Matrix-normal models for fMRI analysis

Multivariate analysis of fMRI data has bene- fited substantially from advances in machine learning. Most recently, a range of prob- abilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including identifying similarity pat- terns in neural data, combining multi-subject datasets, and mapping between brain and be- havior. 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 frame- work. 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 meth- ods can be written as instantiations of the same model, allowing us to generalize them to flexibly modeling structured noise covari- ances. Our formalism permits novel model variants and improved estimation strategies for SRM and RSA using substantially fewer parameters. We empirically demonstrate ad- vantages 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 prototyp- ing tool for MN models that can flexibly reuse noise covariance assumptions and algorithms across models.