Optimal transportation, at its core, is a powerful framework for obtaining structured yet general couplings between general probability measures based on matching underlying characteristics. This framework lends itself naturally to applications in causal inference: from matching estimation, to difference-in-differences and synthetic controls approaches, to instrumental variable estimation, just to name a few. In this talk, I will provide a non-exhaustive overview of potential applications of optimal transport approaches to causal inference. I will focus on providing an overview of general concepts and ideas.
The talk is based on joint work with Rex Hsieh, Myung Jin Lee, Philippe Rigollet, William Torous, and Yuliang Xu.