@Article{CiCP-30-190,
author = {Dai , MingweiDai , ShuyangHuang , JunjunKang , Lican and Lu , Xiliang},
title = {Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {1},
pages = {190--209},
abstract = {<p style="text-align: justify;">Truncated $L_1$ regularization proposed by Fan in [5], is an approximation to
the $L_0$ regularization in high-dimensional sparse models. In this work, we prove the
non-asymptotic error bound for the global optimal solution to the truncated $L_1$ regularized linear regression problem and study the support recovery property. Moreover,
a primal dual active set algorithm (PDAS) for variable estimation and selection is proposed. Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm (PDASC). Data-driven parameter selection rules
such as cross validation, BIC or voting method can be applied to select a proper regularization parameter. The application of the proposed method is demonstrated by
applying it to simulation data and a breast cancer gene expression data set (bcTCGA).</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2020-0250},
url = {http://global-sci.org/intro/article_detail/cicp/18878.html}
}