1. Lec 9: April 25th, 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 9 Slides April 25 th, 2006

2. Lec 9: April 25th, 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 -8 th, you must work alone on this. Announcements

3. Lec 9: April 25th, 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 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

4. Lec 9: April 25th, 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: today L10: Thur, 4/27: short abstracts II L11: Tues, 5/2 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 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 5 d-Separation, (DL), (DO), and equivalence of all Markov properties on BNs. Phylogenetic Trees and Chordal Models Mixture Models Hidden Markov Models (HMMs) Forward (  ) recursion and elimination Summary of Last Time

6. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 6 What queries to we want from an HMM? Forward (  ) recursion and elimination Backwards (  ) recursion and elimination Why do we want these queries anyway? More on inference in HMMs Inference on chains Start of inference on trees. Outline of Today’s Lecture

7. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 7 Books and Sources for Today M. Jordan: Chapters 4,10,12,17,18 “What HMMs can do” handout on web.

8. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 8 HMMs and Bayesian Networks

9. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 9 Goals for HMMs

10. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 10 Learning HMMs with EM, what queries are used?

11. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 11 Learning HMMs with Gradient Descent, what probabilistic queries are needed?

12. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 12 Learning HMMs with Gradient Descent, what probabilistic queries are needed?

13. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 13 Learning HMMs with Gradient Descent, what probabilistic queries are needed?

14. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 14 HMMs, elimination orders, and forward recursion

15. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 15 HMMs, elimination orders, and forward recursion

16. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 16 What does the forward computation mean

17. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 17 HMMs, elimination orders, and backward recursion

18. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 18 HMMs, elimination orders, and backward recursion

19. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 19 What does the backward computation mean

20. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 20 Forward/Backward Elimination

21. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 21 Clique posteriors

22. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 22 Clique posteriors

23. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 23 HMM message passing

24. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 24 HMM message passing 1 2 3 4 1 2 3 4

25. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 25 HMM message passing

26. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 26 HMM message passing

27. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 27 Slightly different HMM junction tree

28. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 28 HMM message passing 1 2 3 4 1 2 3 4

29. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 29 HMM message passing

30. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 30   recursion

31. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 31 Towards More General Inference

32. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 32 Towards More General Inference

33. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 33 Towards More General Inference

34. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 34 Towards More General Inference

35. Lec 9: April 25th, 2006EE512 - Graphical Models - J. BilmesPage 35 Inference in undirected trees