Multivariate Gaussians,semidefinite matrix completion,and convex algebraic geometry |
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Authors: | Bernd Sturmfels Caroline Uhler |
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Institution: | (1) Department of Applied Mathematics of Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan |
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Abstract: | We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum
likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and
to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. These problems
at the interface of statistics and optimization are here examined from the perspective of convex algebraic geometry. |
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Keywords: | |
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