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Activity Number:
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201
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Type:
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Topic Contributed
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Date/Time:
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Monday, August 3, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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IMS
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| Abstract - #303727 |
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Title:
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Trek Separation for Gaussian Graphical Models
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Author(s):
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Seth Sullivant*+
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Companies:
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North Carolina State University
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Address:
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, , ,
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Keywords:
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Graphical Model ; Linear Model ; Algebraic Statistics ; Polynomial
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Abstract:
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Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank in directed and undirected graphical models. Our new trek separation criterion generalizes the familiar d-separation criterion. Proofs are based on the trek rule, the resulting matrix factorizations, and classical theorems of algebraic combinatorics on the expansions of determinants of path polynomials.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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