Accurate inference of functional connectivity, i.e. statistical relationships between brain regions, is critical for understanding brain function. Distinguishing between direct and indirect relationships is particularly important because this corresponds to identifying if brain regions are directly connected. Although solutions exist for linear Gaussian cases, we introduce a general framework that can address nonlinear and non-Gaussian cases, which are more relevant for neural data. Previous model-free methods have limited ability to identify indirect connections because of inadequate scaling with dimensionality. This poor scaling performance reduces the number of nodes, e.g. brain regions, that can be included in conditioning. By contrast, we develop model-free techniques quantifying (1) causality in the time domain and (2) coherence in the frequency domain that scale markedly better and thereby enable minimization of indirect functional connectivity.

Our first model-free framework, graphical directed information (GDI), enables pairwise directed functional connections to be conditioned on substantially more processes, producing a more accurate graph of direct causal functional connectivity in the time domain. GDI correctly inferred the circuitry of simulated arbitrary Gaussian, nonlinear, and conductance-based networks. Furthermore, GDI inferred many connections of a model of a central pattern generator (CPG) circuit in Aplysia, while also reducing many indirect connections. GDI can be used on a variety of scales and data types to provide accurate direct causal connectivity graphs.

Our second model-free framework, partial generalized coherence (PGC), expands prior work by allowing pairwise frequency coupling analyses to be conditioned on other processes, enabling model-free partial frequency coupling results. Our technique scales well with dimensionality, making it possible to condition on many processes and to even produce a partial frequency coupling graph. We analyzed both linear Gaussian and nonlinear simulated networks containing indirect frequency coupling which was correctly eliminated by PGC. We then performed PGC analysis of calcium recordings from the rodent olfactory bulb and quantified the dominant influence of breathing-related activity on the pairwise relationships between glomeruli for low frequencies. Overall, we introduce a technique capable of eliminating indirect frequency coupling in a model-free way.