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Information Geometry for Wasserstein KL Divergence of Gaussian Measures on $\mathbb{R}^n$
We study the Wasserstein Kullback--Leibler divergence (WKL divergence) on the manifold of nondegenerate Gaussian measures over $\mathbb R^n$. In the canonical-divergence construction, the Fisher--Rao metric recovers forward KL along intrinsic mixture geodesics and reverse KL along geodesics of the c
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