| Abstract: |
| We develop a notion of projections between sets of probability measures using the
geometric properties of the 2-Wasserstein space. In contrast to existing methods, it is designed for
multivariate probability measures that need not be regular, is computationally efficient to implement
via regression, and provides a unique solution in general. The idea is to work on tangent cones of
the Wasserstein space using generalized geodesics. Its structure and computational properties make
the method applicable in a variety of settings where probability measures need not be regular, from
causal inference to the analysis of object data. An application to estimating causal effects yields
a generalization of the synthetic controls method for systems with general heterogeneity described
via multivariate probability measures. |
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