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

Time-series forecasting is an important task in both academic and industry,
which can be applied to solve many real forecasting problems like stock,
water-supply, and sales predictions. In this paper, we study the case of
retailers' sales forecasting on Tmall|the world's leading online B2C platform.
By analyzing the data, we have two main observations, i.e., sales seasonality
after we group different groups of retails and a Tweedie distribution after we
transform the sales (target to forecast). Based on our observations, we design
two mechanisms for sales forecasting, i.e., seasonality extraction and
distribution transformation. First, we adopt Fourier decomposition to
automatically extract the seasonalities for different categories of retailers,
which can further be used as additional features for any established regression
algorithms. Second, we propose to optimize the Tweedie loss of sales after
logarithmic transformations. We apply these two mechanisms to classic
regression models, i.e., neural network and Gradient Boosting Decision Tree,
and the experimental results on Tmall dataset show that both mechanisms can
significantly improve the forecasting results.

本文研究了 Tmall 上售货商销售预测的情况，发现销售具有季节性和 Tweedie 分布特征，为此提出了季节性提取和分布转换两种销售预测机制，并将其应用于神经网络和梯度提升决策树等回归模型，实验结果表明两种机制均能显著提高预测效果。