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Unconditional Finiteness of the Number of Critical Points of Gaussian Mixture Densities
Abstract
By slightly adapting Wang's recent important argument for the homoscedastic setting, we prove that every finite heteroscedastic Gaussian mixture has only finitely many critical points, and, consequently, only finitely many modes.
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BibTeX
@misc{okuno2026unconditional,
title = {{Unconditional Finiteness of the Number of Critical Points of Gaussian Mixture Densities}},
author = {Akifumi Okuno},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30334},
eprint = {2608.30334},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30334},
}
RIS
TY - UNPB
TI - Unconditional Finiteness of the Number of Critical Points of Gaussian Mixture Densities
AU - Akifumi Okuno
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30334
UR - https://arxiv.org/abs/2608.30334
AB - By slightly adapting Wang's recent important argument for the homoscedastic setting, we prove that every finite heteroscedastic Gaussian mixture has only finitely many critical points, and, consequently, only finitely many modes.
ER -