Identification of directed influence: Granger causality, Kullback-Leibler divergence, and complexity

Area of Science:

• Neuroscience
• Computational Neuroscience
• Brain Connectivity Analysis

Background:

• Understanding brain function relies on detecting causal interdependencies between activated brain areas using functional neuroimage time series.
• Current statistical methods for inferring directed influences in neuroimaging data are diverse and complex.

Purpose of the Study:

• To demonstrate that existing statistics for directed influence in functional neuroimage time series are fundamentally variants of a single underlying quantity.
• To provide a unified framework for understanding and analyzing directed brain connectivity.

Main Methods:

• Analysis of established statistical measures including directed transfer entropy, transinformation, Kullback-Leibler formulations, conditional mutual information, and Granger causality.
• Utilizing autoregressive modeling to identify the common underlying quantity as a likelihood ratio.
• Deriving the relationship between these measures and the complexity of directed influence.

Main Results:

• All current statistics for directed influence in functional neuroimage time series are shown to be variations of the same core quantity.
• This unifying quantity is identified as a likelihood ratio within autoregressive models.
• The framework establishes connections between Kullback-Leibler divergence, Granger causality, and directed influence complexity.

Conclusions:

• A unified theoretical framework is presented for analyzing directed influences in brain activity.
• This unification simplifies the interpretation of brain connectivity measures derived from neuroimaging data.
• The findings offer a more cohesive approach to understanding brain function through causal interdependencies.