Optimal Transport

In this section we give an introduction to optimal transport (OT), where we present an operator over discrete and/or continuous measures that fulfill all distance properties (positivity, symmetry and triangularity). For historical reasons, the OT distance is also referred as Earth mover’s distance (EMD) in the computer science literature, or Wasserstein distance. Compared to standard divergences such as Kulback-Leibler, OT is well defined when comparing measures of non-overlapping supports, or different number of samples corresponding to empirical measures. We will present the different formulations of OT for discrete and continuous measures, show the metric properties of the operator, and discuss two applications that exploit its properties. The first application considers adding a Wasserstein loss to a classifier to measure semantic relations between classes. The second application discusses the framework of learning a classifier in a target domain where there are no labels available by transporting labels from a source domain where this information is available.

Class: 

Data Science 2: Advanced Topics in Data Science

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