Free complete Wasserstein algebras

Radu Mardare, Prakash Panangaden, Gordon D. Plotkin

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Abstract

We present an algebraic account of the Wasserstein distances Wp on complete metric spaces, for p ≥ 1. This is part of a program of a quantitative algebraic theory of effects in programming languages. In particular, we give axioms, parametric in p, for algebras over metric spaces equipped with probabilistic choice operations. The axioms say that the operations form a barycentric algebra and that the metric satisfies a property typical of the Wasserstein distance Wp. We show that the free complete such algebra over a complete metric space is that of the Radon probability measures with finite moments of order p, equipped with the Wasserstein distance as metric and with the usual binary convex sums as operations.

Original languageEnglish
Article number19
Number of pages16
JournalLogical Methods in Computer Science
Volume14
Issue number3
DOIs
Publication statusPublished - 14 Sep 2018

Keywords

  • Wasserstein distances
  • quantitative algebraic theory
  • programming languages

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