Description length guided nonlinear unified Granger causality analysis

Most Granger causality analysis (GCA) methods still remain a two-stage scheme guided by different mathematical theories; both can actually be viewed as the same generalized model selection issues. Adhering to Occam's razor, we present a unified GCA (uGCA) based on the minimum description length principle. In this research, considering the common existence of nonlinearity in functional brain networks, we incorporated the nonlinear modeling procedure into the proposed uGCA method, in which an approximate representation of Taylor's expansion was adopted. Through synthetic data experiments, we revealed that nonlinear uGCA was obviously superior to its linear representation and the conventional GCA. Meanwhile, the nonlinear characteristics of high-order terms and cross-terms would be successively drowned out as noise levels increased. Then, in real fMRI data involving mental arithmetic tasks, we further illustrated that these nonlinear characteristics in fMRI data may indeed be drowned out at a high noise level, and hence a linear causal analysis procedure may be sufficient. Next, involving autism spectrum disorder patients data, compared with conventional GCA, the network property of causal connections obtained by uGCA methods appeared to be more consistent with clinical symptoms. Author Summary In previous studies on functional brain networks, we have proposed a linear unified Granger causality analysis (uGCA) method based on description length. Considering that functional brain image data is characterized by nonlinear nonstationary signals with complex long- and short-range correlations, we thus proposed a nonlinear uGCA method. Then, through simulated data experiments and logical self-consistent fMRI experiments, its causality identification performance was demonstrated to be superior to that of conventional GCA. At the same time, we further revealed the phenomenon that nonlinear high-order characteristics and nonlinear cross-characteristics were submerged successively at high noise levels, indicating that linear modeling procedures might be sufficient to cope with causality studies based on fMRI data.