  Learning a dynamical system from input/output data is a fundamental task in
the control design pipeline. In the partially observed setting there are two
components to identification: parameter estimation to learn the Markov
parameters, and system realization to obtain a state space model. In both
sub-problems it is implicitly assumed that standard numerical algorithms such
as the singular value decomposition (SVD) can be easily and reliably computed.
When trying to fit a high-dimensional model to data, for example in the
cyber-physical system setting, even computing an SVD is intractable. In this
work we show that an approximate matrix factorization obtained using randomized
methods can replace the standard SVD in the realization algorithm while
maintaining the non-asymptotic (in data-set size) performance and robustness
guarantees of classical methods. Numerical examples illustrate that for large
system models, this is the only method capable of producing a model.
