English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper concerns with the group zero-norm regularized least squaresestimator which, in terms of the variational characterization of the zero-norm,can be obtained from a mathematical program with equilibrium constraints(MPEC). By developing the global exact penalty for the MPEC, this estimator isshown to arise from an exact penalization problem that not only has a favorablebilinear structure but also implies a recipe to deliver equivalent DCestimators such as the SCAD and MCP estimators. We propose a multi-stage convexrelaxation approach (GEP-MSCRA) for computing this estimator, and under arestricted strong convexity assumption on the design matrix, establish itstheoretical guarantees which include the decreasing of the error bounds for theiterates to the true coefficient vector and the coincidence of the iteratesafter finite steps with the oracle estimator. Finally, we implement theGEP-MSCRA with the subproblems solved by a semismooth Newton augmentedLagrangian method (ALM) and compare its performance with that of SLEP andMALSAR, the solvers for the weighted $\ell_{2,1}$-norm regularized estimator,on synthetic group sparse regression problems and real multi-task learningproblems. Numerical comparison indicates that the GEP-MSCRA has significantadvantage in reducing error and achieving better sparsity than the SLEP and theMALSAR do.

GEP-MSCRA for computing the group zero-norm regularized least squares estimator