Matrix-normal models for fMRI analysis

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, combining multi-subject datasets, and mapping between brain and behavior. 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 residual covariances. Our formalism permits novel model variants and improved estimation strategies for SRM and RSA using substantially fewer parameters. We empirically demonstrate advantages of our two new methods: for MN-RSA, we show up to 10x improvement in run-time, 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 the orthonormality constraint of SRM. We also provide a software prototyping tool for MN models that can flexibly reuse residual covariance assumptions and algorithms across models.