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High-dimensional time-series data are becoming increasingly abundant across awide variety of domains, spanning economics, neuroscience, particle physics,and cosmology. Fitting statistical models to such data, to enable parameterestimation and time-series prediction, is an important computational primitive.Existing methods, however, are unable to cope with the high-dimensional natureof these problems, due to both computational and statistical reasons. Wemitigate both kinds of issues via proposing an M-estimator for Reduced-rankSystem IDentification (MR. SID). A combination of low-rank approximations, L-1and L-2 penalties, and some numerical linear algebra tricks, yields anestimator that is computationally efficient and numerically stable. Simulationsand real data examples demonstrate the utility of this approach in a variety ofproblems. In particular, we demonstrate that MR. SID can estimate spatialfilters, connectivity graphs, and time-courses from native resolutionfunctional magnetic resonance imaging data. Other applications and extensionsare immediately available, as our approach is a generalization of the classicalKalman Filter-Smoother Expectation-Maximization algorithm.

An M-Estimator for Reduced-Rank High-Dimensional Linear Dynamical System Identification