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Tangential Wasserstein Projections

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  • Florian Gunsilius
  • Meng Hsuan Hsieh
  • Myung Jin Lee

Abstract

We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and provides a unique solution in regular settings. The idea is to work on regular tangent cones of the Wasserstein space using generalized geodesics. Its structure and computational properties make the method applicable in a variety of settings, from causal inference to the analysis of object data. An application to estimating causal effects yields a generalization of the notion of synthetic controls to multivariate data with individual-level heterogeneity, as well as a way to estimate optimal weights jointly over all time periods.

Suggested Citation

  • Florian Gunsilius & Meng Hsuan Hsieh & Myung Jin Lee, 2022. "Tangential Wasserstein Projections," Papers 2207.14727, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:2207.14727
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    References listed on IDEAS

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