Sparse Causal Discovery in Multivariate Time Series

TL;DR

This paper introduces a sparsity-promoting regularization method for causal discovery in multivariate time series using VAR models, improving the accuracy of identifying causal links.

Contribution

It proposes enforcing sparsity on groups of coefficients for each pair of time series using l1-l2 regularization, enhancing causal graph recovery.

Findings

Outperforms standard methods in simulated data

Achieves comparable results to statistical testing approaches

Efficient active set solver improves computational performance

Abstract

Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsity-promoting regularization. Along this line we here propose that sparsity should be enforced for the subgroups of coefficients that belong to each pair of time series, as the absence of a causal relation requires the coefficients for all time-lags to become jointly zero. Such behavior can be achieved by means of l1-l2-norm regularized regression, for which an efficient active set solver has been proposed recently. Our method is shown to outperform standard methods in recovering simulated causality graphs. The results are on par with a second novel approach which uses multiple statistical testing.