Gaussian Distributions on the Space of Symmetric Positive Definite Matrices from Souriau's Gibbs State for Siegel Domains by Coadjoint Orbit and Moment Map

被引：1

作者：

Barbaresco, Frederic ^{[1
]}

机构：

[1] THALES Land & Air Syst, Limours, France

来源：

GEOMETRIC SCIENCE OF INFORMATION (GSI 2021) | 2021年 / 12829卷

关键词：

Symmetric positive definite matrices; Lie groups thermodynamics; Symplectic geometry; Maximum entropy; Exponential density family; DISCRETE-SERIES; CONTRACTION;

D O I：

10.1007/978-3-030-80209-7_28

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We will introduce Gaussian distribution on the space of Symmetric Positive Definite (SPD) matrices, through Souriau's covariant Gibbs density by considering this space as the pure imaginary axis of the homogeneous Siegel upper half space where Sp (2n,R)/U(n) acts transitively. Gauss density of SPD matrices is computed through Souriau's moment map and coadjoint orbits. We will illustrate the model first for Poincare unit disk, then Siegel unit disk and finally upper half space. For this example, we deduce Gauss density for SPD matrices.

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页码：245 / 255

页数：11