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Statistics > Machine Learning

arXiv:1701.07808 (stat)
[Submitted on 26 Jan 2017 (v1), last revised 2 Apr 2017 (this version, v4)]

Title:Linear convergence of SDCA in statistical estimation

Authors:Chao Qu, Huan Xu
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Abstract: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 $\ell_1$ 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.
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:1701.07808 [stat.ML]
  (or arXiv:1701.07808v4 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.1701.07808

Submission history

From: Chao Qu [view email]
[v1] Thu, 26 Jan 2017 18:37:34 UTC (254 KB)
[v2] Mon, 27 Feb 2017 17:54:55 UTC (277 KB)
[v3] Fri, 10 Mar 2017 22:04:09 UTC (277 KB)
[v4] Sun, 2 Apr 2017 18:43:11 UTC (292 KB)
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