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Unified model selection approach based on minimum description length principle in Granger causality analysis

Granger causality analysis (GCA) provides a powerful tool for uncovering the patterns of brain connectivity mechanism using neuroimaging techniques. Conventional GCA applies two different mathematical theories in a two-stage scheme: (1) the Bayesian information criterion (BIC) or Akaike information criterion (AIC) for the regression model orders associated with endogenous and exogenous information; (2) F-statistics for determining the causal effects of exogenous variables. While specifying endogenous and exogenous effects are essentially the same model selection problem, this could produce different benchmarks in the two stages and therefore degrade the performance of GCA. In this course, we present a unified model selection approach based on the minimum description length (MDL) principle for GCA in the context of the general regression model paradigm. Compared with conventional methods, our approach emphasize that a single mathematical theory should be held throughout the GCA process. Under this framework, all candidate models within the model space might be compared freely in the context of the code length, without the need for an intermediate model. We illustrate its advantages over conventional two-stage GCA approach in a 3-node network and a 5-node network synthetic experiments. The unified model selection approach is capable of identifying the actual connectivity while avoiding the false influences of noise. More importantly, the proposed approach obtained more consistent results in a challenge fMRI dataset for causality investigation, mental calculation network under visual and auditory stimulus, respectively. The proposed approach has potential to accommodate other Granger causality representations in other function space. The comparison between different GC representations in different function spaces can also be naturally deal with in the framework.