Deconfounding Scores and Representation Learning for Causal Effect Estimation with Weak Overlap
This work addresses a key challenge in causal inference for researchers and practitioners dealing with high-dimensional data, though it is incremental as it builds on existing score-based methods.
The paper tackles the problem of high variance in causal effect estimation when treatment groups have weak overlap, especially in high dimensions, by proposing deconfounding scores as feature representations that preserve identification and estimation targets. They show that prognostic scores are overlap-optimal under certain models and validate this with experiments.
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.