Folded concave penalized sparse linear regression: sparsity, statistical performance, and algorithmic theory for local solutions.

ABSTRACT: This paper concerns the folded concave penalized sparse linear regression (FCPSLR), a class of popular sparse recovery methods. Although FCPSLR yields desirable recovery performance when solved globally, computing a global solution is NP-complete. Despite some existing statistical performance analyses on local minimizers or on specific FCPSLR-based learning algorithms, it still remains open questions whether local solutions that are known to admit fully polynomial-time approximation schemes (FPTAS) may already be sufficient to ensure the statistical performance, and whether that statistical performance can be non-contingent on the specific designs of computing procedures. To address the questions, this paper presents the following threefold results: (i) Any local solution (stationar

SUBMITTER: Liu H 

PROVIDER: S-EPMC5720392 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature