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Iterative Regularization with k-support Norm: An Important Complement to Sparse Recovery by de Vazelhes, William; Mukhoty, Bhaskar; Yuan, Xiao-Tong; Gu, Bin is a scholarly article available to read on EtoBox.

What is Iterative Regularization with k-support Norm: An Important Complement to Sparse Recovery about?

Sparse recovery is ubiquitous in machine learning and signal processing. Due to the NP-hard nature of sparse recovery, existing methods are known to suffer either from restrictive (or even unknown) applicability conditions, or high computational cost. Recently, iterative regularization methods have emerged as a promising fast approach because they can achieve sparse recovery in one pass through early stopping, rather than the tedious grid-search used in the traditional methods. However, most of those iterative methods are based on the $\ell_1$ norm which requires restrictive applicability conditions and could fail in many cases. Therefore, achieving sparse recovery with iterative regularization methods under a wider range of conditions has yet to be further explored. To address this issue, we propose a novel iterative regularization algorithm, IRKSN, based on the $k$-support norm regularizer rather than the $\ell_1$ norm. We provide conditions for sparse recovery with IRKSN, and compare them with traditional conditions for recovery with $\ell_1$ norm regularizers. Additionally, we give an early stopping bound on the model error of IRKSN with explicit constants, achieving the standa

Author

de Vazelhes, William; Mukhoty, Bhaskar; Yuan, Xiao-Tong; Gu, Bin

Published

2023

Language

EN