AI 中文总结
本文提出了适用于非泊松BTYD模型的可扩展摊销变分推断方法，该方法将交易假设为威布尔更新过程，在500万客户数据集上拟合仅需8分钟，还可扩展到协变量，显著提升了客户分析概率模型的效率。
AI 中文摘要
尽管现有的“购至死亡（Buy-'Til-You-Die, BTYD）”模型种类繁多，但几乎所有模型都依赖于交易服从泊松过程的便利假设。随着现代客户群体规模不断扩大且日益多样化，营销文献中存在一个重大缺口：能够解释数百万客户间交易时间模式异质性的BTYD模型。本文针对该缺口，引入了一类假设交易服从威布尔（Weibull）更新过程的模型，并基于摊销变分推断方法开发了一种高度可扩展的参数估计方案。该模型在包含500万在线零售客户的专有数据集上拟合仅需8分钟，而当前最先进方法估计需耗时3-4天。我们从理论和实证两方面表明，这种计算性能的显著提升并未伴随模型解释性或预测性能的明显变化。除可扩展性外，基于梯度的变分推断还使模型易于扩展到协变量，我们在包含400万2020年美国大选周期政治捐赠者的公开数据集上对此进行了演示。更广泛地说，本文展示了如何融合近似贝叶斯推断的最新进展与现代机器学习工具，以显著提升客户群体分析概率模型的效率和表达能力。
英文摘要
Despite the wide variety of existing Buy-`Til-You-Die (BTYD) models, nearly all rely upon the convenient assumption of transactions following a Poisson process. As modern customer bases grow larger and more diverse, a major gap in the marketing literature is BTYD models that can account for heterogeneity in timing patterns across millions of customers. This paper addresses that gap, introducing a family of models that assume transactions follow a Weibull renewal process and developing a highly scalable scheme for parameter estimation based on an amortized variational inference procedure. The proposed model fits to a proprietary dataset of 5 million online retail customers in 8 minutes which would take the current state-of-the-art an estimated 3-4 days. We show both theoretically and empirically that this dramatic improvement in computational performance comes with no appreciable change to either model interpretation or predictive performance. Beyond scalability, gradient-based variational inference also makes it easy to extend the model to covariates, which we illustrate on a public dataset of 4 million political donors during the 2020 US General election cycle. More generally, this paper demonstrates how to blend recent advances in approximate Bayesian inference and the tools of modern machine learning to dramatically improve the efficiency and expressivity of probabilistic models for customer base analysis.
