We study decision-making problems where data comprises points from a collection of binary polytopes, capturing aggregate information stemming from various combinatorial selection environments. We propose a nonparametric approach for counterfactual inference in this setting based on a representative agent model, where the available data is viewed as arising from maximizing separable concave utility functions over the respective binary polytopes. Our first contribution is to precisely characterize the selection probabilities representable under this model and show that verifying the consistency of any given aggregated selection dataset reduces to solving a polynomial-sized linear program. Building on this characterization, we develop a nonparametric method for counterfactual prediction. When data is inconsistent with the model, finding a best-fitting approximation for prediction reduces to solving a compact mixed-integer convex program. Numerical experiments based on synthetic data demonstrate the method's flexibility, predictive accuracy, and strong representational power even under model misspecification.

翻译：本研究探讨一类决策问题，其数据来源于一组二元多面体上的点集，这些点集捕捉了多种组合选择环境下产生的聚合信息。我们提出一种基于代表性主体模型的非参数化反事实推断方法，将可用数据视为在各二元多面体上最大化可分离凹效用函数的结果。我们的首要贡献是精确刻画了该模型下可表示的择概率特征，并证明验证任意给定聚合选择数据集的一致性可转化为求解一个多项式规模线性规划问题。基于此特征刻画，我们进一步开发了用于反事实预测的非参数方法。当数据与模型不一致时，寻找最佳拟合近似以进行预测可转化为求解一个紧凑的混合整数凸规划问题。基于合成数据的数值实验表明，该方法即使在模型设定错误的情况下仍具有优异的灵活性、预测精度和强大的表征能力。