Nonparametric sparse estimators for identification of large scale linear systems

Identification of sparse high dimensional linear systems pose sever challenges to off-the-shelf techniques for system identification. This is particularly so when relatively small data sets, as compared to the number of inputs and outputs, have to be used. While input/output selection could be performed via standard selection techniques, computational complexity may however be a critical issue, being combinatorial in the number of inputs and outputs. Parametric estimation techniques which result in sparse models have nowadays become very popular and include, among others, the well known Lasso, LAR and their “grouped” versions Group Lasso and Group LAR. In this paper we introduce a new nonparametric technique which borrows ideas from a recently introduced Kernel estimator called “stable-spline” as well as from sparsity inducing priors which use l1 penalty. We compare the new method with a group LAR-type of algorithm applied to estimation of sparse Vector Autoregressive models and to standard PEM methods.