Independent Vector Analysis with Multivariate Gaussian Model: a Scalable Method by Multilinear Regression

Joint blind source separation (JBSS) is a powerful tool for analyzing multiple linked datasets, distinguished by the key ability to exploit cross-dataset dependencies. Despite this ability generally improving overall estimation performance, joint decompositions also incur considerable computational costs, which can lead to intractable problems with hundreds or thousands of datasets. In this paper, we introduce an efficient method for large-scale JBSS by multilinear regression. We consider a model where out of all datasets, only a selected subset are first decomposed to provide regressors that sufficiently estimate sources across all datasets. These regressors define a per-source cost function that naturally extends independent vector analysis (IVA) with a multivariate Gaussian source prior (IVA-G), a powerful formulation for exploiting cross-dataset dependencies. Using simulated and real fMRI data, we demonstrate significant advantages of this method compared with other JBSS methods.