

18. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 18 Two Views of a Family

19. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 19 Undirected Models

20. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 20 Markov Random Fields

21. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 21 Happy Families MRFs BNs Decomposable models

22. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 22 Can BNs represent C 4 ?

23. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 23 Markov Random Fields->Graph Theory

24. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 24 Examples Subgraph Cycle

25. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 25 Markov Random Fields

26. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 26 Markov Random Fields

27. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 27 Markov Random Fields: interaction

28. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 28 Markov Random Fields: Image Processing Derin, 1989

29. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 29 Summarizing Derin, 1989

30. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 30 Computing Probabilities

31. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 31 Computing Probabilities

32. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 32 Computing Probabilities

33. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 33 Note on sums and evidence

34. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 34 Graph Algorithm Equivalent: Elimination

35. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 35 B A C D EFG HI 1 2 3 4 7 5 6 8 9 Order the Nodes Eliminate the nodes in order Elimination Example: different graph

36. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 36 Result of Elimination

37. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 37 Elimination

38. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 38 Elimination & Directed Graphs

39. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 39 Immoral Elimination

40. Lec 2: March 30th, 2006EE512 - Graphical Models - J. BilmesPage 40 Variable Elimination Algorithm