Exponential families and affine Grassmannians
Danuzia Nascimento Figueir\^edo, Hale Ayta\c{c}, Mathieu Molitor
TL;DR
This paper reveals a deep mathematical connection between minimal exponential families in statistics and affine Grassmannians, providing a new geometric perspective on statistical models.
Contribution
It establishes a one-to-one correspondence between exponential families and affine Grassmannians, linking statistical and geometric structures in a novel way.
Findings
Provides a geometric characterization of exponential families.
Links statistical models to affine Grassmannians.
Offers new tools for analyzing exponential families.
Abstract
We establish a one-to-one correspondence between the set of minimal exponential families of dimension n defined on a finite sample space {\Omega} and the affine Grassmannian associated to an appropriate vector space of functions.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Advanced Topics in Algebra · Mathematics and Applications