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arXiv · 2304.12575

Geodesics of multivariate normal distributions and a Toda lattice type Lax pair

Shimpei Kobayashi
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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.

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Shimpei Kobayashi. 2023-04-25. Geodesics of multivariate normal distributions and a Toda lattice type Lax pair. https://arxiv.org/abs/2304.12575

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