Differentiating Granger Causal Influence and Stimulus-Related Information Flow

Anonymous

Keywords: Information Flow, Granger Causality, Interpreting Network Activity, Connectivity

Abstract: Information flow is becoming an increasingly popular term in the context of understanding neural circuitry, both in neuroscience and in Artificial Neural Networks. Granger causality has long been the tool of choice in the neuroscience literature for identifying functional connectivity in the brain, i.e., pathways along which information flows. However, there has been relatively little work on providing a fundamental theory for information flow, and as part of that, understanding whether Granger causality captures the intuitive direction of information flow in a computational circuit. Recently, Venkatesh et al. [2019] proposed a theoretical framework for identifying stimulus-related information paths in a computational graph. They also provided a counterexample showing that the direction of greater Granger causal influence can be opposite to that of information flow [Venkatesh and Grover, 2015]. Here, we reexamine and expand on this counterexample. In particular, we find that Granger Causal influence can be statistically insignificant in the direction of information flow, while being significant in the opposite direction. By examining the mutual- (and conditional-mutual-) information that each signal shares with the stimulus, we are able to gain a more nuanced understanding of the actual information flows in this system.