Statistical Perspective on Functional and Causal Neural Connectomics: A Comparative Study

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.

Statistical Perspective on Functional and Causal Neural Connectomics: The Time-Aware PC Algorithm

“…We define Y v as a windowed average of recordings over a duration of 50 msec: Y v = X v , v ∈ V , and averaging over different 50 msec windows with a gap of 50 msec between consecutive windows yields different Y v samples. This choice of Y v performs better than considering Y v to be neural recordings at time t: Y v = X v (t), v ∈ V , with different t giving different samples of Y v in previous work [6]. The TPC algorithm computes the rolled CFC-DPGM directly from the signals and, we use a maximum time-delay of interaction of 1 msec.…”

“…The CFC maps how neural activity flows within neural circuits, and provides the possibility for inference of neural pathways essential for brain functioning and behavior, such as sensory-motor-behavioral pathways [5]. Several approaches aim to infer CFC, such as Granger Causality (GC), Dynamic Causal Modeling (DCM), and Directed Probabilistic Graphical Models (DPGM), each having their applicability and challenges, as surveyed in [6]. GC obtains the directed functional connectivity from observed neural activity in a way that tells whether a neuron's past is predictive of another neuron's future, however it is unclear whether the prediction implies causation.…”

“…The utility of DPGM in obtaining CFC from neural data has been investigated in [6]. DPGM, applicable to i.i.d.…”

Consistent Causal Inference from Time Series with PC Algorithm and its Time-Aware Extension

“…, p} and edge u → v if X t1u → X t2v for some t 1 ≤ t 2 , where X t1u → X t2v are defined by a causal model with respect to a graph G with nodes X tu . Some common examples are in interventional, structural and Granger Causality [32,33], and applications in neurosciences [12,13], and econometrics [34]. We call G R as the Rolled Graph of G.…”

Statistical perspective on functional and causal neural connectomics: The Time-Aware PC algorithm

“…The CFC maps how neural activity flows within neural circuits, and provides the possibility for inference of neural pathways essential for brain functioning and behavior, such as sensory-motor-behavioral pathways [ 5 ]. Several approaches aim to infer CFC, such as Granger Causality (GC), Dynamic Causal Modeling (DCM), and Directed Probabilistic Graphical Models (DPGM), each having their applicability and challenges, as surveyed in [ 6 ]. GC obtains the directed functional connectivity from observed neural activity in a way that tells whether a neuron’s past is predictive of another neuron’s future, however it is unclear whether the prediction implies causation.…”