Problem
Research questions and friction points this paper is trying to address.
Multivariate Time Series
Cross-spectral Density
Graph Neural Networks
Temporal Dependencies
Covariance Neural Networks
Inverse Cross-spectral Neural Networks for Multivariate Time Series
🤖 AI Summary
This study addresses the limitation of existing covariance neural networks in capturing joint temporal and inter-variable dependencies in multivariate time series. To this end, we propose the Inverse Cross-Spectral Neural Network, which introduces the inverse cross-spectral density matrix as a graph shift operator for the first time to encode frequency-specific conditional dependencies. Furthermore, a frequency band grouping strategy grounded in spectral smoothness is designed to achieve compact parameterization, enabling end-to-end joint optimization of spectral-domain structures and network parameters. Experiments on synthetic datasets demonstrate that the proposed method significantly outperforms various baseline models.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Inverse Cross-Spectral Neural Networks
Multivariate Time Series
Graph Neural Networks
Inverse Cross-Spectral Density
Joint Learning
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