A Nonparametric Approach with Marginals for Modeling Consumer Choice
利用边际分布建模消费者选择的非参数方法AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究消费者离散选择、随机效用边际分布和商品组合选择概率，最明确对应离散选择方向。
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利用边际分布建模消费者选择的非参数方法
- 研究问题
- 如何仅借助随机效用的边际分布描述消费者选择，检验观测选择概率是否符合模型，并预测未见商品组合的销售与收入？
- 方法与思路
- 作者刻画边际分布模型可表示的选择概率，以多项式规模线性规划检验相容性，并用稳健优化预测及混合整数凸规划拟合。
- 材料陈述的贡献
- 摘要称给出模型相容性的必要充分条件，指出其与随机效用模型互不包含，并报告具有竞争力的预测及更快计算表现。
- 阅读关注点
- 应核对概率刻画的条件、线性规划规模和输入表示，以及不相容数据的拟合目标、稳健预测边界与计算比较设计。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未核实；摘要未提供具体条件和数值，模型相容性及计算优势不保证所有组合预测准确。
原文摘要
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.