(untitled) (Communications in Computational Physics, 2021)
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).