Wasserstein KL-divergence for Gaussian distributions

• URL: http://arxiv.org/abs/2503.24022v1
• Date: Mon, 31 Mar 2025 12:49:01 GMT
• Title: Wasserstein KL-divergence for Gaussian distributions
• Abstract summary: We show that this version is consistent with the geometry of the sample space $Bbb Rn$.<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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 ${\Bbb R}^n$. 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.

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