提出无偏核求积法，精准评估时间序列概率预测模型性能。
Fixing the Pitfalls of Probabilistic Time-Series Forecasting Evaluation by Kernel Quadrature
- 用核求积构建无偏CRPS估计器，避免传统方法偏差。
- 在多个数据集上显著降低评估误差，提升模型排序准确性。
- 适合关注预测评估可靠性的研究人员与工程实践者。
尽管概率时间序列预测模型意义重大，其评估指标常涉及难以计算的积分。最常用的连续排名概率评分（CRPS）是严格适当的评分函数，但其计算需近似处理。我们发现，广泛使用的GluonTS库中的分位数估计器和概率加权矩近似均存在固有估计偏差。这些偏差导致近似结果粗糙，在CRPS值相近时造成模型性能排名失真。为此，本文引入核求积方法，采用无偏CRPS估计器并结合立方构造实现可扩展计算。实验表明，该方法在多个数据集上始终优于两种主流估算器。
原文摘要 · Abstract (English)
Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper scoring function; however, its computation requires approximation. We found that popular CRPS estimators--specifically, the quantile-based estimator implemented in the widely used GluonTS library and the probability-weighted moment approximation--both exhibit inherent estimation biases. These biases lead to crude approximations, resulting in improper rankings of forecasting model performance when CRPS values are close. To address this issue, we introduced a kernel quadrature approach that leverages an unbiased CRPS estimator and employs cubature construction for scalable computation. Empirically, our approach consistently outperforms the two widely used CRPS estimators.
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