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Title: Tangential Wasserstein Projections

Citation Type: Miscellaneous

Publication Year: 2022

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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.

Url: https://arxiv.org/pdf/2207.14727.pdf

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Authors: Gunsilius, Florian; Hsieh, Meng Hsuan; Lee, Myung Jin

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Data Collections: IPUMS USA

Topics: Methodology and Data Collection, Population Data Science

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