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Optimal binning rule for the 2 histograms in Optimal Transport? [closed]

When calculating histograms, there are several optimal binning rules to chose from as alternatives to equal-width bins, such as square-root, Sturges, and Freedman-Diaconis. Are there optimal binning ...
1
vote
0answers
37 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 ...
1
vote
1answer
30 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?
0
votes
0answers
33 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 ...
0
votes
0answers
26 views

Computing Karcher means in the space of all probability densities

Suppose I have samples $X_i \sim \mu_i$, and let us for simplicity assume all the higher moments exist and the supports of probability measures $m_i$ are on some compact subset of $\mathbb{R}^n$. Let ...
4
votes
1answer
235 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 KullbackÔÇôLeibler divergence (a.k.a. relative ...
2
votes
1answer
556 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, ...
39
votes
5answers
12k 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 ...