Abstract
Representation of brain network interactions is fundamental to the translation of neural structure to brain function. As such, methodologies for mapping neural interactions into structural models, i.e., inference of functional connectome from neural recordings, are key for the study of brain networks. While multiple approaches have been proposed for functional connectomics based on statistical associations between neural activity, association does not necessarily incorporate causation. Additional approaches have been proposed to incorporate aspects of causality to turn functional connectomes into causal functional connectomes, however, these methodologies typically focus on specific aspects of causality. This warrants a systematic statistical framework for causal functional connectomics that defines the foundations of common aspects of causality. Such a framework can assist in contrasting existing approaches and to guide development of further causal methodologies. In this work, we develop such a statistical guide. In particular, we consolidate the notions of associations and representations of neural interaction, i.e., types of neural connectomics, and then describe causal modeling in the statistics literature. We particularly focus on the introduction of directed Markov graphical models as a framework through which we define the Directed Markov Property—an essential criterion for examining the causality of proposed functional connectomes. We demonstrate how based on these notions, a comparative study of several existing approaches for finding causal functional connectivity from neural activity can be conducted. We proceed by providing an outlook ahead regarding the additional properties that future approaches could include to thoroughly address causality.
Highlights
The term “connectome” typically refers to a network of neurons and their anatomical links, such as chemical and electrical synapses
The following is a list of acronyms used in this paper: Functional Connectivity (FC), Causal Functional Connectivity (CFC), Granger Causality (GC), Dynamic Causal Model (DCM), Directed Probabilistic Graphical Model (DPGM), Directed Markov Property (DMP), Functional Magnetic Resonance Imaging, Diffusion Tensor Imaging (DTI), Electroencephalography (EEG), Magnetoencephalography (MEG), Associative Functional Connectivity (AFC), Probabilistic Graphical Model (PGM), Markov Property (MP), Lateral geniculate nucleus (LGN), Visual cortex (VC), Superior colliculus (SC), Pulvinar (P), Central nucleus of the amygdala (CeA), paraventricular nucleus (PVN), hypothalamus-pituitaryadrenal axis (HPA), Directed Acyclic Graph (DAG), Peter Clark (PC), Greedy Equivalence Search (GES), Greedy Interventional Equivalence Search (GIES), Continuous Time Recurrent Neural Network (CTRNN), Accuracy (A), Sensitivity (S), True Positive (TP), False Positive (FP), True Negative (TN), False Negative (FN)
A causal model relates the cause and effect, rather than recording correlation in the data and allows the investigator to answer a variety of queries such as associational queries, abductive queries, and interventional queries
Summary
The term “connectome” typically refers to a network of neurons and their anatomical links, such as chemical and electrical synapses. We compare existing approaches for causal functional connectome inference, such as Granger Causality (GC), Dynamic Causal Modeling (DCM) and Directed Probabilistic Graphical Models (DPGM) based on these properties. The following is a list of acronyms used in this paper: Functional Connectivity (FC), Causal Functional Connectivity (CFC), Granger Causality (GC), Dynamic Causal Model (DCM), Directed Probabilistic Graphical Model (DPGM), Directed Markov Property (DMP), Functional Magnetic Resonance Imaging (fMRI), Diffusion Tensor Imaging (DTI), Electroencephalography (EEG), Magnetoencephalography (MEG), Associative Functional Connectivity (AFC), Probabilistic Graphical Model (PGM), Markov Property (MP), Lateral geniculate nucleus (LGN), Visual cortex (VC), Superior colliculus (SC), Pulvinar (P), Central nucleus of the amygdala (CeA), paraventricular nucleus (PVN), hypothalamus-pituitaryadrenal axis (HPA), Directed Acyclic Graph (DAG), Peter Clark (PC), Greedy Equivalence Search (GES), Greedy Interventional Equivalence Search (GIES), Continuous Time Recurrent Neural Network (CTRNN), Accuracy (A), Sensitivity (S), True Positive (TP), False Positive (FP), True Negative (TN), False Negative (FN)
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