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Dually flat structure of von Mises-Fisher distributions
Abstract
The von Mises--Fisher (vMF) distribution is the natural exponential family analogue of the normal distribution on the unit hypersphere. We bring together previous results of its dually flat structure and establish new results on the information geometry of the family of vMF distributions. In particular, we characterize the exponential and mixture autoparallel submanifolds, and give the classification of doubly autoparallel submanifolds. Furthermore, we derive explicit formulas for the unique minimizers of the Kullback-Leibler divergence on these submanifolds and establish the corresponding projection theorems.
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BibTeX
@misc{najafi2026dually,
title = {{Dually flat structure of von Mises-Fisher distributions}},
author = {Behzad Najafi and Morteza Sharifi-Najjar and Ryu Ueno},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39249},
eprint = {2610.39249},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39249},
}
RIS
TY - UNPB
TI - Dually flat structure of von Mises-Fisher distributions
AU - Behzad Najafi
AU - Morteza Sharifi-Najjar
AU - Ryu Ueno
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39249
UR - https://arxiv.org/abs/2610.39249
AB - The von Mises--Fisher (vMF) distribution is the natural exponential family analogue of the normal distribution on the unit hypersphere. We bring together previous results of its dually flat structure and establish new results on the information geometry of the family of vMF distributions. In particular, we characterize the exponential and mixture autoparallel submanifolds, and give the classification of doubly autoparallel submanifolds. Furthermore, we derive explicit formulas for the unique minimizers of the Kullback-Leibler divergence on these submanifolds and establish the corresponding projection theorems.
ER -