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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 ...
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 Kullback–Leibler divergence (a.k.a. relative ...
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, ...
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?
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 ...
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 ...
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 ...