提升地理数据预测的不确定性量化能力，无需额外计算开销。
Positional Encoder Graph Quantile Neural Networks for Geographic Data
- 融合位置编码图网络与分位数神经网络，实现灵活密度估计
- 在基准数据集上同时优于现有方法的准确率与不确定性评估
- 适合需要可靠置信度的空间建模任务，如气象预测
位置编码图神经网络（PE-GNN）是处理连续空间数据的有效模型，但其预测分布常校准不足，限制了对不确定性可靠量化的需求。本文提出位置编码图分位数神经网络（PE-GQNN），结合PE-GNN、分位数神经网络、部分单调神经块及事后校准技术。该框架可在极少假设目标分布的前提下，实现灵活且稳健的条件密度估计，并自然拓展至非空间任务。在基准数据集上的实验表明，PE-GQNN在预测准确性和不确定性量化方面均优于现有方法，且不增加额外计算成本。我们还提供了理论分析，揭示了该公式的重要特例，包括PE-GNN。
原文摘要 · Abstract (English)
Positional Encoder Graph Neural Networks (PE-GNNs) are among the most effective models for learning from continuous spatial data. However, their predictive distributions are often poorly calibrated, limiting their utility in applications that require reliable uncertainty quantification. We propose the Positional Encoder Graph Quantile Neural Network (PE-GQNN), a novel framework that combines PE-GNNs with Quantile Neural Networks, partially monotonic neural blocks, and post-hoc recalibration techniques. The PE-GQNN enables flexible and robust conditional density estimation with minimal assumptions about the target distribution, and it extends naturally to tasks beyond spatial data. Empirical results on benchmark datasets show that the PE-GQNN outperforms existing methods in both predictive accuracy and uncertainty quantification, without incurring additional computational cost. We also provide theoretical insights and identify important special cases arising from our formulation, including the PE-GNN.
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