Exponential Varieties
Algebraic Geometry
2017-05-17 v2 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1412.6185,
title = {Exponential Varieties},
author = {Mateusz Michałek and Bernd Sturmfels and Caroline Uhler and Piotr Zwiernik},
journal= {arXiv preprint arXiv:1412.6185},
year = {2017}
}