2015/03/07 by Shubao Zhang, Hui Qian, Zhang, Shubao +3
Computer Science · Engineering · Mathematics · Psychology · #Artificial intelligence #Computer science #FOS: Computer and information sciences #Information Theory (cs.IT) #Machine Learning (cs.LG) #Machine Learning and Algorithms #Microwave Imaging and Scattering Analysis #Psychology #Sparse and Compressive Sensing Techniques #cs.IT #cs.LG #math.IT
paper · pdf · doi:10.48550/arxiv.1503.02164
published in arXiv (Cornell University) (Cornell University) · arXiv admin note: substantial text overlap with arXiv:1409.4575
arxiv created 2015/03/07 · openalex publication_date 2015/03/07 · arxiv updated 2015/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sparse learning is an important topic in many areas such as machine learning, statistical estimation, signal processing, etc. Recently, there emerges a growing interest on structured sparse learning. In this paper we focus on the ℓq-analysis optimization problem for structured sparse learning (0< q ≤ 1). Compared to previous work, we establish weaker conditions for exact recovery in noiseless case and a tighter non-asymptotic upper bound of estimate error in noisy case. We further prove that the nonconvex ℓq-analysis optimization can do recovery with a lower sample complexity and in a wider range of cosparsity than its convex counterpart. In addition, we develop an iteratively reweighted method to solve the optimization problem under the variational framework. Theoretical analysis shows that our method is capable of pursuing a local minima close to the global minima. Also, empirical results of preliminary computational experiments illustrate that our nonconvex method outperforms both its convex counterpart and other state-of-the-art methods.