Density Ratio-Free Doubly Robust Proxy Causal Learning
This work addresses causal inference challenges for researchers and practitioners when confounders are unobserved but proxies are available, offering a more efficient and robust method, though it is incremental in improving upon prior doubly robust approaches.
The paper tackles the problem of causal function estimation in Proxy Causal Learning (PCL) by proposing two kernel-based doubly robust estimators that combine outcome and treatment bridge approaches, handling continuous and high-dimensional variables without requiring density ratio estimation or kernel smoothing over treatments, and outperforming existing methods on benchmarks.
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.