Lec 4: April 6th, 2006 EE512 - Graphical Models - J. Bilmes Page 1

University of WashingtonDepartment of Electrical Engineering

EE512 Spring, 2006 Graphical Models

Jeff A. Bilmes <bilmes@ee.washington.edu>Jeff A. Bilmes <bilmes@ee.washington.edu>

Lecture 4 Slides

April 6th, 2006

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• Start computing probabilities• elimination algorithm• Beginning of chordal graph theory

Outline of Today’s Lecture

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Books and Sources for Today

• Jordan: Chapters 17.• Lauritzen, 1986. Chapters 1-3.• Any good graph theory text.

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• 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

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• 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

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Junction Tree

A,B,C,D

B,C,D,F

B,E,F F,D,G

E,F,H F,G,I

C4

C2

C3

C5

C1C6

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Junction Tree & r.i.p.

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Junction Tree & r.i.p.

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Decomposability

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Equivalent conditions for G

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Minimal Separators

Minimal (B,E)-Separator Non-minimal (B,E)-Separator

Minimal (B,E)-Separator

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Chordality implies min-seps are complete

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(,) seps complete imply decomposability

AB

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(,) seps complete imply decomposability

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Examples: Decomposable/Chordal?

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Aside: Conditional Independence & Factorization

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Relation to Junction Trees.

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Junction Trees and Decomposability

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Junction Trees and Decomposability

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Junction Trees and Decomposability

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Junction Trees and Decomposability

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Junction Trees and Decomposability

newlink

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Junction Trees and Decomposability

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Junction Trees and Separability

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B

A

C

D

E F G

H I

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

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JTs and well-ordered cliques

1

2 3

4

51

2

3

4

5

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How can we tell if G is chordal?

CompleteSet

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How can we tell if G is chordal?

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How can we recognize chordal graphs?

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How can we recognize chordal graphs?

1 2

3 41

2

3

4

5

6

78

9

10

11