All Questions
Tagged with wasserstein optimization
5
questions
0
votes
0
answers
21
views
how to solve for wasserstein duality easily in a special case when 2-Wasserstein inequality constraint is binding
I was going through this nice paper ” A Simple and General Duality Proof for
Wasserstein Distributionally Robust Optimization”, and one quick qu on applying Theorem 1 to my poject:
What if in my ...
- 61
0
votes
0
answers
23
views
Optimal Mass Distribution Minimizing Average 2-Wasserstein Distance to a Set of Mass Distributions
Given a fixed set of $n$ points in 2D (Earth Movers distance Prpblem), $P = \{p_1, p_2, ..., p_n\}$, I am trying to find the mass distribution $\bar{M}$ that minimizes the average 2-Wasserstein ...
- 770
0
votes
1
answer
181
views
Is there a meaning of distances for 0<p<1 for Wasserstein distance?
The wikipedia link for Wasserstein metric is defined for $p\in[1,\infty)$.
https://en.wikipedia.org/wiki/Wasserstein_metric Given some data the distance can be calculated using an optimization ...
- 3,138
0
votes
1
answer
197
views
Question on Kantorovich-Rubinstein Duality proof
I am currently working on understanding the Kantorovich-Rubinstein duality and Wassertein loss.
The following part of these class notes:
Collecting the terms algebraically we can rewrite the ...
4
votes
1
answer
136
views
Maximiser of $W_1(\mu, \nu)$ can be changed outside of $\text{conv}(\text{supp}(\mu) \cap \text{supp}(\nu))$ (under additional assumptions)
Let $(X, \| \cdot \|)$ be a reflexive Banach space and $\mathbb{P}_n$, $\mathbb{P}_r$ be measures on $X$.
Let the support of $\mathbb{P}_r$, $M := \text{supp}(\mathbb{P}_r)$ be a weakly compact set ...
- 4,878