Learning Sparse and Continuous Graph Structures for Multivariate Time Series Forecasting

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 pre-defined graphs. However, most current models do not incorporate the trade-off between effectiveness and flexibility and lack the guidance of domain knowledge in the design of graph learning algorithms. Besides, they have issues generating sparse graph structures, which pose challenges to end-to-end learning. In this paper, we propose Learning Sparse and Continuous Graphs for Forecasting (LSCGF), a novel deep learning model that joins graph learning and forecasting. Technically, LSCGF leverages the spatial information into convolutional operation and extracts temporal dynamics using the diffusion convolution recurrent network. At the same time, we propose a brand new method named Smooth Sparse Unit (SSU) to learn sparse and continuous graph adjacency matrix. Extensive experiments on three real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters.