Balanced Spatial-Temporal Graph Structure Learning for Multivariate Time Series Forecasting: A Trade-off between Efficiency and Flexibility

Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for predefined graphs. However, current models do not incorporate the trade-off between efficiency and flexibility and make insufficient use of the information contained in time series in the design of graph structure learning algorithms. This paper alleviates the above issues by proposing Balanced Graph Structure Learning for Forecasting (BGSLF), a novel and effective deep learning model that joins graph structure learning and forecasting. Technically, BGSLF leverages the spatial information into convolutional operations and extracts temporal dynamics using the diffusion convolutional recurrent network. The proposed framework emphasizes the trade-off between efficiency and flexibility by introducing Multi-Graph Generation Network (MGN) and Graph Selection Module. In addition, a method named Smooth Sparse Unit (SSU) is designed to sparse the learned graph structures, which conforms to the sparse spatial correlations in the real world. Extensive experiments on four real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters. Our code is publicly available at https://github.com/onceCWJ/BGSLF.