Lec 3: April 4th, 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 3 Slides

April 4th, 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 2 and 3• Lauritzen, 1986.• Any 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• 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 in Jordan’s book (take a look at chapters 17)

• Please audit if you are attending class– it will help to get us a bigger room.– If you need an add code, just send me email.

• 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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Computing Probabilities

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Computing Probabilities

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Computing Probabilities

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Note on sums and evidence

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Graph Algorithm Equivalent: Elimination

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B

A

C

D

E F G

H I1 2

3 4

7

5

6

8

9

Order the Nodes

Eliminate the nodesin order

Elimination Example: different graph

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Result of Elimination

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Elimination

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Elimination

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Elimination & Directed Graphs

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Immoral Elimination

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Moralization

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Variable Elimination Algorithm

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Summary

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More Graph Terminology/Notation

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Graph Terminology/Notation

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Graph Terminology/Notation

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Graph Terminology/Notation

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Ancestral examples

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Separators

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Tree/Forest

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Triangulated/Chordal

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Triangulated/Chordal

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Triangulated/Chordal

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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

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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