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1-Wasserstein Distance on the Standard Simplex by Frohmader, Andrew; Volkmer, Hans is a scholarly article available to read on EtoBox.

What is 1-Wasserstein Distance on the Standard Simplex about?

Wasserstein distances provide a metric on a space of probability measures. We consider the space $\Omega$ of all probability measures on the finite set $\chi = \{1, \dots ,n\}$ where $n$ is a positive integer. 1-Wasserstein distance, $W_1(\mu,\nu)$ is a function from $\Omega \times \Omega$ to $[0,\infty)$. This paper derives closed form expressions for the First and Second moment of $W_1$ on $\Omega \times \Omega$ assuming a uniform distribution on $\Omega \times \Omega$.

Author

Frohmader, Andrew; Volkmer, Hans

Published

2019

Language

EN