Lec 5: April 11th, 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 5 Slides April 11 th, 2006

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 2 Chordal graph theory Elimination and chordality Recognizing chordal graphs How to triangulate a graph (heuristics) Properties of conditional independence Markov properties on graphs Outline of Today’s Lecture

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 3 Books and Sources for Today Jordan: Chapters 17. Lauritzen, Chapters 1-3. Any good graph theory text.

Lec 5: April 11th, 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 L5: Tue, 4/11: chdl/elim, mcs, triang, ci props. 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

Lec 5: April 11th, 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) Check out CSE590AI this week (Weds, CSE609, 3:30-4:20) –Compiling Relational Bayesian Networks for Exact Inference, by Mark Chavira, Adnan Darwiche, and Manfred Jaeger –This is a “search” based method for inference of relational models, that pre-compiles such graph into logic equations. It has an implicit value-specific junction tree in it. We will be covering search based methods for inference in the upcoming weeks discussing what conditions are requried for them to help. 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

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 6 Summary of Last Time

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 7 Examples: decomposition tree and factorization

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 8 Graph, decomposition tree, and junction tree

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 9 How can we tell if G is chordal? Complete Set

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 10 How can we tell if G is chordal?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 11 How can we tell if G is chordal?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 12 How can we tell if G is chordal?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 13 How can we recognize chordal graphs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 14 Maximum Cardinality Search (MCS)

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 15 Maximum Cardinality Search (MCS)

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 16 How can we recognize chordal graphs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 17 How can we recognize chordal graphs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 18 MCS with Junction Tree B A C D EFG HI r.i.p. order:

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 19 Elimination and Bayesian Networks

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 20 Triangulation Heuristics

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 21 Triangulation Heuristics

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 22 Are all trees of maxcliques JTs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 23 Are all trees of maxcliques JTs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 24 Are all trees of maxcliques JTs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 25 Are all trees of maxcliques JTs?

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 26 Junction Trees -> Factorization

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 27 Properties of Conditional Independence

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 28 Properties of Conditional Independence

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 29 Properties of Conditional Independence

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 30 Properties of Conditional Independence

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 31 Properties of Conditional Independence

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 32 Properties of Conditional Independence

Lec 5: April 11th, 2006EE512 - Graphical Models - J. BilmesPage 33 Markov Properties of Graphs