Questions tagged [wasserstein]
The wasserstein tag has no usage guidance.
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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
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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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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
81 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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109 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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443 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
913 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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168 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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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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385 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
300 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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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 ...
