Speaker: Dr. Florian Gunsilius (Emory University)

 

Title: Partial Identification with Schrödinger Bridges

 

 

Abstract: Partial identification provides an alternative to point identification: Instead of pinning down a unique parameter estimate, the goal is to characterize a set guaranteed to contain the true parameter value. Many partial identification approaches take the form of linear optimization problems, which seek the "best- and worst-case scenarios" of a proposed model subject to the constraint that the model replicates correct observable information. However, such linear programs become intractable in settings with multivalued or continuous variables. This paper introduces a novel method to overcome this computational and statistical curse of cardinality: we provide a duality between a general class of optimal transportation problems and the lower bound of a partial identified effect. Building on such duality, we propose a discretization of the instrument realizations and an entropy transform of these potentially infinite-dimensional linear programs. This maps the problem into general versions of multi-marginal Schrödinger bridges, enabling efficient approximation of their solutions. In the process, we establish novel statistical and mathematical properties of such multi-marginal Schrödinger bridges---including consistency of the estimator and an analysis of the asymptotic distribution of entropic approximations to infinite-dimensional linear programs. We illustrate this approach by analyzing instrumental variable models with continuous variables, a setting that has been out of reach for existing methods that do not rely on sampling. 

 

Joint with Bruno Nunes Costa from the University of Michigan.