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Lec 2: March 30th, 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 2 Slides
March 30th, 2006
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 2
• d-separation, 3 canonical BNs, Bayes ball• Undirected Models• Start computing probabilities
Outline of Today’s Lecture
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 3
Books and Sources for Today
• Jordan: Chapters 1 and 2• Derin 1989 (Markov Random Fields)• Lauritzen, 1986.• Any graph theory text.
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 4
• L1: Tues, 3/28: Overview, GMs, Intro BNs.• L2: Thur, 3/30: semantics of BNs + UGMs• L3: Tues, 4/4• 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
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 6
• READING: Chapter 1,2 in Jordan’s book (pick up book from basement of communications copy center).
• Syllabus handout• If you have not signed up before:
– List handout: name, department, and email– List handout: regular makeup slot, and discussion section
• Reminder: course web page: http://ssli.ee.washington.edu/ee512
• 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 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 10
Pictorial d-separation: blocked/unblocked paths
Blocked Paths Unblocked Paths
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 11
• Three 3-node examples of BNs and their conditional independence statements.
V1
V2 V3
2 3 1|V V V
V1
V2 V3
2 3V V2 3V V
2 3 1|V V V
V1
V2 V3
2 3 1|V V V
2 3V V
Three Canonical Cases
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 15
SUVsGreenhouse
GassesGlobal
Warming
LungCancer
SmokingBad
Breath
Genetics Cancer Smoking
Examples of the three cases
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 17
Ex: What are some conditional independences?
D. PooleM. Jordan
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Happy Families
MRFs
BNs
Decomposable models
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Markov Random Fields->Graph Theory
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Markov Random Fields: interaction
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Markov Random Fields: Image Processing
Derin, 1989
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 34
Graph Algorithm Equivalent: Elimination
Lec 2: March 30th, 2006 EE512 - Graphical Models - J. Bilmes Page 35
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