Given data on the choices made by consumers for different offer sets, a key challenge is to develop parsimonious models that describe and predict consumer choice behavior while being amenable to prescriptive tasks such as pricing and assortment optimization. The marginal distribution model (MDM) is one such model, that requires only the specification of marginal distributions of the random utilities. This paper aims to establish necessary and sufficient conditions for given choice data to be consistent with the MDM hypothesis, inspired by the utility of similar characterizations for the random utility model (RUM). This endeavor leads to an exact characterization of the set of choice probabilities that the MDM can represent. Verifying the consistency of choice data with this characterization is equivalent to solving a polynomial-sized linear program. Since the analogous verification task for RUM is computationally intractable and neither of these models subsumes the other, MDM is helpful in striking a balance between tractability and representational power. The characterization is convenient to be used with robust optimization for making data-driven sales and revenue predictions for new unseen assortments. When the choice data lacks consistency with the MDM hypothesis, finding the best-fitting MDM choice probabilities reduces to solving a mixed integer convex program. The results extend naturally to the case where the alternatives can be grouped based on the similarity of the marginal distributions of the utilities. Numerical experiments show that MDM provides better representational power and prediction accuracy than multinominal logit and significantly better computational performance than RUM.

翻译：基于消费者对不同选择集所做出的决策数据，开发既能描述和预测消费者选择行为、又适用于定价与品类组合优化等规范性任务的简约模型，是一项关键挑战。边际分布模型（MDM）正是这样一种模型，其仅需指定随机效用的边际分布。受随机效用模型（RUM）中类似特征化方法的实用性启发，本文旨在为给定选择数据与MDM假设的一致性建立充要条件。这一研究过程导出了MDM所能表示的选择概率集合的精确特征化描述。通过求解多项式规模的线性规划，即可验证选择数据与该特征化描述的一致性。由于RUM的类似验证任务在计算上难以处理，且两类模型互不包含，MDM在可计算性与表示能力之间取得了有效平衡。该特征化描述便于结合鲁棒优化方法，对未见过的全新品类进行数据驱动的销量与收益预测。当选择数据与MDM假设不一致时，寻找最佳拟合的MDM选择概率可转化为求解混合整数凸规划问题。若备选方案可根据效用边际分布的相似性进行分组，本文结论可自然推广至该情形。数值实验表明，MDM在表示能力与预测精度上均优于多项Logit模型，且计算性能显著优于RUM。