We study the problem of modeling purchase of multiple products and utilizing it to display optimized recommendations for online retailers and e-commerce platforms. We present a parsimonious multi-purchase family of choice models called the Bundle-MVL-K family, and develop a binary search based iterative strategy that efficiently computes optimized recommendations for this model. We establish the hardness of computing optimal recommendation sets, and derive several structural properties of the optimal solution that aid in speeding up computation. This is one of the first attempts at operationalizing multi-purchase class of choice models. We show one of the first quantitative links between modeling multiple purchase behavior and revenue gains. The efficacy of our modeling and optimization techniques compared to competing solutions is shown using several real world datasets on multiple metrics such as model fitness, expected revenue gains and run-time reductions. For example, the expected revenue benefit of taking multiple purchases into account is observed to be $\sim5\%$ in relative terms for the Ta Feng and UCI shopping datasets, when compared to the MNL model for instances with $\sim 1500$ products. Additionally, across $6$ real world datasets, the test log-likelihood fits of our models are on average $17\%$ better in relative terms. Our work contributes to the study multi-purchase decisions, analyzing consumer demand and the retailers optimization problem. The simplicity of our models and the iterative nature of our optimization technique allows practitioners meet stringent computational constraints while increasing their revenues in practical recommendation applications at scale, especially in e-commerce platforms and other marketplaces.

翻译：我们研究了多产品购买行为的建模问题，并利用该模型为在线零售商和电子商务平台展示优化推荐。我们提出了一种简洁的多品购买选择模型族——Bundle-MVL-K族，并开发了一种基于二分搜索的迭代策略，可高效计算该模型下的优化推荐。我们证明了计算最优推荐集的难度，并推导了最优解的若干结构性质，这些性质有助于加速计算。本研究是为数不多的将多品购买类选择模型付诸实践的早期尝试之一。我们首次展示了多品购买行为建模与收入增长之间的定量关联。通过多个真实数据集，在模型拟合度、预期收入提升和运行时间减少等多个指标上，验证了我们的建模与优化技术相比竞争方案的有效性。例如，在包含约1500个产品的Ta Feng和UCI购物数据集中，考虑多品购买带来的预期收入相对提升约为5%。此外，在6个真实数据集上，我们模型的测试对数似然拟合度平均相对提升了17%。我们的研究有助于理解多品购买决策、分析消费者需求以及零售商优化问题。模型的简洁性和优化技术的迭代特性，使得从业者能够在大规模实际推荐应用（尤其是电子商务平台和其他市场）中，在满足严格计算约束的同时提升收入。