[2503.08371] Density Ratio-based Proxy Causal Learning Without Density Ratios

Computer Science > Machine Learning arXiv:2503.08371 (cs) [Submitted on 11 Mar 2025 (v1), last revised 26 Mar 2026 (this version, v2)] Title:Density Ratio-based Proxy Causal Learning Without Density Ratios Authors:Bariscan Bozkurt, Ben Deaner, Dimitri Meunier, Liyuan Xu, Arthur Gretton View a PDF of the paper titled Density Ratio-based Proxy Causal Learning Without Density Ratios, by Bariscan Bozkurt and 4 other authors View PDF HTML (experimental) Abstract:We address the setting of Proxy Causal Learning (PCL), which has the goal of estimating causal effects from observed data in the presence of hidden confounding. Proxy methods accomplish this task using two proxy variables related to the latent confounder: a treatment proxy (related to the treatment) and an outcome proxy (related to the outcome). Two approaches have been proposed to perform causal effect estimation given proxy variables; however only one of these has found mainstream acceptance, since the other was understood to require density ratio estimation - a challenging task in high dimensions. In the present work, we propose a practical and effective implementation of the second approach, which bypasses explicit density ratio estimation and is suitable for continuous and high-dimensional treatments. We employ kernel ridge regression to derive estimators, resulting in simple closed-form solutions for dose-response and conditional dose-response curves, along with consistency guarantees. Our methods empirically demo...