Deconfounding Scores and Representation Learning for Causal Effect Estimation with Weak Overlap

TL;DR

This paper introduces deconfounding scores, a new class of feature representations that improve overlap in causal effect estimation, especially in high-dimensional settings, by minimizing overlap divergence.

Contribution

It proposes deconfounding scores as a novel approach to enhance overlap, generalizes classical scores, and characterizes their optimality within a broad model class.

Findings

Proposes deconfounding scores that preserve identification and target estimation.

Derives closed-form expressions for deconfounding scores under generalized linear models.

Shows prognostic scores are overlap-optimal within the proposed class.

Abstract

Overlap, also known as positivity, is a key condition for causal treatment effect estimation. Many popular estimators suffer from high variance and become brittle when features differ strongly across treatment groups. This is especially challenging in high dimensions: the curse of dimensionality can make overlap implausible. To address this, we propose a class of feature representations called deconfounding scores, which preserve both identification and the target of estimation; the classical propensity and prognostic scores are two special cases. We characterize the problem of finding a representation with better overlap as minimizing an overlap divergence under a deconfounding score constraint. We then derive closed-form expressions for a class of deconfounding scores under a broad family of generalized linear models with Gaussian features and show that prognostic scores are overlap-optimal within this class. We conduct extensive experiments to assess this behavior empirically.