Matrix-normal models for fMRI analysis
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by
Michael Shvartsman, Narayanan Sundaram, Mikio C. Aoi, Adam Charles,
Theodore C. Wilke, Jonathan D. Cohen
2017
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.
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