Information Transfer in Linear Multivariate Processes Assessed through Penalized Regression Techniques: Validation and Application to Physiological Networks

The framework of information dynamics allows the dissection of the information processedin a network of multiple interacting dynamical systems into meaningful elements of computationthat quantify the information generated in a target system, stored in it, transferred to it from one ormore source systems, and modified in a synergistic or redundant way. The concepts of informationtransfer and modification have been recently formulated in the context of linear parametric modelingof vector stochastic processes, linking them to the notion of Granger causality and providing efficienttools for their computation based on the state–space (SS) representation of vector autoregressive(VAR) models. Despite their high computational reliability these tools still suffer from estimationproblems which emerge, in the case of low ratio between data points available and the number oftime series, when VAR identification is performed via the standard ordinary least squares (OLS).In this work we propose to replace the OLS with penalized regression performed through theLeast Absolute Shrinkage and Selection Operator (LASSO), prior to computation of the measures ofinformation transfer and information modification. First, simulating networks of several coupledGaussian systems with complex interactions, we show that the LASSO regression allows, also inconditions of data paucity, to accurately reconstruct both the underlying network topology and theexpected patterns of information transfer. Then we apply the proposed VAR-SS-LASSO approach toa challenging application context, i.e., the study of the physiological network of brain and peripheralinteractions probed in humans under different conditions of rest and mental stress. Our results,which document the possibility to extract physiologically plausible patterns of interaction betweenthe cardiovascular, respiratory and brain wave amplitudes, open the way to the use of our newanalysis tools to explore the emerging field of Network Physiology in several practical applications.