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

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

2009-11-25

arxiv.org/abs/0911.4899v1

Mathematics

Statistics Theory

Scientific paper

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

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