  Modeling and identification of high-dimensional stochastic processes is
ubiquitous in many fields. In particular, there is a growing interest in
modeling stochastic processes with simple and interpretable structures. In many
applications, such as econometrics and biomedical sciences, it seems natural to
describe each component of that stochastic process in terms of few factor
variables, which are not accessible for observation, and possibly of few other
components of the stochastic process. These relations can be encoded in
graphical way via a structured dynamic network, referred to as "sparse plus
low-rank (S+L) network" hereafter. The problem of finding the S+L network as
well as the dynamic model can be posed as a system identification problem. In
this paper, we introduce two new nonparametric methods to identify dynamic
models for stochastic processes described by a S+L network. These methods take
inspiration from regularized estimators based on recently introduced kernels
(e.g. "stable spline", "tuned-correlated" etc.). Numerical examples show the
benefit to introduce the S+L structure in the identification procedure.
