  Sparse feature selection has been demonstrated to be effective in handling
high-dimensional data. While promising, most of the existing works use convex
methods, which may be suboptimal in terms of the accuracy of feature selection
and parameter estimation. In this paper, we expand a nonconvex paradigm to
sparse group feature selection, which is motivated by applications that require
identifying the underlying group structure and performing feature selection
simultaneously. The main contributions of this article are twofold: (1)
statistically, we introduce a nonconvex sparse group feature selection model
which can reconstruct the oracle estimator. Therefore, consistent feature
selection and parameter estimation can be achieved; (2) computationally, we
propose an efficient algorithm that is applicable to large-scale problems.
Numerical results suggest that the proposed nonconvex method compares favorably
against its competitors on synthetic data and real-world applications, thus
achieving desired goal of delivering high performance.
