1. Lec 3: April 4th, 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 3 Slides April 4 th, 2006

2. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 2 Start computing probabilities elimination algorithm Beginning of chordal graph theory Outline of Today’s Lecture

3. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 3 Books and Sources for Today Jordan: Chapters 2 and 3 Lauritzen, 1986. Any graph theory text.

4. Lec 3: April 4th, 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: elimination, probs, chordal I 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 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 5 If you see a typo, please tell me during lecture –everyone will then benefit. –note, corrected slides will go on web. READING: Chapter 3 in Jordan’s book (take a look at chapters 17) Please audit if you are attending class –it will help to get us a bigger room. –If you need an add code, just send me email. Reminder: 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

6. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 6 Computing Probabilities

7. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 7 Computing Probabilities

8. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 8 Computing Probabilities

9. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 9 Note on sums and evidence

10. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 10 Graph Algorithm Equivalent: Elimination

11. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 11 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

12. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 12 Result of Elimination

13. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 13 Elimination

14. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 14 Elimination

15. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 15 Elimination & Directed Graphs

16. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 16 Immoral Elimination

17. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 17 Moralization

18. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 18 Variable Elimination Algorithm

19. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 19 Summary

20. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 20 More Graph Terminology/Notation

21. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 21 Graph Terminology/Notation

22. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 22 Graph Terminology/Notation

23. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 23 Graph Terminology/Notation

24. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 24 Ancestral examples

25. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 25 Separators

26. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 26 Tree/Forest

27. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 27 Triangulated/Chordal

28. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 28 Triangulated/Chordal

29. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 29 Triangulated/Chordal

30. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 30 Junction Tree A,B,C,D B,C,D,F B,E,F F,D,G E,F,H F,G,I

31. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 31 Junction Tree & r.i.p.

32. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 32 Junction Tree & r.i.p.

33. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 33 Decomposability

34. Lec 3: April 4th, 2006EE512 - Graphical Models - J. BilmesPage 34 Equivalent conditions for G