Weighted SPICE: A Unifying Approach for Hyperparameter-Free Sparse Estimation

TL;DR

This paper introduces Weighted SPICE, a unifying, hyperparameter-free approach for sparse estimation that connects various existing methods and demonstrates its effectiveness in sparse regression and array processing.

Contribution

It unifies multiple hyperparameter-free sparse estimation methods under a single framework and establishes new theoretical connections among them.

Findings

Weighted SPICE effectively unifies LIKES, SLIM, and IAA methods.

The approach connects SPICE with l1-penalized LAD and square-root LASSO.

Experimental results show competitive performance in sparse regression and array processing.

Abstract

In this paper we present the SPICE approach for sparse parameter estimation in a framework that unifies it with other hyperparameter-free methods, namely LIKES, SLIM and IAA. Specifically, we show how the latter methods can be interpreted as variants of an adaptively reweighted SPICE method. Furthermore, we establish a connection between SPICE and the l1-penalized LAD estimator as well as the square-root LASSO method. We evaluate the four methods mentioned above in a generic sparse regression problem and in an array processing application.