The Benefit of Group Sparsity

Abstract

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.

References in corpus (3)

• Simultaneous analysis of Lasso and Dantzig selector
• Consistency of the group Lasso and multiple kernel learning
• Compressed Sensing and Redundant Dictionaries

Cited by in corpus (8)

• Compressed Sensing of Block-Sparse Signals: Uncertainty Relations and Efficient Recovery
• Support union recovery in high-dimensional multivariate regression
• Network Flow Algorithms for Structured Sparsity
• On the reconstruction of block-sparse signals with an optimal number of measurements
• Estimation of (near) low-rank matrices with noise and high-dimensional scaling
• Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)
• Simultaneous support recovery in high dimensions: Benefits and perils of block ${\ell }_1/{\ell }_{\infty }$-regularization
• Error Bounds for Generalized Group Sparsity