In order to achieve unbiased and efficient estimators of causal effects from observational data, covariate selection for confounding adjustment becomes an important task in causal inference. Despite recent advancements in graphical criterion for constructing valid and efficient adjustment sets, these methods often rely on assumptions that may not hold in practice. We examine the properties of existing graph-free covariate selection methods with respect to both validity and efficiency, highlighting the potential dangers of producing invalid adjustment sets when hidden variables are present. To address this issue, we propose a novel graph-free method, referred to as CMIO, adapted from Mixed Integer Optimization (MIO) with a set of causal constraints. Our results demonstrate that CMIO outperforms existing state-of-the-art methods and provides theoretically sound outputs. Furthermore, we present a revised version of CMIO capable of handling the scenario in the absence of causal sufficiency and graphical information, offering efficient and valid covariate adjustments for causal inference.

翻译：为了从观测数据中获得无偏且高效的因果效应估计，协变量选择用于混杂调整成为因果推断中的重要任务。尽管近年来在基于图准则构建有效且高效调整集方面取得了进展，但这些方法通常依赖于实践中可能不成立的假设。我们检验了现有无图协变量选择方法在有效性和效率方面的性质，并强调了当存在隐藏变量时产生无效调整集的潜在风险。为解决这一问题，我们提出了一种新颖的无图方法，称为CMIO，它基于混合整数优化（MIO）并融入一组因果约束。我们的结果表明，CMIO优于现有最先进方法，并提供理论上可靠的输出。此外，我们提出了CMIO的修订版本，能够处理缺乏因果充分性和图信息的情况，为因果推断提供高效且有效的协变量调整。