Questions tagged [wasserstein]

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Wasserstein distance between Gaussian and the empirical distribution

Wasserstein distance between two gaussians has a well known closed form solution. Does the same hold for the distance between a Gaussian with a fixed variance(say 1) and the empirical data ...
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122 views

Prove the existence of a fixed point of a certain mapping of distributions

Let $\tilde{X}_0$ be some random variable on $\mathbb{R}^n$, with a strictly positive p.d.f.. Define: $$X_0:=(\operatorname{var}{\tilde{X}_0})^{-\frac{1}{2}}(\tilde{X}_0-\mathbb{E}\tilde{X}_0),$$ ...
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103 views

Relation Between Wasserstein Distance and Relative Entropy

Consider the Wasserstein metric of order one $W_1$ (aka the Earth Movers Distance). I would like to know whether it is possible to link $W_1$ and relative entropy and what this would mean intuitively. ...
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35 views

Computing Wassertein Distance

For two probability measures $\mu$ and $\nu$, the Wassertein Distance is defined as $$W_p (\mu , \nu) = \left[ \inf\limits_{\gamma \in \Gamma} |x-y|^p \, d\gamma (x,y) \right] ^{\frac{1}{p}} \, , $$ ...
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232 views

Distance or divergence for ordinal distribution

Measures like KL divergence can be symmetrized (into JS divergence). Bhattacharyya distance serves a similar function. Either is well-suited to both continuous distributions and discrete (e.g. ...
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30 views

Wasserstein distance / EMD of two sets of 2D weighted points?

I am trying to implement a 2D version of the EMD/Wasserstein Distance to measure the distance of sets of 2D weighted points. Let $A = \{a_{1}, a_{2}, ..., a_{m}\}$, be a weighted point set such that $...
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129 views

Earth Movers Distance and Maximum Mean Discrepency

By Kantorovich-Rubinstein duality the Earth Movers Distance (EMD)/Wasserstein Metric is equivalent to Maximum Mean Discrepancy (MMD) correct? See here for a more thorough explanation. Why then does ...
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30 views

Compare statistical distances of multiple distributions

I need a metric that not only gives me the statistical distance between two distributions, but that also is comparable to another distance between two completely different distributions, calculated ...
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44 views

What is the fastest and the most accurate calculation of Wasserstein distance?

It's concerned with the methodologies of Wasserstein distance calculation. There are some ways to calculate Wasserstein distance, such as Sinkhorn iteration aided method [1], Neural networks ...
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63 views

Advantages of Wasserstein barycenters

Which are the advantages of using Wasserstein distance when averaging many probability distribution estimates? How does uncertainty of each affects the computation of the barycenter? Does the ...
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198 views

Difference between the Wasserstein metric, mallows metric and Earth mover's distance

I'm really confused, is there a difference between the Wasserstein metric, mallows metric and Earth mover's distance? If yes What is it? Thank you