# SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks

arXiv: https://arxiv.org/abs/2409.08766 · HTML: https://mlsanity.com/paper/2409.08766/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 13 Sep 2024.

## Builds on (most cited first, 27 of 27)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification](https://mlsanity.com/paper/2011.09588/) (2020)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [Post-hoc Uncertainty Learning using a Dirichlet Meta-Model](https://mlsanity.com/paper/2212.07359/) (2022)
- [Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2208.05908/) (2022)
- [Uncertainty Quantification for Traffic Forecasting: A Unified Approach](https://mlsanity.com/paper/2208.05875/) (2022)
- [Uncertainty Quantification via Spatial-Temporal Tweedie Model for Zero-inflated and Long-tail Travel Demand Prediction](https://mlsanity.com/paper/2306.09882/) (2023)
- [Recurrent Mixture Density Network for Spatiotemporal Visual Attention](https://mlsanity.com/paper/1603.08199/) (2016)
- [STUaNet: Understanding uncertainty in spatiotemporal collective human mobility](https://mlsanity.com/paper/2102.06027/) (2021)
- [MM-GNN: Mix-Moment Graph Neural Network towards Modeling Neighborhood Feature Distribution](https://mlsanity.com/paper/2208.07012/) (2022)
- [Building Calibrated Deep Models via Uncertainty Matching with Auxiliary Interval Predictors](https://mlsanity.com/paper/1909.04079/) (2019)
- [Adaptive Modeling of Uncertainties for Traffic Forecasting](https://mlsanity.com/paper/2303.09273/) (2023)
- [Joint Quantile Regression for Spatial Data](https://mlsanity.com/paper/1910.13119/) (2019)
- [Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity](https://mlsanity.com/paper/1610.07453/) (2016)

## Built on by (most cited first, 5 of 5)

- [UQGNN: Uncertainty Quantification of Graph Neural Networks for Multivariate Spatiotemporal Prediction](https://mlsanity.com/paper/2508.08551/) (2025)
- [GETS: Ensemble Temperature Scaling for Calibration in Graph Neural Networks](https://mlsanity.com/paper/2410.09570/) (2024)
- [Learning Multimodal Embeddings for Traffic Accident Prediction and Causal Estimation](https://mlsanity.com/paper/2512.02920/) (2025)
- [Harnessing Rich Multi-Modal Data for Spatial-Temporal Homophily-Embedded Graph Learning Across Domains and Localities](https://mlsanity.com/paper/2512.11178/) (2025)
- [Public transit gains and spatially uneven travel demand changes after NYC congestion pricing](https://mlsanity.com/paper/2606.17530/) (2026)

## Abstract (arXiv)

Quantifying uncertainty is crucial for robust and reliable predictions. However, existing spatiotemporal deep learning mostly focuses on deterministic prediction, overlooking the inherent uncertainty in such prediction. Particularly, highly-granular spatiotemporal datasets are often sparse, posing extra challenges in prediction and uncertainty quantification. To address these issues, this paper introduces a novel post-hoc Sparsity-awar Uncertainty Calibration (SAUC) framework, which calibrates uncertainty in both zero and non-zero values. To develop SAUC, we firstly modify the state-of-the-art deterministic spatiotemporal Graph Neural Networks (ST-GNNs) to probabilistic ones in the pre-calibration phase. Then we calibrate the probabilistic ST-GNNs for zero and non-zero values using quantile approaches.Through extensive experiments, we demonstrate that SAUC can effectively fit the variance of sparse data and generalize across two real-world spatiotemporal datasets at various granularities. Specifically, our empirical experiments show a 20% reduction in calibration errors in zero entries on the sparse traffic accident and urban crime prediction. Overall, this work demonstrates the theoretical and empirical values of the SAUC framework, thus bridging a significant gap between uncertainty quantification and spatiotemporal prediction.