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

2026-04-01

AI Summary

This work addresses the instability of causal effect estimation in high-dimensional settings with limited overlap (positivity violation), where high variance often undermines reliability. The authors propose the "deconfounding score"—a class of feature representations that jointly optimize identifiability and target estimation by minimizing the overlap divergence between treatment groups. This framework unifies propensity scores and prognostic scores as special cases. Under generalized linear models and Gaussian feature assumptions, the prognostic score is shown to possess optimal overlap properties, and a closed-form solution is derived. Both theoretical analysis and empirical experiments demonstrate that the proposed method significantly improves the accuracy and robustness of causal effect estimation under high-dimensional, weak-overlap conditions.

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.

Problem

• causal effect estimation
• overlap
• positivity
• high-dimensional data
• treatment effect

Innovation

• deconfounding scores
• overlap
• causal effect estimation
• representation learning
• prognostic scores