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 processed
in a network of multiple interacting dynamical systems into meaningful elements of computation
that quantify the information generated in a target system, stored in it, transferred to it from one or
more source systems, and modified in a synergistic or redundant way. The concepts of information
transfer and modification have been recently formulated in the context of linear parametric modeling
of vector stochastic processes, linking them to the notion of Granger causality and providing efficient
tools 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 estimation
problems which emerge, in the case of low ratio between data points available and the number of
time 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 the
Least Absolute Shrinkage and Selection Operator (LASSO), prior to computation of the measures of
information transfer and information modification. First, simulating networks of several coupled
Gaussian systems with complex interactions, we show that the LASSO regression allows, also in
conditions of data paucity, to accurately reconstruct both the underlying network topology and the
expected patterns of information transfer. Then we apply the proposed VAR-SS-LASSO approach to
a challenging application context, i.e., the study of the physiological network of brain and peripheral
interactions probed in humans under different conditions of rest and mental stress. Our results,
which document the possibility to extract physiologically plausible patterns of interaction between
the cardiovascular, respiratory and brain wave amplitudes, open the way to the use of our new
analysis tools to explore the emerging field of Network Physiology in several practical applications