Measuring Connectivity in Linear Multivariate Processes with Penalized Regression Techniques

Abstract

The evaluation of time and frequency domain measures of coupling and causality relies on the parametric representation of linear multivariate processes. The study of temporal dependencies among time series is based on the identification of a Vector Autoregressive model. This procedure is pursued through the definition of a regression problem solved by means of Ordinary Least Squares (OLS) estimator. However, its accuracy is strongly influenced by the lack of data points and a stable solution is not always guaranteed. To overcome this issue, it is possible to use penalized regression techniques. The aim of this work is to compare the behavior of OLS with different penalized regression methods used for a connectivity analysis in different experimental conditions. Bias, accuracy in the reconstruction of network structure and computational time were used for this purpose. Different penalized regressions were tested by means of simulated data implementing different ground-truth networks under different amounts of data samples available. Then, the approaches were applied to real electroencephalographic signals (EEG) recorded from a healthy volunteer performing a motor imagery task. Penalized regressions outperform OLS in simulation settings when few data samples are available. The application on real EEG data showed how it is possible to use features extracted from brain networks for discriminating between two tasks even in conditions of data paucity. Penalized regression techniques can be used for brain connectivity estimation and can be exploited for the computation of all the connectivity estimators based on linearity assumption overcoming the limitations imposed by the classical OLS.