Questions tagged [wasserstein]
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18
questions
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17 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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22 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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39 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 ...
2
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0answers
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 ...
2
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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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0answers
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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1
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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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0answers
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 ...
2
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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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0answers
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. ...
3
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0answers
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:
$$X_0:=(\operatorname{var}{\tilde{X}_0})^{-\frac{1}{2}}(\tilde{X}_0-\mathbb{E}\tilde{X}_0),$$
...
3
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0answers
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 ...
1
vote
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, ...
23
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2answers
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 ...
