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Author Drton, Mathias ♦ Yu, Josephine
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2010-01-18
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics ♦ Probabilities & applied mathematics
Subject Keyword Mathematics - Algebraic Geometry ♦ Mathematics - Optimization and Control ♦ Mathematics - Statistics Theory ♦ 62H05 ♦ 15A99 ♦ 13P25 ♦ 14P10 ♦ math ♦ stat
Abstract We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a polynomial map associated with a simplicial complex supported on cliques of the graph. The images of the maps are convex cones, and the maps can only be surjective onto the cone of zero-constrained positive semidefinite matrices when the associated graph is chordal and the simplicial complex is the clique complex of the graph. Our main result gives a semi-algebraic description of the image of the parametrizations for chordless cycles. The work is motivated by the fact that the considered maps correspond to Gaussian statistical models with hidden variables.
Description Reference: SIAM J. Matrix Anal. Appl. 31 (2010), no. 5, 2665--2680
Educational Use Research
Learning Resource Type Article
Page Count 16


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