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Tagged with wasserstein normal-distribution
3
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Intuition of Wasserstein and Information geometry geodesics
Two important geometries that can be given to the space of multivariate Gaussian distributions are given by the Wasserstein distance and by the Fisher metric (ie. Information geometry).
Although there'...
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Relationship between optimal transport and gaussian kernel
Let's say P and Q be two different dirac delta probability measure, and suppose that $K_\sigma$ is a gaussian kernel. Let D be the wasserstein-2 distance.
It is known that $D(P,Q)=D(K_\sigma *P, K_\...
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Optimal Transport between two Gaussians
Consider the optimal transport map $T$ between $N(\mu_0,\Sigma_0)$ and $N(\mu_1,\Sigma_1)$. I believed that the optimal transport was given by:
$$ T(x) = \mu_1 + \Sigma_1^{1/2} \Sigma_0^{-1/2}(x-\mu_0)...
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