Density Ratio-Free Doubly Robust Proxy Causal Learning

2025-05-26

AI Summary

This paper addresses causal function estimation in proxy causal learning (PCL) under unobserved confounding. Existing approaches rely on density ratio estimation, kernel smoothing, or restrictive assumptions—such as discrete or low-dimensional treatment variables—which limit their applicability and theoretical guarantees. To overcome these limitations, we propose the first density-ratio-free doubly robust kernel method for PCL. Our approach integrates the ideas of outcome and treatment bridges, leveraging kernel mean embeddings and reproducing kernel Hilbert space (RKHS) theory to derive a closed-form estimator. It achieves strong consistency without requiring density ratio estimation, nor assuming treatment discreteness or low dimensionality. Extensive experiments on multiple PCL benchmarks demonstrate that our method significantly outperforms existing doubly robust alternatives that depend on density ratio estimation or kernel smoothing.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Estimating causal functions with unobserved confounders but available proxies
• Combining outcome and treatment bridge methods via kernel-based doubly robust estimators
• Handling continuous and high-dimensional variables without density ratio estimation

Innovation

• Kernel-based doubly robust estimators
• Density ratio-free identification strategy
• Handles continuous high-dimensional variables