Primary Submission Category: Causal Inference and Common Support Violations
Prognostic scores and representation learning for causal effect estimation with weak overlap
Authors: Oscar Clivio, Alexander D’Amour, Alexander Franks, Oscar Clivio, Avi Feller, Chris Holmes,
Presenting Author: David Bruns-Smith*
Overlap, also known as positivity, is a key condition for modern causal machine learning. Many popular estimators suffer from high variance and become brittle when features strongly differ across treatment groups. This is especially challenging in high dimensions: the curse of dimensionality can make overlap implausible. Modern causalML methods typically address this issue only indirectly, leveraging dimension reduction or other representation learning that does not account for overlap. In the limit, such methods reduce features to a scalar, such as the prognostic score (i.e., the conditional counterfactual mean). Building on a venerable empirical literature, we argue that the prognostic score is an unreasonably effective dimension reduction approach, and is a promising default in otherwise complex settings. To show this, we first propose a class of feature representations called deconfounding scores, which preserve both identification and the target of estimation while also improving overlap; the propensity and prognostic scores are two special cases. We characterize the corresponding optimization problem in terms of controlling overlap under an unconfoundedness constraint. We then derive closed-form expressions for overlap-optimal representations under a broad family of generalized linear models with Gaussian covariates and show that this coincides with the prognostic score. We conduct extensive experiments to assess this behavior empirically.