用于保均值概率时间序列预测的两阶段奇数残差流
Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting
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中文总结 AI 辅助
针对概率预测中分布灵活性与均值准确性的权衡，提出两阶段奇数残差流框架，解耦均值预测与不确定性估计，在长短时域预测中同时实现最优确定性精度与出色密度估计性能。
中文摘要 AI 辅助
概率预测在风险敏感型决策中至关重要，尤其在长时域场景下。然而现有方法常面临分布灵活性与均值预测准确性之间的根本权衡：传统参数方法如均值方差估计（MVE）在联合负对数似然（NLL）目标下训练时，点预测精度可能下降；现代灵活生成模型如归一化流和扩散模型通常依赖代价高昂的蒙特卡洛采样，且可能产生次优均值估计。为解决该局限，我们提出两阶段奇数残差流（TORF）框架，将均值预测与不确定性估计解耦。第一阶段，预训练的确定性模型生成准确的均值预测；第二阶段，带严格奇数函数的受限归一化流学习围绕点预测的灵活残差分布，无需采样即可保证第一阶段的均值保留。实验表明，TORF在短、长时域预测中实现了最优的确定性精度（NMAE），同时提供了出色的密度估计性能（CRPS）。
英文摘要
Probabilistic forecasting plays an essential role in risk-sensitive decision-making, particularly in long-horizon settings. However, existing approaches often face a fundamental trade-off between distributional flexibility and accurate mean prediction. Traditional parametric methods, such as Mean Variance Estimation (MVE), can suffer from degraded point accuracy when trained under joint Negative Log-Likelihood (NLL) objectives, while modern-flexible generative models, including Normalizing Flows and Diffusion Models, typically rely on costly Monte Carlo sampling and may yield suboptimal mean estimates. To address this limitation, we propose Two-stage Odd Residual Flows (TORF), a framework that decouples mean forecasting from uncertainty estimation. In the first stage, a pre-trained deterministic model is used to produce an accurate mean prediction. In the second stage, a Restricted Normalizing Flow, with strictly odd functions learns flexible residual distributions around the point forecast, guaranteeing mean preservation from the first stage without sampling. Experiments show that TORF achieves state-of-the-art deterministic accuracy (NMAE) while providing strong density estimation performance (CRPS) on short and long-horizon forecasting.
