# Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks

arXiv: https://arxiv.org/abs/2208.05908 · HTML: https://mlsanity.com/paper/2208.05908/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 11 Aug 2022.

## Builds on (most cited first, 21 of 21)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Predicting Citywide Crowd Flows in Irregular Regions Using Multi-View Graph Convolutional Networks](https://mlsanity.com/paper/1903.07789/) (2019)
- [Contextualized Spatial-Temporal Network for Taxi Origin-Destination Demand Prediction](https://mlsanity.com/paper/1905.06335/) (2019)
- [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)
- [Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging](https://mlsanity.com/paper/2109.12144/) (2021)
- [Predicting origin-destination ride-sourcing demand with a spatio-temporal encoder-decoder residual multi-graph convolutional network](https://mlsanity.com/paper/1910.09103/) (2019)
- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Joint predictions of multi-modal ride-hailing demands: a deep multi-task multigraph learning-based approach](https://mlsanity.com/paper/2011.05602/) (2020)
- [Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filter](https://mlsanity.com/paper/1905.00406/) (2019)
- [Equality of opportunity in travel behavior prediction with deep neural networks and discrete choice models](https://mlsanity.com/paper/2109.12422/) (2021)
- [Multi-Modal Graph Interaction for Multi-Graph Convolution Network in Urban Spatiotemporal Forecasting](https://mlsanity.com/paper/1905.11395/) (2019)

## Built on by (most cited first, 29 of 29)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [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)
- [Graph Neural Networks for Road Safety Modeling: Datasets and Evaluations for Accident Analysis](https://mlsanity.com/paper/2311.00164/) (2023)
- [Uncertainty Quantification of Spatiotemporal Travel Demand with Probabilistic Graph Neural Networks](https://mlsanity.com/paper/2303.04040/) (2023)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Deep hybrid model with satellite imagery: how to combine demand modeling and computer vision for behavior analysis?](https://mlsanity.com/paper/2303.04204/) (2023)
- [Deep trip generation with graph neural networks for bike sharing system expansion](https://mlsanity.com/paper/2303.11977/) (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)
- [UQGNN: Uncertainty Quantification of Graph Neural Networks for Multivariate Spatiotemporal Prediction](https://mlsanity.com/paper/2508.08551/) (2025)
- [HealthMamba: An Uncertainty-aware Spatiotemporal Graph State Space Model for Effective and Reliable Healthcare Facility Visit Prediction](https://mlsanity.com/paper/2602.05286/) (2026)
- [Uncertainty-aware Predict-Then-Optimize Framework for Equitable Post-Disaster Power Restoration](https://mlsanity.com/paper/2508.04780/) (2025)
- [Uncertainty-Aware Crime Prediction With Spatial Temporal Multivariate Graph Neural Networks](https://mlsanity.com/paper/2408.04193/) (2024)
- [SAUC: Sparsity-Aware Uncertainty Calibration for Spatiotemporal Prediction with Graph Neural Networks](https://mlsanity.com/paper/2409.08766/) (2024)
- [XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting with High Volatility](https://mlsanity.com/paper/2310.09847/) (2023)
- [Conditional Prediction ROC Bands for Graph Classification](https://mlsanity.com/paper/2410.15239/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Activity-aware Human Mobility Prediction with Hierarchical Graph Attention Recurrent Network](https://mlsanity.com/paper/2210.07765/) (2022)
- [Mitigating Spatial Disparity in Urban Prediction Using Residual-Aware Spatiotemporal Graph Neural Networks: A Chicago Case Study](https://mlsanity.com/paper/2501.11214/) (2025)
- [Spatio-Temporal Graph Neural Network for Urban Spaces: Interpolating Citywide Traffic Volume](https://mlsanity.com/paper/2505.06292/) (2025)
- [EnergyMamba: An Uncertainty-Aware Graph-Enhanced Selective State Space Model for Energy Consumption Prediction](https://mlsanity.com/paper/2606.00506/) (2026)
- [Recent Advances in Graph-based Machine Learning for Applications in Smart Urban Transportation Systems](https://mlsanity.com/paper/2306.01282/) (2023)
- [Spatio-temporal Prediction of Fine-Grained Origin-Destination Matrices with Applications in Ridesharing](https://mlsanity.com/paper/2503.24237/) (2025)
- [MSRFormer: Road Network Representation Learning using Multi-scale Feature Fusion of Heterogeneous Spatial Interactions](https://mlsanity.com/paper/2509.05685/) (2025)
- [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)
- [Vessel Traffic Flow Prediction on Sparse Data via Spatio-Temporal Graph Neural Networks with a Learnable Tweedie Head](https://mlsanity.com/paper/2606.07694/) (2026)
- [Inferring Urban Mobility Interactions from Aggregated Dynamics](https://mlsanity.com/paper/2609.07349/) (2026)

## Abstract (arXiv)

Origin-Destination (O-D) travel demand prediction is a fundamental challenge in transportation. Recently, spatial-temporal deep learning models demonstrate the tremendous potential to enhance prediction accuracy. However, few studies tackled the uncertainty and sparsity issues in fine-grained O-D matrices. This presents a serious problem, because a vast number of zeros deviate from the Gaussian assumption underlying the deterministic deep learning models. To address this issue, we design a Spatial-Temporal Zero-Inflated Negative Binomial Graph Neural Network (STZINB-GNN) to quantify the uncertainty of the sparse travel demand. It analyzes spatial and temporal correlations using diffusion and temporal convolution networks, which are then fused to parameterize the probabilistic distributions of travel demand. The STZINB-GNN is examined using two real-world datasets with various spatial and temporal resolutions. The results demonstrate the superiority of STZINB-GNN over benchmark models, especially under high spatial-temporal resolutions, because of its high accuracy, tight confidence intervals, and interpretable parameters. The sparsity parameter of the STZINB-GNN has physical interpretation for various transportation applications.