# Quantifying Uncertainty in Deep Spatiotemporal Forecasting

arXiv: https://arxiv.org/abs/2105.11982 · HTML: https://mlsanity.com/paper/2105.11982/

## 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 (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Deep Exploration via Bootstrapped DQN](https://mlsanity.com/paper/1602.04621/) (2016)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors](https://mlsanity.com/paper/2005.07186/) (2020)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Why M Heads are Better than One: Training a Diverse Ensemble of Deep Networks](https://mlsanity.com/paper/1511.06314/) (2015)
- [Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction](https://mlsanity.com/paper/1803.01254/) (2018)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors](https://mlsanity.com/paper/1603.04733/) (2016)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Natural-Parameter Networks: A Class of Probabilistic Neural Networks](https://mlsanity.com/paper/1611.00448/) (2016)
- [Preserving Dynamic Attention for Long-Term Spatial-Temporal Prediction](https://mlsanity.com/paper/2006.08849/) (2020)
- [Quantifying Point-Prediction Uncertainty in Neural Networks via Residual Estimation with an I/O Kernel](https://mlsanity.com/paper/1906.00588/) (2019)
- [Bayesian Inference for Large Scale Image Classification](https://mlsanity.com/paper/1908.03491/) (2019)
- [Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions](https://mlsanity.com/paper/2006.13707/) (2020)
- [Quantifying Uncertainty in Discrete-Continuous and Skewed Data with Bayesian Deep Learning](https://mlsanity.com/paper/1802.04742/) (2018)
- [Covariance-Controlled Adaptive Langevin Thermostat for Large-Scale Bayesian Sampling](https://mlsanity.com/paper/1510.08692/) (2015)

## Built on by (most cited first, 30 of 48)

- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Spatial-Temporal Hypergraph Self-Supervised Learning for Crime Prediction](https://mlsanity.com/paper/2204.08587/) (2022)
- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants](https://mlsanity.com/paper/2211.10575/) (2022)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Uncertainty Quantification for Traffic Forecasting: A Unified Approach](https://mlsanity.com/paper/2208.05875/) (2022)
- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [Looks Too Good To Be True: An Information-Theoretic Analysis of Hallucinations in Generative Restoration Models](https://mlsanity.com/paper/2405.16475/) (2024)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Deep-Ensemble-Based Uncertainty Quantification in Spatiotemporal Graph Neural Networks for Traffic Forecasting](https://mlsanity.com/paper/2204.01618/) (2022)
- [A Hierarchical Spatial Transformer for Massive Point Samples in Continuous Space](https://mlsanity.com/paper/2311.04434/) (2023)
- [Robust Spatiotemporal Traffic Forecasting with Reinforced Dynamic Adversarial Training](https://mlsanity.com/paper/2306.14126/) (2023)
- [Machine Learning for Urban Air Quality Analytics: A Survey](https://mlsanity.com/paper/2310.09620/) (2023)
- [Full Bayesian Significance Testing for Neural Networks](https://mlsanity.com/paper/2401.13335/) (2024)
- [Uncertainty-aware Evaluation of Time-Series Classification for Online Handwriting Recognition with Domain Shift](https://mlsanity.com/paper/2206.08640/) (2022)
- [Online covariance estimation for stochastic gradient descent under Markovian sampling](https://mlsanity.com/paper/2308.01481/) (2023)
- [A Data-driven Region Generation Framework for Spatiotemporal Transportation Service Management](https://mlsanity.com/paper/2306.02806/) (2023)
- [DutyTTE: Deciphering Uncertainty in Origin-Destination Travel Time Estimation](https://mlsanity.com/paper/2408.12809/) (2024)
- [What's Behind the Mask: Estimating Uncertainty in Image-to-Image Problems](https://mlsanity.com/paper/2211.15211/) (2022)
- [Uncertainty-aware Traffic Prediction under Missing Data](https://mlsanity.com/paper/2309.06800/) (2023)
- [SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks](https://mlsanity.com/paper/2409.08766/) (2024)
- [Conformal Prediction for Time-series Forecasting with Change Points](https://mlsanity.com/paper/2509.02844/) (2025)
- [Fairness Uncertainty Quantification: How certain are you that the model is fair?](https://mlsanity.com/paper/2304.13950/) (2023)
- [GAR: Generalized Autoregression for Multi-Fidelity Fusion](https://mlsanity.com/paper/2301.05729/) (2023)

## 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.