article
Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
published
Bernd
Sturmfels
author
Caroline
Uhler
author 49ADD78E-F248-11E8-B48F-1D18A9856A870000-0002-7008-0216
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.
Springer2010
Annals of the Institute of Statistical Mathematics10.1007/s10463-010-0295-4
624603 - 638
yes
Sturmfels, Bernd, and Caroline Uhler. “Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry.” <i>Annals of the Institute of Statistical Mathematics</i>, vol. 62, no. 4, Springer, 2010, pp. 603–38, doi:<a href="https://doi.org/10.1007/s10463-010-0295-4">10.1007/s10463-010-0295-4</a>.
B. Sturmfels and C. Uhler, “Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry,” <i>Annals of the Institute of Statistical Mathematics</i>, vol. 62, no. 4. Springer, pp. 603–638, 2010.
Sturmfels, B., & Uhler, C. (2010). Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. <i>Annals of the Institute of Statistical Mathematics</i>. Springer. <a href="https://doi.org/10.1007/s10463-010-0295-4">https://doi.org/10.1007/s10463-010-0295-4</a>
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 B, Uhler C. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. <i>Annals of the Institute of Statistical Mathematics</i>. 2010;62(4):603-638. doi:<a href="https://doi.org/10.1007/s10463-010-0295-4">10.1007/s10463-010-0295-4</a>
B. Sturmfels, C. Uhler, Annals of the Institute of Statistical Mathematics 62 (2010) 603–638.
Sturmfels, Bernd, and Caroline Uhler. “Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry.” <i>Annals of the Institute of Statistical Mathematics</i>. Springer, 2010. <a href="https://doi.org/10.1007/s10463-010-0295-4">https://doi.org/10.1007/s10463-010-0295-4</a>.
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