Free complete Wasserstein algebras.

RSS Source
Authors
Radu Mardare, Prakash Panangaden, Gordon D. Plotkin

We present an algebraic account of the Wasserstein distances $W_p$ oncomplete metric spaces. This is part of a program of a quantitative algebraictheory of effects in programming languages. In particular, we give axioms,parametric in $p$, for algebras over metric spaces equipped with probabilisticchoice operations. The axioms say that the operations form a barycentricalgebra and that the metric satisfies a property typical of the Wassersteindistance $W_p$. We show that the free complete such algebra over a completemetric space is that of the Radon probability measures on the space with theWasserstein distance as metric, equipped with the usual binary convex sumoperations.

Stay in the loop.

Subscribe to our newsletter for a weekly update on the latest podcast, news, events, and jobs postings.