用稳定分布建模极端波动时间序列的不确定性，效果优于现有方法。
DeepLévy: Learning Heavy-Tailed Uncertainty in Highly Volatile Time Series
- 通过特征函数差异最小化学习稳定分布混合，克服密度函数不可计算难题。
- 在真实与合成数据上，尾部风险指标显著优于当前最优模型。
- 适合需要精准捕捉极端事件风险的金融、气象等高波动场景。
重尾时间序列中的不确定性建模仍是深度概率预测模型的核心挑战，尤其在难以捕捉突发极端事件时表现不佳。尽管莱维稳定分布天然适用于非高斯行为建模，但其概率密度函数的不可解析性严重限制了基于似然的推断。为此，我们提出DeepLévy，一种通过最小化经验与参数特征函数差异来学习稳定分布混合的神经框架。DeepLévy引入混合机制，自适应地学习多成分下上下文相关的权重与参数，实现灵活的多步预测不确定性建模。在真实与合成数据集上的评估表明，DeepLévy在尾部风险指标上显著优于现有先进深度概率预测方法，尤其在极端波动条件下表现突出。
原文摘要 · Abstract (English)
Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While Lévy stable distributions offer a natural framework for modeling such non-Gaussian behaviors, the intractability of their probability density functions severely limits conventional likelihood-based inference. To address this, we introduce DeepLévy, a neural framework that learns mixtures of Lévy stable distributions by minimizing the discrepancy between empirical and parametric characteristic functions. DeepLévy incorporates a mixture mechanism that adaptively learns context-dependent weights and parameters over multiple Lévy components, enabling flexible multi-horizon uncertainty modeling. Evaluations on both real and synthetic datasets demonstrate that DeepLévy outperforms state-of-the-art deep probabilistic forecasting approaches in tail risk metrics, especially under extreme volatility.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。