Discrete Graph Structure Learning for Forecasting Multiple Time Series

TL;DR

This paper introduces a method for learning graph structures in multivariate time series forecasting using neural networks, improving prediction accuracy and efficiency over existing approaches.

Contribution

It presents a novel approach to learn graph structures simultaneously with GNNs by optimizing a probabilistic graph model with differentiable sampling.

Findings

Outperforms bilevel learning approaches in efficiency and accuracy

Applicable to both deep and non-deep learning forecasting models

Simpler and more effective than existing graph learning methods

Abstract

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.