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.

翻译：在科学应用中，从处理变量到结果变量的因果效应估计面临一个关键挑战：未观测混杂因素的存在。本研究假设我们观察到未观测混杂因素的一个单变量（可能为多维）代理变量，且已知该代理变量由混杂因素生成的机制。在该机制满足完备性假设（我们称之为“单代理因果效应可识别性”，简称SPICE）的条件下，我们证明因果效应是可识别的。我们将Kuroki与Pearl（2014）及Pearl（2010）基于代理变量的因果可识别性结论推广至高维情形、更灵活的函数关系及更广泛的分布族。此外，我们开发了基于神经网络的因果效应估计框架SPICE-Net，该框架适用于离散与连续两种处理变量类型。