2013/11/22 by Xiao–Tong Yuan, Ping Li, Yuan, Xiao-Tong +3
Computer Science · Engineering · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1311.5750
openalex publication_date 2013/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance. In this paper, we generalize HTP from compressive sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm iterates between a standard gradient descent step and a hard thresholding step with or without debiasing. We prove that our method enjoys the strong guarantees analogous to HTP in terms of rate of convergence and parameter estimation accuracy. Numerical evidences show that our method is superior to the state-of-the-art greedy selection methods in sparse logistic regression and sparse precision matrix estimation tasks.