Learning Network Granger Causality Using Graph Prior Knowledge

Abstract

Understanding the relationships among multiple entities through Granger causality graphs within multivariate time series data is crucial across various domains, including economics, finance, neurosciences, and genetics. Despite its broad utility, accurately estimating Granger causality graphs in high-dimensional scenarios with few samples remains a persistent chal- lenge. In response, this study introduces a novel model that leverages prior knowledge in the form of a noisy undirected graph to facilitate the learning of Granger causality graphs, while assuming sparsity. In this study we introduce an optimization problem, we propose to solve it with an alternative minimization approach and we proved the convergence of our fitting algorithm, highlighting its effectiveness. Furthermore, we present experimental results derived from both synthetic and real-world datasets. These results clearly illustrate the advantages of our proposed method over existing alternatives, particularly in situations where few samples are available. By incorporating prior knowledge and emphasizing spar- sity, our approach offers a promising solution to the complex problem of estimating Granger causality graphs in high-dimensional, data-scarce environments.