Computation of optimal transport plans, with a view towards statistics
by Dominic Schuhmacher
Abstract: In recent years optimal transport and Wasserstein metrics have become both an object of intensive study in mathematics and an important tool in applied statistics and machine learning for analyzing complex data. From image analysis and retrieval, over biometric applications, to the modelling of chemical reactions and cosmological models of the universe: whenever the available data can be interpreted as mass distributions on some space, optimal transport ideas provide a natural and often powerful approach for the analysis.
In the light of such data sets, computing optimal transport plans between hundreds of thousands of particles still presents challenging mathematical and algorithmic problems. In this talk I give a basic introduction into the theory of optimal transport and present three modern computational methods able to deal with large data sets. We also look at a paradigmatic statistical application.