The unit selection problem aims to identify objects, called units, that are most likely to exhibit a desired mode of behavior when subjected to stimuli (e.g., customers who are about to churn but would change their mind if encouraged). Unit selection with counterfactual objective functions was introduced relatively recently with existing work focusing on bounding a specific class of objective functions, called the benefit functions, based on observational and interventional data -- assuming a fully specified model is not available to evaluate these functions. We complement this line of work by proposing the first exact algorithm for finding optimal units given a broad class of causal objective functions and a fully specified structural causal model (SCM). We show that unit selection under this class of objective functions is $\text{NP}^\text{PP}$-complete but is $\text{NP}$-complete when unit variables correspond to all exogenous variables in the SCM. We also provide treewidth-based complexity bounds on our proposed algorithm while relating it to a well-known algorithm for Maximum a Posteriori (MAP) inference.

翻译：单元选择问题旨在识别对象（称为单元），这些对象在受到刺激时最可能表现出期望的行为模式（例如，即将流失但若被鼓励则会改变主意的客户）。基于反事实目标函数的单元选择方法近年来被提出，现有工作主要关注如何利用观察数据和干预数据来约束一类特定目标函数（称为效益函数），前提是不具备完全指定的模型来评估这些函数。我们通过提出首个精确算法来补充这一研究方向，该算法针对广泛类别的因果目标函数及完全指定的结构因果模型（SCM），寻找最优单元。我们发现，在此类目标函数下的单元选择问题是$\text{NP}^\text{PP}$-完全问题，但当单元变量对应SCM中所有外生变量时，该问题为NP-完全问题。我们还在算法复杂度上给出了基于树宽的上界，并将其与著名的最大后验（MAP）推理算法相关联。