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I see that most of the regularization done involves an entropy term. Has there been any work done on other regularization methods? In particular, I'm wondering if anyone has done a regularization invo …

What would the optimal transport mapping between two sets with a common subset be? The problem I'm thinking about is the following: I'm in $\mathbb{C}^n$ and I have two distributions $\mu$ and $\nu$ l …

I'm reading the paper https://arxiv.org/pdf/1905.10812.pdf where strongly convex approximations to Brenier potentials are approximated. Let $\mathcal{E}$ be a partition of $\mathbb{R}^{d}$ and $ 0\leq …

I conjectured earlier that if $P$ and $Q$ were two probability measures, then we could show $$W^2(P,Q) = \min_{T} [d^2(P,T_{\#}P) + W^2(T_{\#}P,Q)]$$ where $W^2(P,Q)$ denotes the squared Wasserstein-2 …

I know there are concentration bounds on $W(\mu,\hat{\mu})$ where $\mu$ and $\hat{\mu}$ are true and empirical distributions respectively, but is there anything out there on $W(\mu,\nu)$ versus $W(\ha …