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. In this paper, distinct from conventional two-stage GCA, 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. In comparison with conventional methods, our approach emphasizes that model selection should follow a single mathematical theory during 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 illustrated 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 was capable of identifying the actual connectivity while avoiding the false influences of noise. More importantly, the proposed approach obtained more consistent results in a challenging fMRI dataset, in which visual/auditory stimulus with the same presentation design gives identical neural correlates of mental calculation, allowing one to evaluate the performance of different GCA methods. Moreover, 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.