Quantifying Uncertainty in Deep Spatiotemporal Forecasting
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Abstract (arXiv)
Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to generate probabilistic forecasts with confidence intervals is critical to risk assessment and decision making. Hence, a systematic study of uncertainty quantification (UQ) methods for spatiotemporal forecasting is missing in the community. In this paper, we describe two types of spatiotemporal forecasting problems: regular grid-based and graph-based. Then we analyze UQ methods from both the Bayesian and the frequentist point of view, casting in a unified framework via statistical decision theory. Through extensive experiments on real-world road network traffic, epidemics, and air quality forecasting tasks, we reveal the statistical and computational trade-offs for different UQ methods: Bayesian methods are typically more robust in mean prediction, while confidence levels obtained from frequentist methods provide more extensive coverage over data variations. Computationally, quantile regression type methods are cheaper for a single confidence interval but require re-training for different intervals. Sampling based methods generate samples that can form multiple confidence intervals, albeit at a higher computational cost.
Key facts. Cited by 48 papers in the map (data through 14 Oct 2026). Builds on 32 of its 71 references that are in the map. First posted on arXiv 25 May 2021.
Builds on
32 of 71 references.
References · 32
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- 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
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- 2019Bayesian Inference for Large Scale Image Classificationcited by 18
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Citing papers per year: 2022: 12; 2023: 17; 2024: 7; 2025: 9; 2026: 3.
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- 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
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- 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
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- 2023Robust Spatiotemporal Traffic Forecasting with Reinforced Dynamic Adversarial Trainingcited by 9
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- 2025RIPCN: A Road Impedance Principal Component Network for Probabilistic Traffic Flow Forecastingcited by 1
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- 2025Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification4 Nov 2025
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- 2025CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee17 Apr 2025
- 2025Towards An Efficient and Effective En Route Travel Time Estimation Framework5 Apr 2025
- 2025Topology-Aware Conformal Prediction for Stream Networks6 Mar 2025
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- 2024DutyTTE: Deciphering Uncertainty in Origin-Destination Travel Time Estimation23 Aug 2024
- 2024Enhancing Spatio-temporal Quantile Forecasting with Curriculum Learning: Lessons Learned18 Jun 2024
- 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models26 May 2024
- 2024Uncertainty in Graph Neural Networks: A Survey11 Mar 2024
- 2024Full Bayesian Significance Testing for Neural Networks24 Jan 2024
- 2023A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Space8 Nov 2023
- 2023Uncertainty Quantification of Deep Learning for Spatiotemporal Data: Challenges and Opportunities4 Nov 2023
- 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning26 Oct 2023
- 2023Graph Deep Learning for Time Series Forecasting24 Oct 2023
- 2023Machine Learning for Urban Air Quality Analytics: A Survey14 Oct 2023
- 2023Uncertainty-aware Traffic Prediction under Missing Data13 Sep 2023
- 2023A Comparative Study of Loss Functions: Traffic Predictions in Regular and Congestion Scenarios29 Aug 2023
- 2023Uncertainty Quantification for Image-based Traffic Prediction across Cities11 Aug 2023
- 2023Online covariance estimation for stochastic gradient descent under Markovian sampling3 Aug 2023
- 2023Robust Spatiotemporal Traffic Forecasting with Reinforced Dynamic Adversarial Training25 Jun 2023
- 2023A Data-driven Region Generation Framework for Spatiotemporal Transportation Service Management5 Jun 2023
- 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun 2023
- 2023Fairness Uncertainty Quantification: How certain are you that the model is fair?27 Apr 2023
- 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey25 Mar 2023
- 2023A Survey on Uncertainty Quantification Methods for Deep Learning26 Feb 2023
- 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models31 Jan 2023
- 2023GAR: Generalized Autoregression for Multi-Fidelity Fusion13 Jan 2023
- 2022Copula Conformal Prediction for Multi-step Time Series Forecasting6 Dec 2022
- 2022What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problems28 Nov 2022
- 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants19 Nov 2022
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- 2022A review of predictive uncertainty estimation with machine learning17 Sep 2022
- 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey8 Sep 2022
- 2022Towards Learning in Grey Spatiotemporal Systems: A Prophet to Non-consecutive Spatiotemporal Dynamics17 Aug 2022
- 2022Uncertainty Quantification for Traffic Forecasting: A Unified Approach11 Aug 2022
- 2022Uncertainty-aware Evaluation of Time-Series Classification for Online Handwriting Recognition with Domain Shift17 Jun 2022
- 2022Probabilistic Symmetry for Multi-Agent Dynamics4 May 2022
- 2022Spatial-Temporal Hypergraph Self-Supervised Learning for Crime Prediction18 Apr 2022
- 2022Deep-Ensemble-Based Uncertainty Quantification in Spatiotemporal Graph Neural Networks for Traffic Forecasting4 Apr 2022
- 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 109
- 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
- 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learningcited by 20
- 2024ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equationscited by 0
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- 2026Graph Representation via Elements of Discrete Morse and Cobordism Theoriescited by 0
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- 2025Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks29 Jun 2025
- 2024ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations2 Nov 2024
- 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning26 Oct 2023
- 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun 2023
- 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models31 Jan 2023
- 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
- 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 81
- 2022Spatial-Temporal Hypergraph Self-Supervised Learning for Crime Predictioncited by 39
- 2022A review of predictive uncertainty estimation with machine learningcited by 29
- 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 29
- 2023Graph Deep Learning for Time Series Forecastingcited by 26
- 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
- 2024Uncertainty in Graph Neural Networks: A Surveycited by 23
- 2022Uncertainty Quantification for Traffic Forecasting: A Unified Approachcited by 22
- 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Modelscited by 12
- 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
- 2025Relational Conformal Prediction for Correlated Time Seriescited by 11
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- 2026UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engression1 Apr 2026
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- 2025Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantification4 Nov 2025
- 2025Conformal Prediction for Time-series Forecasting with Change Points2 Sep 2025
- 2025Non-exchangeable Conformal Prediction for Temporal Graph Neural Networks2 Jul 2025
- 2025CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee17 Apr 2025
- 2025Towards An Efficient and Effective En Route Travel Time Estimation Framework5 Apr 2025
- 2025Topology-Aware Conformal Prediction for Stream Networks6 Mar 2025
- 2025Relational Conformal Prediction for Correlated Time Series13 Feb 2025
- 2024SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks13 Sep 2024
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