Granger Causality for Ill‐Posed Problems: Ideas, Methods, and Application in Life Sciences

Abstract

Granger causality, based on a vector autoregressive model, is one of the most popular methods for uncovering the temporal dependencies between time series. The application of Granger causality to detect inference among a large number of variables (such as genes) requires a variable selection procedure. To address the lack of informative data, so-called regularization procedures are applied. In this chapter, we review current literature on Granger causality with Lasso regularization techniques for ill-posed problems (i.e., problems with multiple solutions). We discuss regularization procedures for inverse and ill-posed problems and present our recent approaches. These approaches are evaluated in a case study on gene regulatory networks reconstruction.

Information dynamics of brain–heart physiological networks during sleep

“…interactions can be entirely linear even for non-Gaussian processes). The role played by nonlinear dynamics should be more properly assessed, comparing the information measures based on linear regression with those computed either from the parameters of the particular multivariate distribution that fits the observed data [56], or from the utilization of model-free approaches [25,26,[57][58][59]. We aim to perform such a comparison in a future contribution, in order to determine the extent to which nonlinearities contribute to the generation of predictive information in brain-heart physiological networks during sleep.…”