1. Lec 4: April 6th, 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 4 Slides April 6 th, 2006

2. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 2 Start computing probabilities elimination algorithm Beginning of chordal graph theory Outline of Today’s Lecture

3. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 3 Books and Sources for Today Jordan: Chapters 17. Lauritzen, 1986. Chapters 1-3. Any good graph theory text.

4. Lec 4: April 6th, 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: chrdal, sep, decomp, elim,mcs 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 4: April 6th, 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 & 17 in Jordan’s book Lauritzen chapters 1-3 (on reserve in library) Reminder: HW is due tomorrow at 5:00pm –either leave in my inbox EE1-518 or email directly to TA, Chris Bartels. 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 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 6 Junction Tree A,B,C,D B,C,D,F B,E,F F,D,G E,F,H F,G,I C4C4 C2C2 C3C3 C5C5 C1C1 C6C6

7. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 7 Junction Tree & r.i.p.

8. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 8 Junction Tree & r.i.p.

9. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 9 Decomposability

10. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 10 Equivalent conditions for G

11. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 11 Minimal Separators Minimal (B,E)-Separator Non-minimal (B,E)-Separator Minimal (B,E)-Separator

12. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 12 Chordality implies min-seps are complete

13. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 13 ( ,  ) seps complete imply decomposability A B

14. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 14 ( ,  ) seps complete imply decomposability

15. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 15 Examples: Decomposable/Chordal?

16. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 16 Aside: Conditional Independence & Factorization

17. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 17 Relation to Junction Trees.

18. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 18 Junction Trees and Decomposability

19. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 19 Junction Trees and Decomposability

20. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 20 Junction Trees and Decomposability

21. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 21 Junction Trees and Decomposability

22. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 22 Junction Trees and Decomposability new link

23. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 23 Junction Trees and Decomposability

24. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 24 Junction Trees and Separability

25. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 25 B A C D EFG HI Graph, JT, and its separators A,B,C,D B,C,D,F B,E,F F,D,G E,F,H F,G,I Junction Tree: tree of cliques With separators A,B,C,D B,C,D,F B,E,F F,D,G E,F,H F,G,I BCD BF FD EF FG

26. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 26 JTs and well-ordered cliques 1 2 3 4 5 1 2 3 4 5

27. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 27 How can we tell if G is chordal? Complete Set

28. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 28 How can we tell if G is chordal?

29. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 29 How can we recognize chordal graphs?

30. Lec 4: April 6th, 2006EE512 - Graphical Models - J. BilmesPage 30 How can we recognize chordal graphs? 12 3 4 1 2 3 4 5 6 7 8 9 10 11