mlsanityData to 7 Oct 2026

Uncertainty Quantification of Spatiotemporal Travel Demand with Probabilistic Graph Neural Networks

arXiv 2303.04040 ↗First posted 7 Mar 2023cs.LG stat.AP stat.MLcited by 12

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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.

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

Builds on

17 of 60 references.

References · 17

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  4. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  5. 2021A Survey of Uncertainty in Deep Neural Networkscited by 675
  6. 2015Weight Uncertainty in Neural Networkscited by 554
  7. 2018Deep Multi-View Spatial-Temporal Network for Taxi Demand Predictioncited by 162
  8. 2018High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approachcited by 117
  9. 2020Inductive Graph Neural Networks for Spatiotemporal Krigingcited by 90
  10. 2019Sparse Graph Attention Networkscited by 41
  11. 2020How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Surveycited by 38
  12. 2017Short-Term Forecasting of Passenger Demand under On-Demand Ride Services: A Spatio-Temporal Deep Learning Approachcited by 34
5 more
  1. 2018Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problemscited by 32
  2. 2022Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networkscited by 29
  3. 2022Uncertainty Quantification for Traffic Forecasting: A Unified Approachcited by 22
  4. 2019Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filtercited by 13
  5. 2021A Novel Regression Loss for Non-Parametric Uncertainty Optimizationcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 2; 2025: 3; 2026: 2.

12 papers.

  1. 2024Uncertainty in Graph Neural Networks: A Surveycited by 20
  2. 2023Uncertainty Quantification via Spatial-Temporal Tweedie Model for Zero-inflated and Long-tail Travel Demand Predictioncited by 19
  3. 2023ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networkscited by 8
  4. 2023Uncertainty-Aware Probabilistic Graph Neural Networks for Road-Level Traffic Accident Predictioncited by 8
  5. 2023Uncertainty-aware Traffic Prediction under Missing Datacited by 5
  6. 2023Fairness-Enhancing Vehicle Rebalancing in the Ride-hailing Systemcited by 3
  7. 2025Topology-Aware Conformal Prediction for Stream Networkscited by 3
  8. 2025Independent Mobility GPT (IDM-GPT): A Self-Supervised Multi-Agent Large Language Model Framework for Customized Traffic Mobility Analysis Using Machine Learning Modelscited by 2
  9. 2026T-STAR: A Context-Aware Transformer Framework for Short-Term Probabilistic Demand Forecasting in Dock-Based Shared Micro-Mobilitycited by 1
  10. 2024Advancing Transportation Mode Share Analysis with Built Environment: Deep Hybrid Models with Urban Road Networkcited by 0
  11. 2025CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guaranteecited by 0
  12. 2026Quantile-Free Uncertainty Quantification in Graph Neural Networkscited by 0