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, which 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 usefulness 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 then 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. Numerical results using real world data and synthetic data demonstrate that MDM exhibits competitive representational power and prediction performance compared to RUM and parametric models while being significantly faster in computation than RUM.

翻译：给定消费者在不同商品集合中所作选择的数据，一个关键挑战在于构建简约模型，用以描述和预测消费者选择行为，同时使其适用于定价和品类优化等规范性任务。边际分布模型（MDM）正是这样一种模型，它仅需设定随机效用的边际分布。受随机效用模型（RUM）类似特征刻画实用性的启发，本文旨在建立给定选择数据与MDM假设相容的充分必要条件。这一研究最终导出了MDM所能表征的选择概率集合的精确特征刻画。验证选择数据与该特征刻画的相容性等价于求解一个多项式规模线性规划问题。由于RUM的同类验证任务在计算上难以处理，且两种模型互不包含，MDM有助于在可处理性与表征能力之间取得平衡。进一步地，该特征刻画结合鲁棒优化方法，可用于对新出现的未知商品集合进行数据驱动的销量与收益预测。当选择数据与MDM假设不相容时，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。基于真实数据与合成数据的数值实验表明，与RUM及参数模型相比，MDM展现出具有竞争力的表征能力与预测性能，同时计算速度显著快于RUM。