The Jacobian and Hessian of the Kullback-Leibler Divergence between Multivariate Gaussian Distributions (Technical Report)
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916817520295936 |
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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 |