Optimal Transport to a Variety
Abstract
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric and the given distribution. The Wasserstein distance between the distribution and the variety is the minimum of a linear functional over a union of transportation polytopes. We obtain a description in terms of the solutions of a finite number of systems of polynomial equations. The case analysis is based on the ground metric. A detailed analysis is given for the two bit independence model.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.11716
 Bibcode:
 2019arXiv190911716C
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  Metric Geometry;
 Mathematics  Statistics Theory;
 Optimization Control;
 Metric Geometry;
 Statistics Theory
 EPrint:
 17 pages, 5 figures and 2 tables