Exponential varieties
Copyright policy )Exponential varieties
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.
- Freie Universität Berlin Germany
- Polish Academy of Learning Poland
- University of California, Berkeley United States
- Institute of Science and Technology Austria Austria
- Massachusetts Institute of Technology United States
Special varieties, convex optimization, Computational problems in statistics, hyperbolic polynomials, Mathematics - Statistics Theory, ML degree, Statistics Theory (math.ST), semidefinite programming, Convex sets in \(n\) dimensions (including convex hypersurfaces), Mathematics - Algebraic Geometry, exponential families, algebraic statistics, FOS: Mathematics, Statistical distribution theory, Algebraic Geometry (math.AG)
Special varieties, convex optimization, Computational problems in statistics, hyperbolic polynomials, Mathematics - Statistics Theory, ML degree, Statistics Theory (math.ST), semidefinite programming, Convex sets in \(n\) dimensions (including convex hypersurfaces), Mathematics - Algebraic Geometry, exponential families, algebraic statistics, FOS: Mathematics, Statistical distribution theory, Algebraic Geometry (math.AG)
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