Lec 6: April 13th, 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 6 Slides April 13 th, 2006

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 2 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) –Möbius Inversion Lemma handout (to be on web site) 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

Lec 6: April 13th, 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 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 6: April 13th, 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: Today 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 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!!

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 5 updated decomposition tree Eliminatable Triangulated simplicial nodes (like a leaf node) chordal graphs have a perfect elimination ordering recognizing chordal graphs: MCS MCS also gives cliques perfect DAGs Triangulation Heuristics (min-fill, min-degree, min-weight) MST on graph of cliques Summary of last time

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 6 when are trees of maxcliques JTs? max/min spanning trees conditional independence relations logical axioms of conditional independence relations axioms and positivity independence and knowledge independence and separation completeness conjecture Markov properties on MRFs, (G),(L),(P) Factorization property on MRF, (F) Outline of Today’s Lecture

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 7 Books and Sources for Today M. Jordan: Chapters 17. S. Lauritzen, Chapters 1-3. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Any good graph theory text.

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 8 Are all trees of maxcliques JTs?

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 9 Are all trees of maxcliques JTs?

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 10 Are all trees of maxcliques JTs?

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 11 Are all trees of maxcliques JTs?

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 12 Junction Trees -> Factorization

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 13 The Conditional Independence Relation

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 14 The Conditional Independence Relation

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 15 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 16 Properties of Conditional Independence C2: C3: C4: C5: Pearl’s eggs:

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 17 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 18 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 19 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 20 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 21 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 22 Properties of Conditional Independence

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 23 Completeness Conjecture -- True??

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 24 Markov Properties of Graphs

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 25 (G) Global Markov Property

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 26 (L) Local Markov Property

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 27 (P) Pairwise Markov Property

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 28 Properties of Markov Properties

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 29 Properties of Markov Properties

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 30 Block Independence Lemma

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 31 (F) Factorization Property

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 32 The alphabetical theorem: (F)=>(G)=>(L)=>(P)

Lec 6: April 13th, 2006EE512 - Graphical Models - J. BilmesPage 33 The alphabetical theorem: (F)=>(G)=>(L)=>(P)