Density Ratio-Free Doubly Robust Proxy Causal Learning
Bariscan Bozkurt, Houssam Zenati, Dimitri Meunier, Liyuan Xu, Arthur Gretton
TL;DR
The paper tackles estimating causal dose-response under unobserved confounding using Proxy Causal Learning (PCL). It develops two kernel-based, doubly robust estimators (DRKPV and DRPMMR) that fuse outcome-bridge and treatment-bridge identifications without explicit density ratio estimation, leveraging conditional mean embeddings in RKHS to yield closed-form, scalable solutions for continuous/high-dimensional treatments. The authors prove uniform consistency and demonstrate superior performance over baselines on synthetic and real datasets, with robustness to bridge-function misspecification. This work advances practical causal inference under hidden confounding by providing scalable, theoretically-grounded methods with strong empirical impact for policy evaluation and beyond.
Abstract
We study the problem of causal function estimation in the Proxy Causal Learning (PCL) framework, where confounders are not observed but proxies for the confounders are available. Two main approaches have been proposed: outcome bridge-based and treatment bridge-based methods. In this work, we propose two kernel-based doubly robust estimators that combine the strengths of both approaches, and naturally handle continuous and high-dimensional variables. Our identification strategy builds on a recent density ratio-free method for treatment bridge-based PCL; furthermore, in contrast to previous approaches, it does not require indicator functions or kernel smoothing over the treatment variable. These properties make it especially well-suited for continuous or high-dimensional treatments. By using kernel mean embeddings, we have closed-form solutions and strong consistency guarantees. Our estimators outperform existing methods on PCL benchmarks, including a prior doubly robust method that requires both kernel smoothing and density ratio estimation.