# Scalable Amortized Variational Inference for Non-Poisson Buy-'Til-You-Die Models

arXiv: https://arxiv.org/abs/2608.19022 · HTML: https://mlsanity.com/paper/2608.19022/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 90 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 24 of 24)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Autoencoding Variational Inference For Topic Models](https://mlsanity.com/paper/1703.01488/) (2017)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Neural Point Process for Learning Spatiotemporal Event Dynamics](https://mlsanity.com/paper/2112.06351/) (2021)
- [Inference Compilation and Universal Probabilistic Programming](https://mlsanity.com/paper/1610.09900/) (2016)
- [WHAI: Weibull Hybrid Autoencoding Inference for Deep Topic Modeling](https://mlsanity.com/paper/1803.01328/) (2018)
- [Amortized Variational Inference: When and Why?](https://mlsanity.com/paper/2307.11018/) (2023)
- [Bayesian Attention Belief Networks](https://mlsanity.com/paper/2106.05251/) (2021)
- [Sawtooth Factorial Topic Embeddings Guided Gamma Belief Network](https://mlsanity.com/paper/2107.02757/) (2021)
- [Forward Amortized Inference for Likelihood-Free Variational Marginalization](https://mlsanity.com/paper/1805.11542/) (2018)
- [Count Models Based on Weibull Interarrival Times](https://mlsanity.com/paper/1307.5759/) (2013)
- [A Variational Autoencoder for Probabilistic Non-Negative Matrix Factorisation](https://mlsanity.com/paper/1906.05912/) (2019)
- [Complex Contagion of Campaign Donations](https://mlsanity.com/paper/1601.07679/) (2016)
- [Scalable Weibull Graph Attention Autoencoder for Modeling Document Networks](https://mlsanity.com/paper/2410.09696/) (2024)
- [CLVAE: A Variational Autoencoder for Long-Term Customer Revenue Forecasting](https://mlsanity.com/paper/2604.22636/) (2026)

## Abstract (arXiv)

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.