Minimum-entropy causal inference and its application in brain network analysis

Identification of the causal relationship between multivariate time series is a ubiquitous problem in data science. Granger causality measure (GCM) and conditional Granger causality measure (cGCM) are widely used statistical methods for causal inference and effective connectivity analysis in neuroimaging research. Both GCM and cGCM have frequency-domain formulations that are developed based on a heuristic algorithm for matrix decompositions. The goal of this work is to generalize GCM and cGCM measures and their frequency-domain formulations by using a theoretic framework for minimum entropy (ME) estimation. The proposed ME-estimation method extends the classical theory of minimum mean squared error (MMSE) estimation for stochastic processes. It provides three formulations of cGCM that include Geweke's original time-domain cGCM as a special case. But all three frequency-domain formulations of cGCM are different from previous methods. Experimental results based on simulations have shown that one of the proposed frequency-domain cGCM has enhanced sensitivity and specificity in detecting network connections compared to other methods. In an example based on in vivo functional magnetic resonance imaging, the proposed frequency-domain measure cGCM can significantly enhance the consistency between the structural and effective connectivity of human brain networks.