Sparsity exploitation via discovering graphical models in multi-variate
  time-series forecasting
Ngoc-Dung Do Truong Son Hy Duy Khuong Nguyen
Graph neural networks (GNNs) have been widely applied in multi-variate
time-series forecasting (MTSF) tasks because of their capability in capturing
the correlations among different time-series. These graph-based learning
approaches improve the forecasting performance by discovering and understanding
the underlying graph structures, which represent the data correlation. When the
explicit prior graph structures are not available, most existing works cannot
guarantee the sparsity of the generated graphs that make the overall model
computational expensive and less interpretable. In this work, we propose a
decoupled training method, which includes a graph generating module and a GNNs
forecasting module. First, we use Graphical Lasso (or GraphLASSO) to directly
exploit the sparsity pattern from data to build graph structures in both static
and time-varying cases. Second, we fit these graph structures and the input
data into a Graph Convolutional Recurrent Network (GCRN) to train a forecasting
model. The experimental results on three real-world datasets show that our
novel approach has competitive performance against existing state-of-the-art
forecasting algorithms while providing sparse, meaningful and explainable graph
structures and reducing training time by approximately 40%. Our PyTorch
implementation is publicly available at https://github.com/HySonLab/GraphLASSO