Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting (2103.07719v1)

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 \textit{jointly} in the \textit{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/

Overview of "Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting"

This paper introduces the Spectral Temporal Graph Neural Network (StemGNN), designed to enhance the accuracy of multivariate time-series forecasting. The primary challenge in this domain is simultaneously capturing intra-series temporal correlations and inter-series dependencies, which the authors address by modeling these relationships jointly in the spectral domain.

Methodological Insights

StemGNN leverages a novel amalgamation of Graph Fourier Transform (GFT) and Discrete Fourier Transform (DFT) within an end-to-end framework. The GFT component captures inter-series correlations by transforming structural multivariate time-series into a representation where time-series for each node become linearly independent. Subsequently, DFT decomposes each time-series component into the frequency domain, facilitating the recognition of clear patterns that can be efficiently processed by convolution and sequential learning modules.

A significant innovation is the data-driven approach adopted by StemGNN to learn inter-series correlations autonomously, without reliance on pre-defined priors. This is achieved through a latent correlation layer using self-attention mechanisms, which infers the adjacency weight matrix from the data itself, allowing for flexible adaptation to any multivariate dataset.

Empirical Evaluation

Extensive empirical validation demonstrates that StemGNN achieves superior performance across various datasets, encompassing domains such as traffic, energy, and healthcare. Specifically, StemGNN outperforms existing models with an average improvement of 8.1% on Mean Absolute Error (MAE) and 13.3% on Root Mean Squared Error (RMSE). This is achieved without the need for pre-defined topological information, evidencing the model’s robustness and generalizability.

Theoretical and Practical Implications

From a theoretical perspective, the integration of GFT and DFT in the spectral domain presents a paradigm shift in modeling temporal and structural dependencies in time-series data. This approach not only enhances interpretability through clearer pattern representation but also promises more effective capturing of correlations and dependencies.

Practically, the potential applications of StemGNN are vast. In the context of traffic management, for instance, accurate forecasting can significantly improve urban planning and congestion mitigation. Similarly, in health monitoring or epidemic forecasting, like COVID-19, StemGNN's ability to capture complex interdependencies could aid in early intervention and policy formulation.

Future Directions

Future research could explore scalability improvements of StemGNN, particularly focusing on reducing computational complexity associated with large-scale graph operations. Additionally, investigating applications in sectors such as finance and supply chain could yield significant societal benefits.

In conclusion, StemGNN is a promising advancement in multivariate time-series forecasting, demonstrating effectiveness and adaptability without dependency on traditionally required predefined structures. Its application to real-world problems and potential facilitation of strategic decisions highlights its value in advancing the field of AI and machine learning.