Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
Sturmfels B, Uhler C. 2010. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. 62(4), 603–638.
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Sturmfels, Bernd;
Uhler, CarolineISTA 
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.
Publishing Year
Date Published
2010-08-01
Journal Title
Annals of the Institute of Statistical Mathematics
Publisher
Springer
Acknowledgement
B. Sturmfels is supported in part by NSF grants DMS-0456960 and DMS-0757236. C. Uhler is supported by an International Fulbright Science and Technology Fellowship.
Volume
62
Issue
4
Page
603 - 638
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Cite this
Sturmfels B, Uhler C. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. 2010;62(4):603-638. doi:10.1007/s10463-010-0295-4
Sturmfels, B., & Uhler, C. (2010). Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. Springer. https://doi.org/10.1007/s10463-010-0295-4
Sturmfels, Bernd, and Caroline Uhler. “Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry.” Annals of the Institute of Statistical Mathematics. Springer, 2010. https://doi.org/10.1007/s10463-010-0295-4.
B. Sturmfels and C. Uhler, “Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry,” Annals of the Institute of Statistical Mathematics, vol. 62, no. 4. Springer, pp. 603–638, 2010.
Sturmfels B, Uhler C. 2010. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Annals of the Institute of Statistical Mathematics. 62(4), 603–638.
Sturmfels, Bernd, and Caroline Uhler. “Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry.” Annals of the Institute of Statistical Mathematics, vol. 62, no. 4, Springer, 2010, pp. 603–38, doi:10.1007/s10463-010-0295-4.
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