Sparse plus low rank network identification: A nonparametric approach

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.