Statistics Department Seminar Series: Florian Gunsilius, Assistant Professor, Department of Economics, University of Michigan

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.

Florian Gunsilius is an Assistant Professor of Economics (Econometrics) at the University of Michigan. His research interests are nonparametric approaches for statistical identification, estimation, and inference. His current focus is on developing geometric methods for causal inference and statistical optimal transport theory.

https://www.floriangunsilius.com/