Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 1 Jeff A. Bilmes University of Washington Department of Electrical Engineering EE512 Spring,

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Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 1 Jeff A. Bilmes University of Washington Department of Electrical Engineering EE512 Spring, 2006 Graphical Models Jeff A. Bilmes Lecture 16 Slides May 25 th, 2006

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 2 READING: –M. Jordan: Chapters 13,14,15 (on Gaussians and Kalman) 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 No more homework this quarter, concentrate on final projects!! Makeup class, please fill out form passed out today. Announcements

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 3 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: phylogenetic trees, HMMs L9: Tue, 4/25: HMMs, inference on trees L10: Thur, 4/27: Inference on trees, start poly L11: Tues, 5/2: polytrees, start JT inference L12: Thur, 5/4: Inference in JTs Tues, 5/9: away Thur, 5/11: away L13: Tue, 5/16: JT, GDL, Shenoy-Schafer L14: Thur, 5/18: GDL, Search, Gaussians I L15: Mon, 5/22: laptop crash  L16: Tues, 5/23: search, Gaussians I L17: Thur, 5/25: Gaussians Mon, 5/29: Holiday L18: Tue, 5/30 L19: Thur, 6/1: final presentations Class Road Map

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 4 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: 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 L--: Tues, 5/9 L--: Thur, 5/11: 1 page progress report L13: Tue, 5/16: L14: Thur, 5/18: 1 page progress report L15: Mon, 5/22: 6-8pm L16: Tues, 5/23 L17: Thur, 5/25: 1 page progress report L18: Tue, 5/30 L19: Thur, 6/1: final presentations L20: Tue, 6/6 4-page papers due (like a conference paper), Only.pdf versions accepted. Final Project Milestone Due Dates 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). No need to repeat what was on previous progress reports/abstracts, I have those available to refer to. Progress reports must report who did what so far!!

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 5 other forms of exact probabilistic inference inference (cut- set conditioning, recursive conditioning, search and cache-based schemes, comparisons with SAT/CSP). Start Gaussian Graphical Models Summary of Last Time

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 6 Gaussian Graphical Models Outline of Today’s Lecture

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 7 Books and Sources for Today Jordan chapters Mardia, Multivariate Analysis Anderson, Multivariate Analysis

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 8 Gaussians

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 9 Gaussians Contours 

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 10 Properties

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 11 Why we care

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 12 Partitioned Gaussian

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 13 Gaussian Marginal Independence

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 14 Partitioned Matrices

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 15 Shur Complement

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 16 Conditional Gaussian

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 17 Conditional Gaussian

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 18 Conditional Gaussian Parameterization

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 19 Conditional Gaussian Parameterization

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 20 Conditional Gaussian Parameterization

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 21 Gaussians and MRFs

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 22 Gaussians and Bayesian Networks

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 23 Gaussians and Bayesian Networks

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 24 Gaussians and Bayesian Networks

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 25 Gaussians and Bayesian Networks

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 26 Cholesky Factorization

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 27 Cholesky Factorization and regression coefficients

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 28 Gaussians and Bayesian Networks

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 29 Cholesky Factorization and regression coefficients

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 30 Inference in Gaussian Graphical Models

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 31 Kalman Model

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 32 Kalman Model

Lec 16: May 25th, 2006EE512 - Graphical Models - J. BilmesPage 33 Kalman Model