Estimation of a sparse group of sparse vectors

TL;DR

This paper introduces a Bayesian penalized likelihood method for estimating sparse groups of sparse vectors, achieving adaptive minimaxity and competitive performance with existing methods like sparse group lasso.

Contribution

It proposes a new computationally efficient Bayesian MAP estimator for sparse group sparse vectors with proven adaptive minimaxity.

Findings

Estimator is computationally fast.

Achieves adaptive minimaxity across various sparsity regimes.

Performs competitively with sparse group lasso in simulations.

Abstract

We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their "significant" components, and can be performed by a computationally fast algorithm. The resulting estimators are developed within Bayesian framework and can be viewed as MAP estimators. We establish their adaptive minimaxity over a wide range of sparse and dense settings. The presented short simulation study demonstrates the efficiency of the proposed approach that successfully competes with the recently developed sparse group lasso estimator.