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Wasserstein KL-Divergence for Gaussian Distributions
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DOI：10.1007/978-3-032-03921-7_10.png)
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Abstract
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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.
Keywords:
Wasserstein geometry
Kullback-Leibler divergence
Gaussian distributions
Ottometric
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