Geodesics of multivariate normal distributions and a Toda lattice type Lax pair
Differential Geometry
2023-07-12 v3 Dynamical Systems
Abstract
We study geodesics of multivariate normal distributions with respect to the Fisher metric. First it will be shown that a computational formula for geodesics can be understood using the block Cholesky decomposition and a natural Riemannian submersion. Next a mid point algorithm for geodesics will be obtained. And finally a new Toda lattice type Lax pair will be derived from the geodesic and the block Cholesky decomposition.
Keywords
Cite
@article{arxiv.2304.12575,
title = {Geodesics of multivariate normal distributions and a Toda lattice type Lax pair},
author = {Shimpei Kobayashi},
journal= {arXiv preprint arXiv:2304.12575},
year = {2023}
}