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Tagged with wasserstein geodesic
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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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Are linear interpolation curves on Wasserstein spaces absolutely continuous?
Let $\mathcal{P}_2$ the space of absolutely continuous probability measures on $\mathbb{R}^d$ with finite second moment equipped with the $2$-Wasserstein metric.
Fix $\mu_0, \mu_1 \in \mathcal{P}_2.$
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Density associated with Wasserstein geodesic
Suppose we have two absolutely continuous distribution functions $F$ and $G$ with densities $f$ and $g,$ respectively. Assuming a quadratic cost function, the Wasserstein geodesic at time $t$ is the ...
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