Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemics

2026-03-07

AI Summary

This work proposes a deep generative spatiotemporal regression method to address the unreliability of point forecasts and inadequate uncertainty quantification in epidemic prediction, which arise from complex spatiotemporal nonlinear dependencies. The approach introduces a lightweight deep generative architecture as a “distributional lens,” coupled with a pre-additive noise mechanism, enabling endogenous uncertainty modeling under low-frequency data and achieving, for the first time in spatiotemporal regression, intrinsic uncertainty quantification. Theoretical analysis establishes the geometric ergodicity and asymptotic stationarity of the model dynamics. Extensive experiments on six real-world epidemic datasets demonstrate that the method consistently outperforms existing benchmarks across multiple forecast horizons, significantly improving both point prediction accuracy and the reliability of probabilistic forecasts.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point forecasts generated by spatiotemporal models are unreliable in assigning uncertainty to future epidemic events. Probabilistic forecasting of epidemics is therefore crucial for providing the best or worst-case scenarios rather than a simple, often inaccurate, point estimate. We present deep spatiotemporal engression methods to generate accurate and reliable probabilistic forecasts on low-frequency epidemic datasets. The proposed methods act as distributional lenses, and out-of-sample probabilistic forecasts are generated by sampling from the trained models. Our frameworks encapsulate lightweight deep generative architectures, wherein uncertainty is quantified endogenously, driven by a pre-additive noise component during model construction. We establish geometric ergodicity and asymptotic stationarity of the spatiotemporal engression processes under mild assumptions on the network weights and pre-additive noise process. Comprehensive evaluations across six epidemiological datasets over three forecast horizons demonstrate that the proposal consistently outperforms several temporal and spatiotemporal benchmarks in both point and probabilistic forecasting. Additionally, we explore the explainability of the proposal to enhance the models'practical application for informed, timely public health interventions.

Problem

• probabilistic forecasting
• epidemic prediction
• spatiotemporal modeling
• uncertainty quantification
• nonlinear dynamics

Innovation

• deep generative spatiotemporal engression
• probabilistic forecasting
• pre-additive noise
• geometric ergodicity
• epidemic prediction