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