Density Ratio-Free Doubly Robust Proxy Causal Learning

TL;DR

This paper introduces density ratio-free, kernel-based doubly robust estimators for proxy causal learning, effectively handling high-dimensional and continuous treatments without density ratio estimation or kernel smoothing.

Contribution

It proposes the first density ratio-free doubly robust estimators using kernel mean embeddings for proxy causal learning, with strong theoretical guarantees and improved empirical performance.

Findings

Outperforms existing methods on PCL benchmarks

Provides closed-form solutions with uniform consistency guarantees

Handles high-dimensional and continuous treatments effectively

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 propose the first density-ratio free doubly robust estimators for proxy causal learning, which have closed form solutions and strong uniform 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.