用谱分析提升多变量时间序列预测精度
Sonnet: Spectral Operator Neural Network for Multivariable Time Series Forecasting
- 引入可学习小波与科普曼算子，从频域建模变量关系
- 在47个任务中34项最优，平均MAE降低2.2%
- 适合需要捕捉复杂时序依赖的工业级预测场景
多变量时间序列预测方法可通过整合外生变量信息显著提升预测精度。由于能够捕捉长程序列依赖，变换器架构被广泛应用于各类时间序列模型中。然而，直接应用变换器往往难以有效建模变量间随时间变化的复杂关系。为此，我们提出一种新架构——谱算子神经网络（Sonnet）。Sonnet 对输入施加可学习的小波变换，并结合科普曼算子进行谱分析。其预测能力基于多变量相干注意力（MVCA），该操作利用谱相干性建模变量间的依赖关系。实证分析表明，Sonnet 在47个预测任务中有34项表现最佳，相较于最先进基线，平均均方绝对误差（MAE）降低2.2%。此外，我们还证明，MVCA可弥补普通注意力机制在多种深度学习模型中的不足，在最具挑战性的任务中平均降低MAE达10.7%。
原文摘要 · Abstract (English)
Multivariable time series forecasting methods can integrate information from exogenous variables, leading to significant prediction accuracy gains. The transformer architecture has been widely applied in various time series forecasting models due to its ability to capture long-range sequential dependencies. However, a naïve application of transformers often struggles to effectively model complex relationships among variables over time. To mitigate against this, we propose a novel architecture, termed Spectral Operator Neural Network (Sonnet). Sonnet applies learnable wavelet transformations to the input and incorporates spectral analysis using the Koopman operator. Its predictive skill relies on the Multivariable Coherence Attention (MVCA), an operation that leverages spectral coherence to model variable dependencies. Our empirical analysis shows that Sonnet yields the best performance on $34$ out of $47$ forecasting tasks with an average mean absolute error (MAE) reduction of $2.2\%$ against the most competitive baseline. We further show that MVCA can remedy the deficiencies of naïve attention in various deep learning models, reducing MAE by $10.7\%$ on average in the most challenging forecasting tasks.
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