2017/01/26 by Chao Qu, Huan Xu, Qu, Chao +1
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1701.07808
openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider stochastic dual coordinate (SDCA) \em without strongly convex assumption or convex assumption. We show that SDCA converges linearly under mild conditions termed restricted strong convexity. This covers a wide array of popular statistical models including Lasso, group Lasso, and logistic regression with ℓ1 regularization, corrected Lasso and linear regression with SCAD regularizer. This significantly improves previous convergence results on SDCA for problems that are not strongly convex. As a by product, we derive a dual free form of SDCA that can handle general regularization term, which is of interest by itself.