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Results tagged with wasserstein-distance
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user 64449
1
vote
Accepted
Distance between empirical measures and thickened version
The claim follows by a synchronous coupling: $X = x_I$ and $X^{\epsilon} = x_I + \sqrt{\epsilon} \sum_{j=1}^{\infty} \sqrt{\lambda_j} \rho_j e_j$ where $I \sim \operatorname{Uniform}(\{1, \dots, n \ …
- 6,045
2
votes
Accepted
Bounding $2$-Wasserstein distance and the $L^1$ distance
Referring to the proof of Prop 3.21 in Malrieu 2001, after the triangle inequality is applied twice, two of the terms are bounded via the upper bound $$
W_2(u_t,u_t^{(1,N)}) \vee W_2(\mu_{1,N},\bar{u} …
- 6,045
1
vote
Closed-form formula for Wasserstein distance between uniform discrete distribution and discr...
Here is a general upper/lower bound on the Wasserstein distance between $\mu$ and $\nu$ based on a maximal coupling with respect to their total variation distance: $$
(1/2) \min_{x_i \ne x_j} c(x_i, x …
- 6,045