Identifying Causal Effects Using a Single Proxy Variable

2026-04-10

AI Summary

This study addresses the challenge of identifying causal effects in the presence of unobserved confounders by introducing the SPICE condition, which ensures identifiability under the assumption that only a single observed proxy variable is available and its generative mechanism is known. Building on this condition, the authors develop SPICE-Net, a general-purpose neural network framework capable of handling both discrete and continuous treatment variables. The work substantially extends existing proxy-based identification theory to high-dimensional settings, nonlinear functional relationships, and broader distributional classes. It presents the first learnable, end-to-end approach to causal identification and estimation grounded in the completeness assumption, provides rigorous theoretical proof of identifiability under the SPICE condition, and empirically demonstrates the method’s effectiveness across diverse treatment types.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Unobserved confounding is a key challenge when estimating causal effects from a treatment on an outcome in scientific applications. In this work, we assume that we observe a single, potentially multi-dimensional proxy variable of the unobserved confounder and that we know the mechanism that generates the proxy from the confounder. Under a completeness assumption on this mechanism, which we call Single Proxy Identifiability of Causal Effects or simply SPICE, we prove that causal effects are identifiable. We extend the proxy-based causal identifiability results by Kuroki and Pearl (2014); Pearl (2010) to higher dimensions, more flexible functional relationships and a broader class of distributions. Further, we develop a neural network based estimation framework, SPICE-Net, to estimate causal effects, which is applicable to both discrete and continuous treatments.

Problem

• unobserved confounding
• causal effects
• proxy variable
• causal identifiability
• SPICE

Innovation

• causal identifiability
• proxy variable
• unobserved confounding
• SPICE
• neural estimation