TY - JOUR
T1 - Truncated $L_1$ Regularized Linear Regression: Theory and Algorithm
AU - Dai , Mingwei
AU - Dai , Shuyang
AU - Huang , Junjun
AU - Kang , Lican
AU - Lu , Xiliang
JO - Communications in Computational Physics
VL - 1
SP - 190
EP - 209
PY - 2021
DA - 2021/04
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0250
UR - https://global-sci.org/intro/article_detail/cicp/18878.html
KW - High-dimensional linear regression, sparsity, truncated $L_1$ regularization, primal
dual active set algorithm.
AB - <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>