Wasserstein KL-divergence for Gaussian distributions
Publikationstyp
Conference Paper
Date Issued
2025-10
Sprache
English
First published in
Number in series
16034
Start Page
91
End Page
101
Citation
7th International Conference on Geometric Science of Information, GSI 2025
Contribution to Conference
Scopus ID
Publisher
Springer
ISBN of container
978-3-032-03921-7
978-3-032-03920-0
We introduce a new version of the KL-divergence for Gaussian distributions which is based on Wasserstein geometry and referred to as WKL-divergence. We show that this version is consistent with the geometry of the sample space {R}^n. In particular, we can evaluate the WKL-divergence of the Dirac measures concentrated in two points which turns out to be proportional to the squared distance between these points.
Subjects
Wasserstein geometry
Kullback-Leibler divergence
Gaussian distributions
Otto metric
DDC Class
005.7: Data