Estimating overlap‑optimal representations in general settings

Develop procedures that, from finite samples and beyond the Gaussian–GLM setup, estimate feature representations φ(X) that are overlap‑optimal for Average Treatment effect on the Treated (ATT) estimation, i.e., representations that minimize the overlap divergence O(φ(X)) while preserving identification of the ATT under ignorability.

Background

The paper introduces deconfounding scores—representations that preserve identification of the ATT under ignorability—and defines an overlap divergence O(Z) that links overlap to the semiparametric efficiency bound. In a Gaussian design with generalized linear models, the authors analytically characterize a family of deconfounding scores and show prognostic scores are overlap‑optimal within this class.

However, these analytical results rely on restrictive assumptions (Gaussian covariates and generalized linear models), and the authors highlight the need for methods that can learn overlap‑optimal representations from finite samples in broader, more realistic settings.