The Jacobian and Hessian of the Kullback-Leibler Divergence between Multivariate Gaussian Distributions (Technical Report)

Fuente: arXiv
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Autore principale: Maroñas, Juan
Natura: Preprint
Pubblicazione: 2025
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author Maroñas, Juan
author_facet Maroñas, Juan
contents This document shows how to obtain the Jacobian and Hessian matrices of the Kullback-Leibler divergence between two multivariate Gaussian distributions, using the first and second-order differentials. The presented derivations are based on the theory presented by \cite{magnus99}. I've also got great inspiration from some of the derivations in \cite{minka}. Since I pretend to be at most didactic, the document is split into a summary of results and detailed derivations on each of the elements involved, with specific references to the tricks used in the derivations, and to many of the underlying concepts.
format Preprint
id arxiv_https___arxiv_org_abs_2506_23996
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Jacobian and Hessian of the Kullback-Leibler Divergence between Multivariate Gaussian Distributions (Technical Report)
Maroñas, Juan
Machine Learning
Optimization and Control
This document shows how to obtain the Jacobian and Hessian matrices of the Kullback-Leibler divergence between two multivariate Gaussian distributions, using the first and second-order differentials. The presented derivations are based on the theory presented by \cite{magnus99}. I've also got great inspiration from some of the derivations in \cite{minka}. Since I pretend to be at most didactic, the document is split into a summary of results and detailed derivations on each of the elements involved, with specific references to the tricks used in the derivations, and to many of the underlying concepts.
title The Jacobian and Hessian of the Kullback-Leibler Divergence between Multivariate Gaussian Distributions (Technical Report)
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2506.23996