1. Lec 11: May 2nd, 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 11 Slides May 2 nd, 2006

2. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 2 READING: –M. Jordan: Chapters 4,10,12,17,18 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 Reminder: take-home Midterm: May 5 th -12 th, you must work alone on this. Note: I am gone all next week (May 8 th -12 th ). Subsequent weeks we will have makeup classes on Mondays at 6:00pm. Announcements

3. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 3 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 L5: Tue, 4/11: chdl/elim, mcs, triang, ci props. L6: Thur, 4/13: MST,CI axioms, Markov prps. L7: Tues, 4/18: Mobius, HC-thm, (F)=(G) L8: Thur, 4/20: phylogenetic trees, HMMs L9: Tue, 4/25: HMMs, inference on trees L10: Thur, 4/27: Inference on trees, start poly L11: Tues, 5/2: polytrees, start JT inference 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

4. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 4 L1: Tues, 3/28: L2: Thur, 3/30: L3: Tues, 4/4: L4: Thur, 4/6: L5: Tue, 4/11: L6: Thur, 4/13: L7: Tues, 4/18: L8: Thur, 4/20: Team Lists, short abstracts I L9: Tue, 4/25: L10: Thur, 4/27: short abstracts II L11: Tues, 5/2: today L12: Thur, 5/4: abstract II + progress L13: Tues, 5/9 L14: Thur, 5/11: 1 page progress report L15: Tue, 5/16 L16: Thur, 5/18: 1 page progress report L17: Tues, 5/23 L18: Thur, 5/25: 1 page progress report L19: Tue, 5/30 L20: Thur, 6/1: final presentations L21: Tue, 6/6 4-page papers due (like a conference paper). Final Project Milestone Due Dates Team lists, abstracts, and progress reports must be turned in, in class and using paper (dead tree versions only). Final reports must be turned in electronically in PDF (no other formats accepted). Progress reports must report who did what so far!!

5. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 5 Inference on trees Inference on undirected trees Example: voting tallying by message passing in trees Begin inference on poly trees Summary of Last Time

6. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 6 inference on poly trees Begin exact inference on junction trees Outline of Today’s Lecture

7. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 7 Books and Sources for Today M. Jordan: Chapters 4,10,12,17,18 J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988.

8. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 8 Bottom up Inference in undirected trees

9. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 9 Inference in undirected trees

10. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 10 Inference in undirected trees

11. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 11 Inference in undirected trees

12. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 12 Inference in undirected trees

13. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 13 Inference in polytrees

14. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 14 Inference in polytrees

15. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 15 Required Messages

16. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 16 Inference in polytrees

17. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 17 Inference in polytrees

18. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 18 Required Messages

19. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 19 Inference in polytrees

20. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 20 Inference in polytrees

21. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 21 Inference in polytrees: summary

22. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 22 What if cycles exist?

23. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 23 Ex: messages not valid

24. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 24 Inference

25. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 25 Inference: outline

26. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 26 Inference: moralization

27. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 27 Examples: assigning prob to clique potentials

28. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 28 Examples: assigning prob to clique potentials

29. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 29 Evidence

30. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 30 Goal calculation & Evidence

31. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 31 Example potentials

32. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 32 Goal

33. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 33 Potentials as marginals

34. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 34 Potentials don’t start as marginals

35. Lec 11: May 2nd, 2006EE512 - Graphical Models - J. BilmesPage 35 Potentials don’t start as marginals