Matrix-normal models for fMRI analysis

TL;DR

This paper introduces a matrix-normal formalism that unifies various fMRI analysis methods, enabling flexible modeling, improved efficiency, and new variants, demonstrated through empirical advantages in runtime and accuracy.

Contribution

The paper presents a unified matrix-normal framework for multiple fMRI analysis methods, allowing for parameter reduction, new model variants, and improved estimation strategies.

Findings

MN-RSA achieves up to 10x faster runtime and 6x lower RMSE.

MN-SRM offers modest improvements in reconstruction and relaxes constraints.

The formalism enables flexible reuse of noise modeling assumptions and algorithms.

Abstract

Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity patterns in neural data (Representational Similarity Analysis and its empirical Bayes variant, RSA and BRSA; Intersubject Functional Connectivity, ISFC), combining multi-subject datasets (Shared Response Mapping; SRM), and mapping between brain and behavior (Joint Modeling). Although these methods share some underpinnings, they have been developed as distinct methods, with distinct algorithms and software tools. We show how the matrix-variate normal (MN) formalism can unify some of these methods into a single framework. In doing so, we gain the ability to reuse noise modeling assumptions, algorithms, and code across models. Our primary theoretical contribution shows how some of these methods can be written as instantiations of the same model, allowing us to generalize them to flexibly modeling structured noise covariances. Our formalism permits novel model variants and improved estimation strategies: in contrast to SRM, the number of parameters for MN-SRM does not scale with the number of voxels or subjects; in contrast to BRSA, the number of parameters for MN-RSA scales additively rather than multiplicatively in the number of voxels. We empirically demonstrate advantages of two new methods derived in the formalism: for MN-RSA, we show up to 10x improvement in runtime, up to 6x improvement in RMSE, and more conservative behavior under the null. For MN-SRM, our method grants a modest improvement to out-of-sample reconstruction while relaxing an orthonormality constraint of SRM. We also provide a software prototyping tool for MN models that can flexibly reuse noise covariance assumptions and algorithms across models.