用残差扩散模型提升时间序列概率预测的准确性与不确定性建模。
RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting
- 结合点预测与残差条件扩散，用双向Mamba网络建模时间依赖。
- 在8个数据集上实现更低的CRPS和更好覆盖率，推理速度快。
- 适合需要高精度不确定性估计的时间序列任务，如金融、能源预测。
概率时间序列预测（PTSF）在需要准确且具备不确定性感知的决策场景中至关重要。然而，现有方法在分布建模上表现不佳，且训练与评估指标存在不匹配。我们发现，将强点估计器与标准差等于其训练误差的零均值高斯分布相结合，即可达到最先进的性能。本文提出RDIT，一个即插即用的框架，融合点估计、残差条件扩散与双向Mamba网络。我们理论证明，通过调整至最优标准差可最小化连续排名概率评分（CRPS），并推导出实现分布匹配的算法。在八个多元时间序列数据集、多种预测时长上的实验表明，RDIT在降低CRPS、加快推理速度和提升覆盖率方面优于强基线。
原文摘要 · Abstract (English)
Probabilistic Time Series Forecasting (PTSF) plays a critical role in domains requiring accurate and uncertainty-aware predictions for decision-making. However, existing methods offer suboptimal distribution modeling and suffer from a mismatch between training and evaluation metrics. Surprisingly, we found that augmenting a strong point estimator with a zero-mean Gaussian, whose standard deviation matches its training error, can yield state-of-the-art performance in PTSF. In this work, we propose RDIT, a plug-and-play framework that combines point estimation and residual-based conditional diffusion with a bidirectional Mamba network. We theoretically prove that the Continuous Ranked Probability Score (CRPS) can be minimized by adjusting to an optimal standard deviation and then derive algorithms to achieve distribution matching. Evaluations on eight multivariate datasets across varied forecasting horizons demonstrate that RDIT achieves lower CRPS, rapid inference, and improved coverage compared to strong baselines.
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