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Symmetrization and the Wasserstein Metric

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Symmetrization generally takes on the form of multiplying your observed data by random signs—i.e. +/- 1’s. This simple idea, however, has a wide range of applications from inequalities in Banach spaces to bootstrap methods in statistics. In this talk, we will discuss the symmetrization inequality, its connection to a variety of topics in mathematical analysis, probability, and statistics, and how it can be viewed from the lens of optimal transport theory. In general, the asymmetry of the data is not taken into account when using symmetrization tools. We aim to rectify that with the use of the Wasserstein metric as a measure of such asymmetry.

This talk is part of the Cambridge Analysts' Knowledge Exchange (C.A.K.E.) series.

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