Inferring time-varying brain connectivity graph based on a new method for link estimation

Causal interaction estimation among neuronal groups plays an important role in the assessment of brain functions. These directional relations can be best illustrated by means of graphical modeling which is a mathematical representation of a network. Here, we propose an efficient framework to derive a graphical model for the statistical analysis of multivariate processes from observed time series in a data-driven pipeline to explore the interregional brain interactions. A major part of this analysis is devoted to the graph link estimation, which is a measure capable of dealing with the multivariate analysis obstacles. In this paper, we use the Transfer Entropy (TE) measure and focus on its calculation that requires efficient estimation of high dimensional conditional probability distributions. Our method is based on the simplification of high dimensional parts of the conventional TE definition and especially devoted to the reduction of estimation dimension through searching for the most informative contents of the high dimensional parts. To this end, we exploit the causal Markov properties for time series graphs and prove that only a specified subset of involved variables plays an important role in multivariate TE estimation. We demonstrate the performance of our method for stationary processes using some numerical simulated examples as well as real neurophysiological data.