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.
Revenue forecasts guide acquisition budgets, demand planning, and customer-based valuations, yet an aggregate forecast does not show whether change reflects acquisition, repeat purchasing, spending per order, or offsetting movements. Using weekly transaction panels for 966 companies in 25 industries, the authors develop the Customer-Based Multi-task Transformer (CBMT), which learns shared structure, retains separate primitive forecasts, and aligns their combination with downstream revenue. CBMT's mean total-sales error is 30% below the strongest representative established customer-base benchmark. It is also 2.65% below a Transformer that forecasts total sales directly, although the paired difference is not statistically significant (p=.222), and it beats separately estimated single-task forecasts for 74.3% of firms. CBMT's source MAE is lower in 23 of 24 benchmark-by-outcome comparisons, with the remaining difference not statistically distinguishable from zero. Firms whose primitives co-move more strongly are more likely to benefit from joint forecasting; selected-family scenario-3 comparisons are consistent with gains from shared representation and revenue alignment but remain diagnostic rather than causal. Accuracy deteriorates for all models when customer-base dynamics are highly volatile, and CBMT's advantage narrows there. Calibration-period routing rules do not improve average accuracy over always deploying CBMT. The results show how coordinated customer-base forecasts support revenue planning and when they warrant greater caution.
Muhammad Jawad Mufti, Omar Hammad, Haitham Saleh +1cs.LG
Customer churn prediction is a central task in customer analytics, particularly in non-contractual, pay-per-use service environments where disengagement is not explicitly observed and must be inferred from behavioral inactivity. Existing churn prediction approaches often rely on simplified temporal assumptions or single-point representations of customer behavior, which limit their ability to support continuous risk assessment, interpretability, and realistic deployment over time. This study proposes a temporally explicit churn prediction framework that models customer behavior using rolling behavioral windows, enabling repeated and instance-level churn risk estimation as customer activity evolves. Customer behavior is summarized within a fixed 30-day observation window, followed by a 30-day future churn evaluation window, ensuring a clear temporal separation between behavioral evidence and churn outcomes. The framework integrates feature-based and sequence-based learning approaches within a unified temporal design. The proposed approach is evaluated on a large-scale, real-world dataset from a non-contractual service platform. Empirical results demonstrate strong and stable predictive performance, with accuracy reaching 87.6% and ROC-AUC of 0.94 for the feature-based model, while the sequence-based model achieves recall as high as 96.1% by capturing temporal disengagement patterns. Evaluation on future unseen data confirms meaningful robustness under temporal shift, with accuracy remaining above 83% and ROC-AUC exceeding 0.91 without model retraining. Overall, the findings highlight that carefully designed temporal framing, rather than model complexity alone, is critical for achieving robust, interpretable, and deployment-ready churn prediction. The study provides a practical foundation for churn-oriented decision support in dynamic service environments.