On the Generalizability of Linear and Non-Linear Region of Interest-Based Multivariate Regression Models for fMRI Data

TL;DR

This study compares linear ridge regression and non-linear symbolic regression for multivariate analysis of task-based fMRI data, evaluating their generalizability and overfitting tendencies across different validation contexts.

Contribution

It provides a comparative analysis of linear and non-linear multivariate regression methods for fMRI data, highlighting their similar performance and overfitting risks.

Findings

Neither method is objectively superior in modeling fMRI data.

Both models show comparable generalization performance.

Overfitting tendencies are similar for linear and non-linear approaches.

Abstract

In contrast to conventional, univariate analysis, various types of multivariate analysis have been applied to functional magnetic resonance imaging (fMRI) data. In this paper, we compare two contemporary approaches for multivariate regression on task-based fMRI data: linear regression with ridge regularization and non-linear symbolic regression using genetic programming. The data for this project is representative of a contemporary fMRI experimental design for visual stimuli. Linear and non-linear models were generated for 10 subjects, with another 4 withheld for validation. Model quality is evaluated by comparing $R$ scores (Pearson product-moment correlation) in various contexts, including single run self-fit, within-subject generalization, and between-subject generalization. Propensity for modelling strategies to overfit is estimated using a separate resting state scan. Results suggest that neither method is objectively or inherently better than the other.