Identifying Causal Effects Using a Single Proxy Variable
2026-04-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the problem of estimating the effect of a treatment on an outcome when there are hidden factors influencing both—known as unobserved confounding. They assume there is a measurable proxy that relates to the hidden factor and they understand how this proxy is generated. Under a key assumption called Single Proxy Identifiability of Causal Effects (SPICE), they show it is possible to identify the true causal effect. They improve upon earlier work by handling more complex scenarios and introduce a neural network method called SPICE-Net to estimate these effects for different types of treatments.
Unobserved confoundingCausal effectsProxy variableIdentifiabilityCompleteness assumptionNeural networksCausal inferenceTreatment effectsSPICEEstimation framework
Authors
Silvan Vollmer, Niklas Pfister, Sebastian Weichwald
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.