Online Hyperparameter-Free Sparse Estimation Method

TL;DR

This paper introduces an online sparse estimation method that eliminates the need for hyperparameter tuning, offering a computationally efficient alternative to LASSO with comparable performance.

Contribution

The paper presents a novel online estimator for sparse vectors that does not require hyperparameter tuning, based on a covariance matching approach and related to square-root LASSO.

Findings

Performs comparably to LASSO and RLS in numerical tests.

Eliminates the need for hyperparameter tuning.

Maintains similar computational complexity as existing online methods.

Abstract

In this paper we derive an online estimator for sparse parameter vectors which, unlike the LASSO approach, does not require the tuning of any hyperparameters. The algorithm is based on a covariance matching approach and is equivalent to a weighted version of the square-root LASSO. The computational complexity of the estimator is of the same order as that of the online versions of regularized least-squares (RLS) and LASSO. We provide a numerical comparison with feasible and infeasible implementations of the LASSO and RLS to illustrate the advantage of the proposed online hyperparameter-free estimator.