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Graphical Models - EE512 Lecture 7 Overview and Important Dates (Spring 2006)

This document covers Lecture 7 of EE512 (Graphical Models) at the University of Washington, presented by Jeff A. Bilmes. Key topics include the factorization property on Markov Random Fields (MRFs), Möbius Inversion Lemma, and the Hammersley/Clifford theorem. Important announcements regarding office hours, upcoming reading materials, and project milestone due dates are provided. Students are encouraged to participate actively, report typographical errors, and submit their progress reports, abstracts, and final papers electronically.

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Graphical Models - EE512 Lecture 7 Overview and Important Dates (Spring 2006)

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  1. University of WashingtonDepartment of Electrical Engineering EE512 Spring, 2006 Graphical ModelsJeff A. Bilmes <bilmes@ee.washington.edu> Lecture 7 Slides April 18th, 2006 EE512 - Graphical Models - J. Bilmes

  2. Announcements • 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) • Möbius Inversion Lemma handout (to be on web site) • 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 • Reminder: take-home Midterm: May 5th-8th, you must work alone on this. EE512 - Graphical Models - J. Bilmes

  3. Class Road Map • 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: MST,CI axioms, Markov prps. • L7: Tues, 4/18: Mobius, HC-thm, (F)=(G) • 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 EE512 - Graphical Models - J. Bilmes

  4. Final Project Milestone Due Dates • L1: Tues, 3/28: • L2: Thur, 3/30: • L3: Tues, 4/4: • L4: Thur, 4/6: • L5: Tue, 4/11: • L6: Thur, 4/13: • L7: Tues, 4/18: Today • L8: Thur, 4/20: Team Lists, short abstracts I • L9: Tue, 4/25: • L10: Thur, 4/27: short abstracts II • L11: Tues, 5/2 • L12: Thur, 5/4: abstract II + progress • L13: Tues, 5/9 • L14: Thur, 5/11: 1 page progress report • L15: Tue, 5/16 • L16: Thur, 5/18: 1 page progress report • L17: Tues, 5/23 • L18: Thur, 5/25: 1 page progress report • L19: Tue, 5/30 • L20: Thur, 6/1: final presentations • L21: Tue, 6/6 4-page papers due (like a conference paper). • Team lists, abstracts, and progress reports must be turned in, in class and using paper (dead tree versions only). • Final reports must be turned in electronically in PDF (no other formats accepted). • Progress reports must report who did what so far!! EE512 - Graphical Models - J. Bilmes

  5. Summary of Last Time • when are trees of maxcliques JTs? • max/min spanning trees • conditional independence relations • logical axioms of conditional independence relations • axioms and positivity • independence and knowledge • independence and separation • completeness conjecture • Markov properties on MRFs, (G),(L),(P) EE512 - Graphical Models - J. Bilmes

  6. Outline of Today’s Lecture • Factorization property on MRF, (F) • When (F) = (G) = (L) = (P) • inclusion-exclusion • Möbius Inversion lemma • Hammersley/Clifford theorem, when (G) => (F) • Factorization and decomposability • Factorization and junction tree • Directed factorization (DF), and (G) • Markov blanket • Bayesian networks and moralization EE512 - Graphical Models - J. Bilmes

  7. Books and Sources for Today • M. Jordan: Chapters 17. • S. Lauritzen, 1996. Chapters 1-3. • J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988. • Any good graph theory text. EE512 - Graphical Models - J. Bilmes

  8. Properties of Markov Properties EE512 - Graphical Models - J. Bilmes

  9. Markov Properties of Graphs EE512 - Graphical Models - J. Bilmes

  10. Properties of Markov Properties EE512 - Graphical Models - J. Bilmes

  11. (F) Factorization Property EE512 - Graphical Models - J. Bilmes

  12. The alphabetical theorem: (F)  (G)  (L)  (P) EE512 - Graphical Models - J. Bilmes

  13. The alphabetical theorem: (F)  (G)  (L)  (P) EE512 - Graphical Models - J. Bilmes

  14. The equivalence theorem: (F)  (G)  (L)  (P) EE512 - Graphical Models - J. Bilmes

  15. Inclusion-Exclusion EE512 - Graphical Models - J. Bilmes

  16. Möbius Inversion Lemma EE512 - Graphical Models - J. Bilmes

  17. Möbius Inversion Lemma EE512 - Graphical Models - J. Bilmes

  18. Hammersley/Clifford EE512 - Graphical Models - J. Bilmes

  19. Hammersley/Clifford EE512 - Graphical Models - J. Bilmes

  20. Hammersley/Clifford EE512 - Graphical Models - J. Bilmes

  21. Hammersley/Clifford EE512 - Graphical Models - J. Bilmes

  22. Hammersley/Clifford EE512 - Graphical Models - J. Bilmes

  23. Hammersley/Clifford by pairwise Markov property since we have unity ratios pairwise Markov property and chain rule EE512 - Graphical Models - J. Bilmes

  24. Hammersley/Clifford EE512 - Graphical Models - J. Bilmes

  25. Factorization and decomposability EE512 - Graphical Models - J. Bilmes

  26. Factorization and decomposability EE512 - Graphical Models - J. Bilmes

  27. (G), factorization, and decomposability EE512 - Graphical Models - J. Bilmes

  28. Recursive application + positivity EE512 - Graphical Models - J. Bilmes

  29. Recursive application + positivity EE512 - Graphical Models - J. Bilmes

  30. (DF) EE512 - Graphical Models - J. Bilmes

  31. (DF) and (G) EE512 - Graphical Models - J. Bilmes

  32. Markov Blanket EE512 - Graphical Models - J. Bilmes

  33. Recall from Lecture 3: Ancestral Sets EE512 - Graphical Models - J. Bilmes

  34. Preservation of (DF) in ancestral sets EE512 - Graphical Models - J. Bilmes

  35. Example (DF) – (G) EE512 - Graphical Models - J. Bilmes

  36. Example (DF) – (G) EE512 - Graphical Models - J. Bilmes

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