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.

介绍了一种名为空间 - 时间 Tweedie 图神经网络（STTD）的新方法，该方法应用 Tweedie 分布来参数化旅行需求分布，结合空间和时间嵌入来解决高分辨率 O-D 矩阵中的稀疏性和长尾特征，并有效提高了预测的精度和置信区间的准确性。

利用时空 Tweedie 模型进行 0 膨胀和长尾旅行需求预测的不确定性量化

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

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.

本研究针对细粒度的 OD 矩阵的稀疏性和不确定性问题，设计了一种基于空间 - 时间零膨胀负二项式图神经网络 (STZINB-GNN) 方法，通过扩散和时间卷积网络分析空间和时间相关性，并融合以参数化出行需求的概率分布，提高了预测精度和可解释性。实验结果在高空间 - 时间分辨率下表现出了该方法的优越性。