使用泄漏工具变量界定因果效应
Bounding Causal Effects with Leaky Instruments
AI总结：
针对工具变量违反排他性准则导致因果效应估计偏差的问题，提出基于凸优化的泄漏工具变量部分识别方法，给出平均处理效应的尖锐界与不确定性推断。
摘要：
工具变量（IV）是在存在未观测混杂时估计因果效应的一种流行且强大的工具。然而，经典方法依赖于强假设，例如 exclusion criterion（排他性准则），该准则指出工具变量的效应必须完全通过处理来中介。这一假设在实践中往往不成立。当 IV 方法被不恰当地应用于不满足排他性准则的数据时，估计的因果效应可能会产生严重偏差。在本研究中，我们提出了一种新颖的解决方案，在给定一组 leaky instruments（泄漏工具变量）的情况下，对线性系统提供 partial（部分）识别；这些工具变量被允许在某种有限程度上违反排他性准则。我们推导了一个凸优化目标，在一些常见的信息泄漏形式下，为平均处理效应提供可证明的尖锐界，并实现了推断程序以量化所得估计的不确定性。我们在一系列模拟数据实验中展示了该方法，其表现优于当前最先进方法。配套的 R 包 leakyIV 可从 CRAN 获取。
英文摘要：
Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the $\textit{exclusion criterion}$, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides $\textit{partial}$ identification in linear systems given a set of $\textit{leaky instruments}$, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.
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