Questions tagged [wasserstein]
The Wasserstein metric or Earth Movers Distance is a distance function between probability distributions.
59
questions
0
votes
0
answers
5
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 ...
- 21
0
votes
0
answers
21
views
What are the most common information matrices in statistics and machine learning? [closed]
The Fisher information matrix is extremely popular in information theory, probability, machine learning, and statistics. I recently came across another information matrix, the Wasserstein information ...
- 1
0
votes
0
answers
9
views
Proof for equivalence definition of convergence in the Wasserstein space
From "An Invitation to Statistics in Wasserstein Space" (Victor M. Panaretos and
Yoav Zemel)
Theorem 2.2.1 (Convergence in Wasserstein Space) Let $\mu, \mu_n \in \mathscr{W}_p(\mathscr{X})$. ...
- 309
0
votes
0
answers
86
views
Does Sliced Wasserstein Distance assume that the two distributions are zero-mean?
Sliced Wasserstein distance (SWD) depends on Radon transform, which is defined as $\mathbb{R}I(t,\theta) = \int \delta(t-\theta^Tx)I(x) \, dx$. The definition of SWD, however, does not use the ...
- 236
0
votes
0
answers
64
views
What metrics could I use to compare multiple 2-dimensional histograms/sinograms?
I have a set of two-dimensional shapes, each represented by one or more closed paths, which enclose one continuous area. My objective is to establish a measure of similarity between these shapes. I do ...
- 101
0
votes
0
answers
31
views
How to quantify the dissimilarity across different types of variables?
I have two dataframes with the same columns but with varying sample sizes. I want to compare corresponding columns for homogeneity (i.e., do they come from the same distribution?). There are different ...
- 433
1
vote
0
answers
16
views
How to apply a seasonal index into an eCDF?
I am doing a Before/After analysis, which is aiming at evaluating the effect of a change. Assume I have made a change at the beginning of June-2022, and I want to evaluate the effect of the change ...
- 111
1
vote
0
answers
110
views
Wasserstein-1 distance between two joint distributions
Let me define random variables $A, B, C, D$ that are independent of each other. Additionally, PDFs of $A, B$ are the same, and PDFs of $C, D$ are the same too
In such a case, is the following correct?
...
- 11
1
vote
2
answers
635
views
Normalized Wasserstein distance
The wasserstein_distance will be smaller the longer u_values and v_values are.
...
- 133
2
votes
0
answers
121
views
Why is the Wasserstein distance not used in Variational Inference
I just started learning the concept of variational inference in the context of variational Autoencoder, so please excuse me if the answer is obvious. I would like to know why traditionally, KL-...
- 21
2
votes
1
answer
453
views
GAN : Why does a perfect discriminator mean no gradient for the generator?
(Note : this is a cross-post from Artificial Intelligence. As I got no answer there in two weeks, I'm trying my luck on a more popuplated SE site. I know this is against SE's policy on cross-posting ...
- 1,184
2
votes
0
answers
33
views
How to calculate the max possible earth mover distance between histograms, given the buckets?
I have two histograms and am able to calculate the EMD / Wasserstein metric between them using the algorithm described here. In order to better communicate the implication of this metric, I want to ...
- 41
1
vote
1
answer
309
views
Earth Mover (Wasserstein) distance for ordinal discrete data
I am doing data analysis for my Masters research and which includes some Likert scale type questions. I have been calculating some distances between the responses for these questions. All this has ...
- 101
0
votes
0
answers
41
views
Is there a functionality that gets pairwise distance with metric as wasserstein distance
I understand that there is a implementation in scipy for two 1-D matrixes, but what i need is a fast implementation for pairwise vectors in a 2D vector, like this https://scikit-learn.org/stable/...
3
votes
1
answer
464
views
Is there an R or python package to calculate wasserstein metric between negative binomial distributions?
As the title says I am looking for an R or python package which can calculate wasserstein distance (aka earthmovers distance between) two lists (vectors) of sampled values from a negative binomial ...
- 368
0
votes
0
answers
18
views
Transform Earth mover's distance/Wasserstein metric to percentance (0 to 1 or 0% to 100%) [duplicate]
Ok, I do some calculations between binned histograms via the use of Wasserstein metric and more specifically this python library.. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats....
- 137
1
vote
0
answers
61
views
Can I adjust the Wasserstein GAN loss function for my particular data?
I am working on building Generative Adversarial Networks for the purpose of generating synthetic flight data. The GAN will be trained on actual time-series flight data in the form of a (n,m,9) array ...
0
votes
0
answers
211
views
Wasserstein distance between multivariate lognormal distributions
Wikipedia gives the following formula for normal distributions:
What changes, if any, do I need to make to handle multivariate lognormal distributions instead?
- 33
0
votes
0
answers
257
views
I need help understanding the meaning of the loss values of a WGAN with Gradient Penalty
I am currently working on training a Auxiliary Classifier Wasserstein GAN with Gradient Penalty. I based my implementation off of https://keras.io/examples/generative/wgan_gp/ (to which I added the ...
4
votes
1
answer
1k
views
Wasserstein distance and Kolmogorov-Smirnov statistic as measures of effect size
So I've been dealing with 2 sample hypothesis testing with very large samples (around 20,000s each). Whenever I test for the equality of distribution I always reject the null hypothesis, even though ...
- 53
0
votes
0
answers
79
views
Measure for evaluating a density estimation procedure
Given an implementation of a multivariate density estimation scheme, what would be a suitable measure to evaluate the accuracy of the procedure?
I am currently evaluating the procedure using three ...
- 2,126
0
votes
0
answers
280
views
Interpretation of upper bound on the Wasserstein Distance
I am trying to interpret the 2-Wasserstein distance and the upper bound on it. Let's say I have 2-Wasserstein distance between two distributions to be $x$, and I have an upper bound on it which gives ...
- 215
2
votes
1
answer
966
views
Intuition on Wasserstein Distance
I've been trying to familiarize myself with the Wasserstein distance and saw this answer on StackExchange by @antike that at first made a lot of sense, but then it didn't (to me, of course).
In the ...
- 173
0
votes
1
answer
166
views
How can one compute the "average" of a dataset of histograms that minimizes the mean Earth Mover's Distance between all data points and average?
It is my understanding that when the distance metric is euclidean distance, the mean of a dataset minimizes the average distance between all data points and the computed "mean".
In the case ...
1
vote
0
answers
39
views
What is this probability distribution?
Thank you in advance for any suggestions or feedback.
I have a discrete 1D probability distribution represented as a vector $\textbf{p}$, $p_i = p(x_i)$.
I am interested in finding the Wasserstein (...
1
vote
1
answer
1k
views
When is my Wasserstein GAN-GP overfitting?
I have a hard time interpreting the WGAN-GP losses attached. At which epoch is D and/or G overfitting? The quality improves a lot overtime, yet the generator loss at later epochs does not appear on ...
0
votes
0
answers
725
views
Wasserstein distance for categorical data? Relationship to TVD?
Is the Wasserstein distance applicable for categorical data? e.g. if we have the distribution of different coloured balls in two bags,
...
1
vote
0
answers
129
views
Reference for Wasserstein distance for generalized exponential family and generalized extreme value probability distributions
The Wikipedia page gives the analytical results for computing the Wasserstein metric between two multivariate normal distributions, and I thought it used to give results for several other commonly ...
- 297
-1
votes
1
answer
93
views
K-Lipschitz for the Wasserstein GANs
I am trying to follow this blog for Wasserstein loss for Generative Adversarial Networks:
From GAN to WGAN.
Actually, I am trying to follow the logic behind the K-Lipschitz continuity. This post in ...
- 85
1
vote
1
answer
54
views
How to check whether a partitioning is more balanced?
For example consider the following two partitions that add approximately to 100 percent.
Partition 1 : 41% 36% 14% 5% 2% 1% <1% <1%
Partition 2 : 82% 10% 4% 3% <1% <1% <1% <1%
...
- 210
0
votes
0
answers
77
views
Horizontal vs Vertical optimal transport of probability distributions
Optimal transport has a primal and dual form. My question is: Is the primal formulation of OT intended for horizontal movement of probability mass, whereas the dual formulation is more geared towards ...
- 3,481
0
votes
0
answers
228
views
Does Wasserstein distance require the source and target distributions to have the same mass?
If we minimize the Wasserstein loss,
$$W_1 (P_S, P_T) = \underset{\gamma \in \Pi}{\text{min }} \sum_{x,y} |x-y|\gamma(x,y)$$
which means we are looking for the coupling $\gamma(x,y)$ that minimizes ...
- 3,481
1
vote
0
answers
207
views
Properties of Sinkhorn distance
I am reading the paper by Cuturi http://www.marcocuturi.net/Papers/cuturi13sinkhorn.pdf and I am curious about the properties of Sinkhorn distance and wondering what properties of the Sinkhorn ...
6
votes
1
answer
3k
views
What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance?
What is the intuitive difference between Wasserstein-1 distance and Wasserstein-2 distance, and how to know which one to use?
- 3,481
1
vote
1
answer
4k
views
What are the advantages of Wasserstein distance compared to Jensen-Shannon divergence?
What is the practical difference between Wasserstein metric and Jensen-Shannon divergence? Wasserstein metric is also referred to as Earth mover's distance.
From Wikipedia:
Wasserstein metric is a ...
- 3,481
2
votes
0
answers
150
views
How to Show Wasserstein Metric is Sum Invariant?
A paper I'm trying to understand states that that Wasserstein metric obeys certain properties, which I'd like to prove. This metric is defined for two random variables $U, V$ and $p \in (1, \infty)$ ...
- 915
8
votes
1
answer
3k
views
Multivariate Wasserstein metric for $n$-dimensions
I am a vegetation ecologist and poor student of computer science who recently learned of the Wasserstein metric. Application of this metric to 1d distributions I find fairly intuitive, and inspection ...
- 81
1
vote
1
answer
597
views
Optimal critic in Wasserstein GAN (WGAN)
In the Wasserstein GAN (generative adversarial network) paper they say that the critic needs to be optimal.
What does this mean practically?
They do more training iterations of critic (5) than the ...
- 43
1
vote
0
answers
562
views
Weight Clipping range with WGAN and relation with other factors
For a while, my code with WGAN has failed to generate quality images through a complicated multi-class database. My issue has been with implementation and not code.
Recently I read the WGAN-GP paper ...
- 109
0
votes
1
answer
155
views
Large gradient magnitude in WGAN-GP
I've implemented a minimal WGAN-GP on MNIST (code here).it kinda works and outputs some digits but loss/gradient magnitudes are so huge, for example:
$GradientPenalty \approx 10^{19}$
$D(\hat{x})- D(...
- 101
4
votes
1
answer
905
views
Upper Bound on the Wasserstein Distance
I'm interested to know if it's possible to construct an upper bound on the Wasserstein distance in terms of the Kolgomorov distance.
The Wasserstein distance can we written as
$$W_{1}\left(F, G\...
- 319
3
votes
1
answer
2k
views
Why is "weight clipping" needed for Wasserstein GANs?
I am reading the original paper on the Wasserstein GAN:
https://arxiv.org/pdf/1701.07875.pdf
and I came across this paragraph:
I don't understand the statement: "$\mathcal{W}$ is compact implies ...
- 141
1
vote
0
answers
50
views
Statistical estimators distance for close empirical distributions
Is it valid to argue that two empirical distributions $ p_1, p_2 $ having small Wasserstein distance $W_r(\cdot)$ for an order $ r $ will yield close MLE estimators for a statistical model ...
- 944
1
vote
0
answers
421
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 $...
- 210
9
votes
2
answers
3k
views
Relation Between Wasserstein Distance and KL-Divergence (Relative Entropy)
Consider the Wasserstein metric of order one $W_1$ (a.k.a. the Earth Movers Distance). I would like to know whether it is possible to link $W_1$ and Kullback–Leibler divergence (a.k.a. relative ...
- 91
9
votes
3
answers
9k
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 ...
- 155
7
votes
1
answer
3k
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 ...
- 671
2
votes
1
answer
192
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 ...
- 5,726
4
votes
1
answer
252
views
Computing Wasserstein 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}} \, , $$
...
- 225
1
vote
1
answer
348
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 ...
- 233