TSB-HB: A Hierarchical Bayesian Extension of the TSB Model for Intermittent Demand Forecasting

2025-11-16

AI Summary

Intermittent demand forecasting faces challenges including sparse observations, cold starts for new items, and product discontinuation. Classical methods (e.g., Croston, TSB) lack generative foundations, while deep learning models require large-scale data and suffer from poor interpretability. This paper proposes TSB-HB—a hierarchical Bayesian model that jointly models demand occurrence (via Beta-Binomial) and nonzero demand size (via Log-Normal), leveraging hierarchical priors to enable partial pooling across items. This design preserves item-level heterogeneity while enhancing robustness in estimating sparse demand sequences. TSB-HB delivers calibrated probabilistic forecasts and maintains strong interpretability. Evaluated on the UCI Online Retail dataset and an M5 subset, it significantly outperforms baselines—including Croston, SBA, and TSB—achieving substantial reductions in RMSE and RMSSE. These results demonstrate its generalizability and practical utility for intermittent demand forecasting.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

Problem

• Forecasting intermittent demand with sparse observations
• Addressing cold-start items and obsolescence issues
• Improving accuracy while maintaining model interpretability

Innovation

• Hierarchical Bayesian extension of TSB model
• Beta-Binomial distribution for demand occurrence
• Log-Normal distribution for demand sizes