mlsanityData to 14 Oct 2026

Quantifying Uncertainty in Deep Spatiotemporal Forecasting

arXiv 2105.11982 ↗First posted 25 May 2021cs.AI cs.LG stat.APcited by 48

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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

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
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  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
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20 more
  1. 2017Concrete Dropoutcited by 227
  2. 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
  3. 2020Efficient and Scalable Bayesian Neural Nets with Rank-1 Factorscited by 171
  4. 2018Deep Multi-View Spatial-Temporal Network for Taxi Demand Predictioncited by 162
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  15. 2019Bayesian Inference for Large Scale Image Classificationcited by 18
  16. 2020Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functionscited by 18
  17. 2018Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learningcited by 13
  18. 2015Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Samplingcited by 10
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 12; 2023: 17; 2024: 7; 2025: 9; 2026: 3.

48 papers.

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  1. 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
  2. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 109
  3. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
  4. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 81
  5. 2022Spatial-Temporal Hypergraph Self-Supervised Learning for Crime Predictioncited by 39
  6. 2022A review of predictive uncertainty estimation with machine learningcited by 29
  7. 2022Copula Conformal Prediction for Multi-step Time Series Forecastingcited by 29
  8. 2023Graph Deep Learning for Time Series Forecastingcited by 26
  9. 2022Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constantscited by 24
  10. 2024Uncertainty in Graph Neural Networks: A Surveycited by 23
  11. 2022Uncertainty Quantification for Traffic Forecasting: A Unified Approachcited by 22
  12. 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learningcited by 20
36 more
  1. 2024Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Modelscited by 12
  2. 2022Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Surveycited by 11
  3. 2025Relational Conformal Prediction for Correlated Time Seriescited by 11
  4. 2022Deep-Ensemble-Based Uncertainty Quantification in Spatiotemporal Graph Neural Networks for Traffic Forecastingcited by 10
  5. 2023A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Spacecited by 10
  6. 2023Robust Spatiotemporal Traffic Forecasting with Reinforced Dynamic Adversarial Trainingcited by 9
  7. 2023Machine Learning for Urban Air Quality Analytics: A Surveycited by 8
  8. 2024Full Bayesian Significance Testing for Neural Networkscited by 8
  9. 2022Uncertainty-aware Evaluation of Time-Series Classification for Online Handwriting Recognition with Domain Shiftcited by 7
  10. 2023Online covariance estimation for stochastic gradient descent under Markovian samplingcited by 7
  11. 2023A Data-driven Region Generation Framework for Spatiotemporal Transportation Service Managementcited by 6
  12. 2024DutyTTE: Deciphering Uncertainty in Origin-Destination Travel Time Estimationcited by 6
  13. 2022What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problemscited by 5
  14. 2023Uncertainty-aware Traffic Prediction under Missing Datacited by 5
  15. 2024SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networkscited by 5
  16. 2025Conformal Prediction for Time-series Forecasting with Change Pointscited by 5
  17. 2023Fairness Uncertainty Quantification: How certain are you that the model is fair?cited by 4
  18. 2023GAR: Generalized Autoregression for Multi-Fidelity Fusioncited by 3
  19. 2025Topology-Aware Conformal Prediction for Stream Networkscited by 3
  20. 2025Towards An Efficient and Effective En Route Travel Time Estimation Frameworkcited by 3
  21. 2025Non-exchangeable Conformal Prediction for Temporal Graph Neural Networkscited by 3
  22. 2022Probabilistic Symmetry for Multi-Agent Dynamicscited by 2
  23. 2024Enhancing Spatio-temporal Quantile Forecasting with Curriculum Learning: Lessons Learnedcited by 2
  24. 2022Towards Learning in Grey Spatiotemporal Systems: A Prophet to Non-consecutive Spatiotemporal Dynamicscited by 1
  25. 2023Uncertainty Quantification for Image-based Traffic Prediction across Citiescited by 1
  26. 2023Uncertainty Quantification of Deep Learning for Spatiotemporal Data: Challenges and Opportunitiescited by 1
  27. 2025RIPCN: A Road Impedance Principal Component Network for Probabilistic Traffic Flow Forecastingcited by 1
  28. 2026UQ-SHRED: uncertainty quantification of shallow recurrent decoder networks for sparse sensing via engressioncited by 1
  29. 2022Time series quantile regression using random forestscited by 0
  30. 2023A Comparative Study of Loss Functions: Traffic Predictions in Regular and Congestion Scenarioscited by 0
  31. 2024ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equationscited by 0
  32. 2025CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guaranteecited by 0
  33. 2025Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networkscited by 0
  34. 2025Tackling Incomplete Data in Air Quality Prediction: A Bayesian Deep Learning Framework for Uncertainty Quantificationcited by 0
  35. 2026SafeImpute: Reliable Clinical Data Imputation via Conformal Selectioncited by 0
  36. 2026Graph Representation via Elements of Discrete Morse and Cobordism Theoriescited by 0