发表机构
Sapienza University of Rome（罗马第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出逆互谱神经网络（iCSNN），利用逆互谱密度矩阵作为移位算子，捕捉多元时间序列的频率条件依赖，并通过联合学习优化，在合成数据上超越多种基线。
AI 中文摘要
协方差神经网络及其扩展已成为处理多元数据的有效工具，它们直接从二阶统计量中导出图移位算子。然而，这些架构是为独立同分布观测设计的，并未完全捕捉多元时间序列中时间依赖与跨变量依赖的联合结构。在本工作中，我们引入了逆互谱神经网络（iCSNNs），一类用于平稳多元时间序列的图神经网络，其移位算子是逆互谱密度（iCSD）矩阵。这些算子编码了变量间特定频率的条件关系，利用了谱表示定理提供的分解。利用谱平滑性，频率被分组为共享单一iCSD算子的频带，从而产生一个紧凑的参数化，保留了过程的频率依赖结构。我们进一步提出了一种联合学习程序，以同时估计傅里叶域依赖结构和iCSNN参数，使iCSD算子适应下游任务。在合成数据上测试时，iCSNN优于来自不同方法论家族的基线方法。
英文摘要
CoVariance Neural Networks and their extensions have emerged as effective tools for processing multivariate data, deriving graph shift operators directly from second-order statistics. These architectures, however, are designed for independent and identically distributed observations and do not fully capture the joint structure of temporal and cross-variable dependencies in multivariate time series. In this work, we introduce Inverse Cross-Spectral Neural Networks (iCSNNs), a class of graph neural networks for stationary multivariate time series whose shift operators are the inverse cross-spectral density (iCSD) matrices. These operators encode frequency-specific conditional relationships among variables, exploiting the decomposition provided by the spectral representation theorem. Leveraging spectral smoothness, frequencies are grouped into bands sharing a single iCSD operator, yielding a compact parametrisation that retains the frequency-dependent structure of the process. We further propose a joint learning procedure to estimate both the Fourier-domain dependence structure and the iCSNN parameters, adapting the iCSD operators to the downstream task. When tested on synthetic data, iCSNN outperforms baselines from different methodological families.
