# Uncertainty Quantification via Spatial-Temporal Tweedie Model for Zero-inflated and Long-tail Travel Demand Prediction

arXiv: https://arxiv.org/abs/2306.09882 · HTML: https://mlsanity.com/paper/2306.09882/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 16 Jun 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Contextualized Spatial-Temporal Network for Taxi Origin-Destination Demand Prediction](https://mlsanity.com/paper/1905.06335/) (2019)
- [Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2208.05908/) (2022)
- [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)
- [Dynamic Origin-Destination Matrix Prediction with Line Graph Neural Networks and Kalman Filter](https://mlsanity.com/paper/1905.00406/) (2019)
- [Uncertainty Quantification of Spatiotemporal Travel Demand with Probabilistic Graph Neural Networks](https://mlsanity.com/paper/2303.04040/) (2023)
- [CDGNet: A Cross-Time Dynamic Graph-based Deep Learning Model for Traffic Forecasting](https://mlsanity.com/paper/2112.02736/) (2021)

## Built on by (most cited first, 19 of 19)

- [Generalized Graph Prompt: Toward a Unification of Pre-Training and Downstream Tasks on Graphs](https://mlsanity.com/paper/2311.15317/) (2023)
- [TC-RAG:Turing-Complete RAG's Case study on Medical LLM Systems](https://mlsanity.com/paper/2408.09199/) (2024)
- [Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspective](https://mlsanity.com/paper/2412.09972/) (2024)
- [Utilize the Flow before Stepping into the Same River Twice: Certainty Represented Knowledge Flow for Refusal-Aware Instruction Tuning](https://mlsanity.com/paper/2410.06913/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [GCoT: Chain-of-Thought Prompt Learning for Graphs](https://mlsanity.com/paper/2502.08092/) (2025)
- [Uncertainty-Aware Probabilistic Graph Neural Networks for Road-Level Traffic Accident Prediction](https://mlsanity.com/paper/2309.05072/) (2023)
- [CaT-GNN: Enhancing Credit Card Fraud Detection via Causal Temporal Graph Neural Networks](https://mlsanity.com/paper/2402.14708/) (2024)
- [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)
- [Infinite-Horizon Graph Filters: Leveraging Power Series to Enhance Sparse Information Aggregation](https://mlsanity.com/paper/2401.09943/) (2024)
- [Alleviating Performance Disparity in Adversarial Spatiotemporal Graph Learning Under Zero-Inflated Distribution](https://mlsanity.com/paper/2504.00721/) (2025)
- [Causally-Aware Spatio-Temporal Multi-Graph Convolution Network for Accurate and Reliable Traffic Prediction](https://mlsanity.com/paper/2408.13293/) (2024)
- [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)
- [Rethinking Graph Domain Adaptation: A Spectral Contrastive Perspective](https://mlsanity.com/paper/2510.13254/) (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)
- [Structure-Aware Graph Multi-Task Learning for Dynamic Sparse OD Demand Prediction](https://mlsanity.com/paper/2606.21022/) (2026)
- [Inferring Urban Mobility Interactions from Aggregated Dynamics](https://mlsanity.com/paper/2609.07349/) (2026)

## Abstract (arXiv)

Understanding Origin-Destination (O-D) travel demand is crucial for transportation management. However, traditional spatial-temporal deep learning models grapple with addressing the sparse and long-tail characteristics in high-resolution O-D matrices and quantifying prediction uncertainty. This dilemma arises from the numerous zeros and over-dispersed demand patterns within these matrices, which challenge the Gaussian assumption inherent to deterministic deep learning models. To address these challenges, we propose a novel approach: the Spatial-Temporal Tweedie Graph Neural Network (STTD). The STTD introduces the Tweedie distribution as a compelling alternative to the traditional 'zero-inflated' model and leverages spatial and temporal embeddings to parameterize travel demand distributions. Our evaluations using real-world datasets highlight STTD's superiority in providing accurate predictions and precise confidence intervals, particularly in high-resolution scenarios.