Kernel Single Proxy Control for Deterministic Confounding

2023-08-08

arXiv.org

AI Summary

This paper addresses causal effect estimation under unobserved confounding using only a single proxy variable, with particular focus on deterministic outcome generation. We propose a kernel-based two-stage regression framework that integrates maximum moment restriction estimation, performing function approximation and functional optimization within a reproducing kernel Hilbert space. Theoretically, we establish estimation consistency under the single-proxy setting—breaking the conventional double-proxy identification requirement for the first time—and rigorously generalize and strengthen the COCA framework. Empirically, our method accurately recovers true causal effects on challenging synthetic benchmarks, significantly outperforming existing single-proxy baselines.

Abstract

We consider the problem of causal effect estimation with an unobserved confounder, where we observe a proxy variable that is associated with the confounder. Although Proxy causal learning (PCL) uses two proxy variables to recover the true causal effect, we show that a single proxy variable is sufficient for causal estimation if the outcome is generated deterministically, generalizing Control Outcome Calibration Approach (COCA). We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.

Problem

• Estimating causal effects with unobserved confounders.
• Using single proxy variables for causal recovery.
• Developing kernel-based methods for continuous treatments.

Innovation

• Kernel-based methods for causal effect estimation
• Two-stage regression and maximum moment restriction
• Deterministic outcome enables causal recovery