Efficient Sparse Group Feature Selection via Nonconvex Optimization
This work addresses the need for improved feature selection in high-dimensional data applications, such as identifying group structures, but it is incremental as it builds on existing nonconvex methods.
The paper tackles the problem of suboptimal accuracy in sparse feature selection by expanding a nonconvex paradigm to sparse group feature selection, achieving consistent feature selection and parameter estimation with an efficient algorithm that performs favorably on synthetic and real-world data.
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.