[論文レビュー] Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting

Defu Cao, Yujing Wang+9 more|arXiv (Cornell University)|Mar 13, 2021

Time Series Analysis and Forecasting参考文献 36被引用数 190

ひとこと要約

StemGNN は、スペクトル領域で inter-series correlations（系列間相関）と temporal dependencies（時系列依存性）を Graph Fourier Transform および Discrete Fourier Transform を用いて共同でモデル化し、事前定義されたトポロジーなしに最先端の multivariate time-series forecasting を達成します。

ABSTRACT

Multivariate time-series forecasting plays a crucial role in many real-world applications. It is a challenging problem as one needs to consider both intra-series temporal correlations and inter-series correlations simultaneously. Recently, there have been multiple works trying to capture both correlations, but most, if not all of them only capture temporal correlations in the time domain and resort to pre-defined priors as inter-series relationships. In this paper, we propose Spectral Temporal Graph Neural Network (StemGNN) to further improve the accuracy of multivariate time-series forecasting. StemGNN captures inter-series correlations and temporal dependencies \ extit{jointly} in the \ extit{spectral domain}. It combines Graph Fourier Transform (GFT) which models inter-series correlations and Discrete Fourier Transform (DFT) which models temporal dependencies in an end-to-end framework. After passing through GFT and DFT, the spectral representations hold clear patterns and can be predicted effectively by convolution and sequential learning modules. Moreover, StemGNN learns inter-series correlations automatically from the data without using pre-defined priors. We conduct extensive experiments on ten real-world datasets to demonstrate the effectiveness of StemGNN. Code is available at https://github.com/microsoft/StemGNN/

研究の動機と目的

• Motivate and tackle multivariate time-series forecasting by jointly modeling intra-series temporal patterns and inter-series correlations.
• Propose a spectral-domain neural architecture that integrates GFT and DFT to extract meaningful representations for forecasting.
• Enable automatic learning of inter-series relationships without relying on predefined topologies.
• Incorporate forecasting and backcasting in an end-to-end framework to enhance representation learning.

提案手法

• Introduce StemGNN, which applies Graph Fourier Transform to capture inter-series relations, followed by Discrete Fourier Transform to model temporal frequency patterns, then spectral-domain convolution and inverse transforms.
• Use Spe-Seq Cell to decompose each time-series in the frequency domain via DFT, 1D convolution, and GLU, enabling frequency-domain feature learning.
• Incorporate a latent correlation layer that learns inter-series dependencies from data through self-attention, avoiding predefined graphs.
• Stack two StemGNN blocks with residual connections in a Spectral Graph Convolution module, and employ forecasting and backcasting branches with a shared encoder.
• Train with a combined loss: forecasting loss (MSE/MAE) plus backcasting loss to improve representation quality.
• Adopt a rolling strategy for multi-step ahead prediction during inference.

実験結果

リサーチクエスチョン

• RQ1 Can inter-series correlations and temporal dependencies be effectively captured jointly in the spectral domain to improve forecasting accuracy?
• RQ2 Is automatic learning of inter-series relationships (latent graphs) superior to predefined topologies for multivariate forecasting?
• RQ3 Does a dual forecasting-backcasting objective improve representation power and predictive performance?
• RQ4 How does StemGNN perform across diverse real-world multivariate time-series datasets without relying on prior graphs?

主な発見

• StemGNN achieves state-of-the-art performance on nine public multivariate time-series benchmarks, outperforming baselines on average by notable margins.
• The latent correlation layer learns interpretable inter-series relationships without human-defined topology, often matching or exceeding expert-specified graphs.
• Ablation studies show that removing components such as the Spe-Seq Cell, GFT, DFT, residual connections, or backcasting degrades performance, underscoring their necessity.
• Visualization on traffic data demonstrates meaningful, geographically sensible learned correlations among sensors.
• In a COVID-19 case study, StemGNN accurately forecasts multi-week trends and reveals plausible inter-country dependencies among outbreak dynamics.