Discrete Graph Structure Learning for Forecasting Multiple Time Series
This work addresses the challenge of improving multivariate time series forecasting for applications in fields like statistics and economics by integrating graph structure learning, though it appears incremental as it builds on existing graph neural network techniques.
The authors tackled the problem of forecasting multiple time series by learning an explicit graph structure simultaneously with a graph neural network when the graph is unknown, resulting in a method that is simpler, more efficient, and better performing than existing approaches, including a recent bilevel learning method and various deep or non-deep learning models.
Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.