Exponential varieties

M. Michałek, B. Sturmfels, C. Uhler, P. Zwiernik, Proceedings of the London Mathematical Society 112 (2016) 27–56.


Journal Article | Published | English
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Abstract
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.
Publishing Year
Date Published
2016-01-07
Journal Title
Proceedings of the London Mathematical Society
Volume
112
Issue
1
Page
27 - 56
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Cite this

Michałek M, Sturmfels B, Uhler C, Zwiernik P. Exponential varieties. Proceedings of the London Mathematical Society. 2016;112(1):27-56. doi:10.1112/plms/pdv066
Michałek, M., Sturmfels, B., Uhler, C., & Zwiernik, P. (2016). Exponential varieties. Proceedings of the London Mathematical Society, 112(1), 27–56. https://doi.org/10.1112/plms/pdv066
Michałek, Mateusz, Bernd Sturmfels, Caroline Uhler, and Piotr Zwiernik. “Exponential Varieties.” Proceedings of the London Mathematical Society 112, no. 1 (2016): 27–56. https://doi.org/10.1112/plms/pdv066.
M. Michałek, B. Sturmfels, C. Uhler, and P. Zwiernik, “Exponential varieties,” Proceedings of the London Mathematical Society, vol. 112, no. 1, pp. 27–56, 2016.
Michałek M, Sturmfels B, Uhler C, Zwiernik P. 2016. Exponential varieties. Proceedings of the London Mathematical Society. 112(1), 27–56.
Michałek, Mateusz, et al. “Exponential Varieties.” Proceedings of the London Mathematical Society, vol. 112, no. 1, Oxford University Press, 2016, pp. 27–56, doi:10.1112/plms/pdv066.

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