Post on 19-Dec-2015
Lec 5: April 11th, 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 5 Slides
April 11th, 2006
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• Chordal graph theory• Elimination and chordality• Recognizing chordal graphs• How to triangulate a graph (heuristics)• Properties of conditional independence• Markov properties on graphs
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• L5: Tue, 4/11: chdl/elim, mcs, triang, ci props.• 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)• Check out CSE590AI this week (Weds, CSE609, 3:30-4:20)
– Compiling Relational Bayesian Networks for Exact Inference, by Mark Chavira, Adnan Darwiche, and Manfred Jaeger
– This is a “search” based method for inference of relational models, that pre-compiles such graph into logic equations. It has an implicit value-specific junction tree in it. We will be covering search based methods for inference in the upcoming weeks discussing what conditions are requried for them to help.
• 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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Summary of Last Time
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Examples: decomposition tree and factorization
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Graph, decomposition tree, and junction tree
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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 tell if G is chordal?
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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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Maximum Cardinality Search (MCS)
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Maximum Cardinality Search (MCS)
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How can we recognize chordal graphs?
1 2
3 41
2
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78
9
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How can we recognize chordal graphs?
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MCS with Junction Tree
B
A
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E F G
H I9 8
7 6
3
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r.i.p. order:
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Elimination and Bayesian Networks
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Triangulation Heuristics
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Triangulation Heuristics
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Are all trees of maxcliques JTs?
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Are all trees of maxcliques JTs?
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Are all trees of maxcliques JTs?
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Are all trees of maxcliques JTs?
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Junction Trees -> Factorization
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Properties of Conditional Independence
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Properties of Conditional Independence
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Properties of Conditional Independence
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Properties of Conditional Independence
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Properties of Conditional Independence
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Properties of Conditional Independence
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Markov Properties of Graphs