Forecasting intermittent time series with Gaussian Processes and Tweedie likelihood

2025-02-26

AI Summary

This paper addresses the challenge of probabilistic forecasting for intermittent count time series—characterized by zero-inflation and heavy-tailed distributions—which cause substantial modeling bias and poor high-quantile estimation in standard models (e.g., Poisson, negative binomial). We propose TweedieGP: the first Bayesian probabilistic forecasting framework that embeds a fully parametric Tweedie likelihood within a Gaussian process prior. Unlike conventional approaches, TweedieGP jointly models zero-generation and positive-count dynamics without restrictive simplifying assumptions, and supports end-to-end variational inference. Extensive experiments on thousands of real-world intermittent series demonstrate that TweedieGP significantly improves overall probabilistic forecast accuracy, as measured by the Continuous Ranked Probability Score (CRPS ↓), and substantially outperforms state-of-the-art methods—particularly for upper quantiles (e.g., 95th percentile and above). The framework thus delivers a more robust, interpretable, and principled Bayesian solution 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

• 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
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We introduce the use of Gaussian Processes (GPs) for the probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function and marginalizes it out when making predictions. We couple the latent GP variable with two types of forecast distributions: the negative binomial (NegBinGP) and the Tweedie distribution (TweedieGP). While the negative binomial has already been used in forecasting intermittent time series, this is the first time in which a fully parameterized Tweedie density is used for intermittent time series. We properly evaluate the Tweedie density, which is both zero-inflated and heavy tailed, avoiding simplifying assumptions made in existing models. We test our models on thousands of intermittent count time series. Results show that our models provide consistently better probabilistic forecasts than the competitors. In particular, TweedieGP obtains the best estimates of the highest quantiles, thus showing that it is more flexible than NegBinGP.

Problem

• Forecasting intermittent time series
• Using Gaussian Processes with Tweedie likelihood
• Evaluating zero-inflated, heavy-tailed distributions

Innovation

• Gaussian Processes for forecasting
• Tweedie likelihood first use
• Bayesian framework with uncertainty