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On $\ell_1$-regularized estimation for nonlinear models that have sparse underlying linear structures

Statistics Theory 2009-11-26 v1 Probability Machine Learning Statistics Theory

Abstract

In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of 0\ell_0-regularized estimation. In this note, we show that 1\ell_1-regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned work.

Keywords

Cite

@article{arxiv.0911.4899,
  title  = {On $\ell_1$-regularized estimation for nonlinear models that have sparse underlying linear structures},
  author = {Zhiyi Chi},
  journal= {arXiv preprint arXiv:0911.4899},
  year   = {2009}
}
R2 v1 2026-06-21T14:16:04.243Z