All Questions
Tagged with wasserstein metric-spaces
7
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Can a finite Wasserstein metric on Euclidean support be embedded in a Euclidean space?
Thanks for everyone's help with understanding finite metric embeddings in Euclidean space. I have a follow-up question.
Say we have the Wasserstein distance between $n$ distributions in Euclidean ...
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Does this relation between Wasserstein distances hold: $W_1(\mu,\nu)\leq W_2(\mu,\nu) \leq ... \leq W_\infty(\mu,\nu)$?
I stumbled upon this interesting statement in this paper:
"One interesting observation is that the Wasserstein ambiguity
set with the Wasserstein order p = 2 is less conservative, because the 2-...
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1
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Quantitative bound on Wasserstein distances by $L^p$ distances?
Given two smooth probability densities $f$ and $g$ on $\mathbb{R}$ (or $\mathbb{R}_+$) with finite $p$-th moments. I am wondering if anyone is aware of some explicit upper bound on $W_p(f,g)$ in terms ...
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Sufficient Conditions on Metric Space for Wasserstein Distance?
For a metric space $M$ and the Wasserstein 1-distance $W_1$, what qualifying assumptions do we need for $M$? I have seen we only need $M$ be compact, $M$ be a Polish space, or $M$ be a Radon space. ...
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Derive the $d=1$ form of the Wasserstein distance
QUESTION
Given
How to pass from the general definition of the Wasserstein distance (let's call it Equation (1)):
to the closed forms with d=1, here below (let's call them Equation (2) and Equation(3)...
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Wasserstein distance of convolution of measures
Let $\mu_1, \mu_2,\nu_1,\nu_2$ be measures on $\mathbb{R}^d$. It is well known that the $p$-Wasserstein distance satisfies
$$\mathcal{W}_p(\nu_1 *\mu_1, \nu_1 *\mu_2) = \mathcal{W}_p(\mu_1,\mu_2),$$
...
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Covering with sets of negligible boundary
I am studying causality theory in Lorentzian length spaces, and I have a question about geometric measure theory in general (it will help me with a proof I am trying to finish):
Suppose we have a ...
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