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 <[email protected]>Jeff A. Bilmes <[email protected]>
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