Title: Partial Identification via Optimal Transport under Complex Constraints on Treatments and Potential Outcome Measures
Primary area: causal reasoning
Keywords: causality; partial identification

Abstract: We investigate causal effect estimation in settings where the potential outcomes under treatment and control are supported on \emph{distinct} measurable spaces, rendering classical estimands such as the average treatment effect ill-defined. To address this challenge, we introduce a novel framework for \emph{partial identification} based on optimal transport (OT), which quantifies the minimal expected cost required to couple the outcome distributions 
 and 
 across heterogeneous domains. Our first contribution is to establish valid partial identification bounds for this OT-based causal estimation and accommodate the inherent support mismatch between potential outcomes. Secondly, we extend our framework to incorporate covariate information, formulating a covariate-adjusted OT problem that yields tighter identification intervals by leveraging observed covariate distributions, and also extend to the designed-based experimental settings. Finally, through extensive simulations and empirical studies, we demonstrate the practical utility and robustness of our approach, highlighting its advantages over existing methods in scenarios involving heterogeneous outcome spaces and covariate structures. Our results provide a principled and flexible methodology for causal inference in complex settings where traditional assumptions do not hold.

TL;DR: Partial Identification of Causal Effect under Distinct Measures