分离均值预测与不确定性建模,实现高精度概率预测。
Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting

- 先用确定性模型精准预测均值,再用奇函数流建模残差分布。
- 在短/长时序预测上均达最优点预测(NMAE)和密度估计(CRPS)。
- 无需采样即可保证均值不变,适合风险敏感决策场景。
概率预测在长期决策中至关重要,但现有方法常面临分布灵活性与均值预测准确性之间的权衡。传统参数化方法如均值方差估计(MVE)在联合负对数似然(NLL)目标下点预测性能下降;现代生成模型如归一化流和扩散模型依赖昂贵的蒙特卡洛采样,且均值估计不优。为此,我们提出两阶段奇残差流(TORF),将均值预测与不确定性建模解耦:第一阶段使用预训练确定性模型生成精确均值预测;第二阶段采用仅含奇函数的受限归一化流,在点预测周围学习灵活残差分布,确保均值不变且无需采样。实验表明,TORF在短/长时序预测任务中同时达到最优的确定性准确率(NMAE)和密度估计性能(CRPS)。
原文摘要 · Abstract (English)
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.
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