# Uncertainty Quantification of Spatiotemporal Travel Demand with Probabilistic Graph Neural Networks

arXiv: https://arxiv.org/abs/2303.04040 · HTML: https://mlsanity.com/paper/2303.04040/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 17 of 17)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [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)
- [Sparse Graph Attention Networks](https://mlsanity.com/paper/1912.00552/) (2019)
- [How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Survey](https://mlsanity.com/paper/2005.11691/) (2020)
- [Short-Term Forecasting of Passenger Demand under On-Demand Ride Services: A Spatio-Temporal Deep Learning Approach](https://mlsanity.com/paper/1706.06279/) (2017)
- [Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems](https://mlsanity.com/paper/1808.08798/) (2018)
- [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)
- [Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filter](https://mlsanity.com/paper/1905.00406/) (2019)
- [A Novel Regression Loss for Non-Parametric Uncertainty Optimization](https://mlsanity.com/paper/2101.02726/) (2021)

## Built on by (most cited first, 12 of 12)

- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Uncertainty Quantification via Spatial-Temporal Tweedie Model for Zero-inflated and Long-tail Travel Demand Prediction](https://mlsanity.com/paper/2306.09882/) (2023)
- [ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networks](https://mlsanity.com/paper/2305.06480/) (2023)
- [Uncertainty-Aware Probabilistic Graph Neural Networks for Road-Level Traffic Accident Prediction](https://mlsanity.com/paper/2309.05072/) (2023)
- [Uncertainty-aware Traffic Prediction under Missing Data](https://mlsanity.com/paper/2309.06800/) (2023)
- [Fairness-Enhancing Vehicle Rebalancing in the Ride-hailing System](https://mlsanity.com/paper/2401.00093/) (2023)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Independent Mobility GPT (IDM-GPT): A Self-Supervised Multi-Agent Large Language Model Framework for Customized Traffic Mobility Analysis Using Machine Learning Models](https://mlsanity.com/paper/2502.18652/) (2025)
- [T-STAR: A Context-Aware Transformer Framework for Short-Term Probabilistic Demand Forecasting in Dock-Based Shared Micro-Mobility](https://mlsanity.com/paper/2602.06866/) (2026)
- [Advancing Transportation Mode Share Analysis with Built Environment: Deep Hybrid Models with Urban Road Network](https://mlsanity.com/paper/2405.14079/) (2024)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [Quantile-Free Uncertainty Quantification in Graph Neural Networks](https://mlsanity.com/paper/2605.04847/) (2026)

## Abstract (arXiv)

Recent studies have significantly improved the prediction accuracy of travel demand using graph neural networks. However, these studies largely ignored uncertainty that inevitably exists in travel demand prediction. To fill this gap, this study proposes a framework of probabilistic graph neural networks (Prob-GNN) to quantify the spatiotemporal uncertainty of travel demand. This Prob-GNN framework is substantiated by deterministic and probabilistic assumptions, and empirically applied to the task of predicting the transit and ridesharing demand in Chicago. We found that the probabilistic assumptions (e.g. distribution tail, support) have a greater impact on uncertainty prediction than the deterministic ones (e.g. deep modules, depth). Among the family of Prob-GNNs, the GNNs with truncated Gaussian and Laplace distributions achieve the highest performance in transit and ridesharing data. Even under significant domain shifts, Prob-GNNs can predict the ridership uncertainty in a stable manner, when the models are trained on pre-COVID data and tested across multiple periods during and after the COVID-19 pandemic. Prob-GNNs also reveal the spatiotemporal pattern of uncertainty, which is concentrated on the afternoon peak hours and the areas with large travel volumes. Overall, our findings highlight the importance of incorporating randomness into deep learning for spatiotemporal ridership prediction. Future research should continue to investigate versatile probabilistic assumptions to capture behavioral randomness, and further develop methods to quantify uncertainty to build resilient cities.