Questions tagged [wasserstein]

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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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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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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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84 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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59 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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1answer
234 views

Calculate Earth Mover's Distance for two grayscale images

I am trying to calculate EMD (a.k.a. Wasserstein Distance) for these two grayscale (299x299) images/heatmaps: Right now, I am calculating the histogram/distribution of both images. The histograms ...
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99 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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1answer
63 views

Prerequisites for Wasserstein GAN/Autoencoder

Can someone who read WGAN/WAE papers and understood Wasserstein part, could you share how you prepared necessary Optimal Transport background? The mentioned papers seem little tough if you don't have ...
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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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1answer
153 views

Implementation of WAE-GAN does not match with the description in the paper

According to the litterature and specifically to this paper, the wasserstein autoencoders is an encoder-decoder architecture. So it must contain encoder and decoder parts. in the algorithm ...
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187 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
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632 views

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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1answer
1k views

Wasserstein Loss is very sensitive to model architecture

I am working on a class project where I compare the performance of GAN and WGAN. Since the only difference between GAN and WGAN is the Wasserstein loss, I chose one neural network model architecture ...
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219 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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116 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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461 views

In a WGAN, when is the generator's loss function ever used? [closed]

I've been building a Wasserstein GAN in Keras recently following the original Arjovsky implementation in PyTorch and ran across an issue I've yet to understand. To my knowledge, the critic network is ...
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1answer
355 views

Distance measure between discrete distributions (that contains 0) and uniform

I'm trying to choose a district metric that falls between 0 to 1 and lets me compare the distance between a uniform probability distribution and any given probability distribution (could be random, ...
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6k views

What is the advantages of Wasserstein metric compared to Kullback-Leibler divergence?

What is the practical difference between Wasserstein metric and Kullback-Leibler divergence? Wasserstein metric is also referred to as Earth mover's distance. From Wikipedia: Wasserstein (or ...