Identifying Causal Effects Using a Single Proxy Variable

TL;DR

This paper introduces SPICE, a method to identify causal effects using a single proxy for unobserved confounders, extending previous results and providing a neural network-based estimation framework.

Contribution

It generalizes proxy-based causal identifiability to higher dimensions and develops SPICE-Net, a neural network approach for estimating causal effects.

Findings

Causal effects are identifiable under the SPICE assumptions.

SPICE-Net effectively estimates causal effects for both discrete and continuous treatments.

The framework extends prior proxy-based identifiability results to more complex scenarios.

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.