Exponential varieties
Name
1412.6185.pdf
Description
Accepted version
Size
1.35 MB
Format
Adobe PDF
Checksum (MD5)
48b15f11afd0e55e24126ba3b32a5614
Author(s)
Michałek, Mateusz
Sturmfels, Bernd
Uhler, Caroline
Zwiernik, Piotr
Date Issued
2016
Journal
Proceedings of the London Mathematical Society
Publisher
Wiley
Citation
Michalek, Mateusz, et al. "Exponential Varieties." Proceedings of the London Mathematical Society 112 (2016): 27-56.
Version
Author's final manuscript
Abstract
© 2016 London Mathematical Society. Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1112/PLMS/PDV066
