Reweighted nuclear norm regularization: A SPARSEVA approach

TL;DR

This paper introduces a computationally efficient method for high-order FIR and ARX model estimation using reweighted nuclear norm regularization within the SPARSEVA framework, employing PEC for tuning parameter selection.

Contribution

It proposes a novel combination of reweighted nuclear norm regularization with SPARSEVA and PEC to reduce computational cost in high-order model estimation.

Findings

The method achieves accurate model estimation with less computation.

Numerical examples validate the effectiveness of the proposed approach.

It closely aligns with cross-validation but is more efficient.

Abstract

The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.