Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
By Bernd Sturmfels, Caroline Uhler. 2009
96 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/06864e8493eef65ce15ca9a60e0e91cad42747f8
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Raman Sanyal
- Frank Sottile
- Bernd Sturmfels
- Eric Katz
- Martyn Marshall
- Michael Joswig
- Jenia Tevelev
- Adam Van Tuyl
In Discrete Mathematics and Combinatorics
In Statistics and Probability
Citations in the corpus
- Orbitopes (2009, methodology): “are consistent with those used in the paper [35] where these cones consist of concentration matrices and sufficient statistics of a certain Gaussian model.”