Brain signal analysis improves by modeling complex noise patterns
Beyond Gaussian Assumptions: Distribution-Aware Channel Capacity for Effective Connectivity
Machine Learning
Summary
Estimating how different parts of the brain interact often assumes a simple type of noise called Gaussian noise, which can miss important details. The authors found that brain signals and their noise usually don’t follow this simple pattern. They created a new way to measure brain connectivity that considers these more complex noise patterns, resulting in more accurate insight into brain interactions. Their method uses advanced mathematical tools to better capture information flow in brain signals across different species and conditions.
What this means in practice
- •For neurotechnology developers: Improve brain-computer interface accuracy by modeling non-Gaussian noise in neural signals for better directed connectivity estimation.
- •For medical imaging analysts: Enhance interpretation of multimodal brain scans by applying distribution-aware connectivity measures to reveal detailed brain interactions.
Authors
Jianan Jian, Jacob Kang, Nurahmed Multezem, Benjamin Li, Nan Xu
Abstract
Effective-connectivity estimation from brain signals often relies on Gaussian residual modeling, which enables tractable estimation but can discard informative distributional structure and distort inferred directed interactions when empirical residuals are non-Gaussian. We show across multiple modalities, species, and experimental conditions that both brain signals and fitted channel residuals frequently deviate from Gaussianity. We therefore introduce a distribution-aware, information-theoretic measure of effective connectivity based on channel capacity under general residual distributions. To estimate the resulting capacity from empirical, potentially non-Gaussian residuals, we develop a dual-flow min-max estimator based on normalizing flows, in which a generator searches over admissible input distributions under a power constraint while an observer estimates output entropy. We provide a theoretical characterization of the estimator, showing that the observer objective recovers differential entropy up to a KL approximation term, that the formulation reduces to classical Gaussian capacity as a special case, and that residual entropy can alter achievable information rates beyond variance; game-gap and error analyses further characterize optimization and approximation sources. In brain-like simulations with known directed connectivity, Dual-flow achieves the highest AUROC and AUPRC across ten conditions spanning diverse network topologies, hidden drivers, feedback, and heterogeneous hemodynamics, compared with Gaussian capacity, Granger causality, VAR-LiNGAM, and GIMME. Applied to multimodal brain signals, the method reveals time- and condition-resolved directed interactions consistent with known neurobiological circuitry. Together, these results establish a principled distribution-aware framework for effective-connectivity estimation beyond Gaussian residual modeling.