Generating Nonlinear Models of Functional Connectivity from Functional Magnetic Resonance Imaging Data with Genetic Programming

The brain is a nonlinear computational system; however, most methods employed in finding functional connectivity models with functional magnetic resonance imaging (fMRI) data produce strictly linear models - models incapable of truly describing the underlying system.Genetic programming is used to develop nonlinear models of functional connectivity from fMRI data. The study builds on previous work and observes that nonlinear models contain relationships not found by traditional linear methods. When compared to linear models, the nonlinear models contained fewer regions of interest and were never significantly worse when applied to data the models were fit to. Nonlinear models could generalize to unseen data from the same subject better than traditional linear models (intrasubject). Nonlinear models could not generalize to unseen data recorded from other subjects (intersubject) as well as the linear models, and reasons for this are discussed. This study presents the problem that many, manifestly different models in both operators and features, can effectively describe the system with acceptable metrics.

I. Introduction

The brain is a provably nonlinear computational system¹. Although the literature explicitly acknowledges this [1], [2], [3], [4], [5], [6], it is deemphasized or ignored, especially when working with functional Magnetic Resonance Imaging (fMRI) data. To better understand the brain as a computational system, researchers will create functional connectivity models of the brain — network relationship models of the statistical relationships between the spatially distributed regions of the brain during cognition. Despite being an intrinsically nonlinear system, almost all strategies for functional connectivity mod-eling use linear tools (Pearson Product-moment correlation coefficient, general linear model).