Report
Fast Saddle-Point Algorithm for Generalized Dantzig Selector and FDR Control with the Ordered l1-Norm
| العنوان: | Fast Saddle-Point Algorithm for Generalized Dantzig Selector and FDR Control with the Ordered l1-Norm |
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| المؤلفون: | Lee, Sangkyun, Brzyski, Damian, Bogdan, Malgorzata |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Mathematics - Optimization and Control |
| الوصف: | In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal $O(1/k)$ rate of convergence. Compared to the optimal non-SP algorithms, ours do not require specification of sensitive parameters that affect algorithm performance or solution quality. We also provide a new analysis showing a possibility of local acceleration to achieve the rate of $O(1/k^2)$ in special cases even without strong convexity or strong smoothness. As an application, we propose a GDS equipped with the ordered $\ell_1$-norm, showing its false discovery rate control properties in variable selection. Algorithm performance is compared between ours and other alternatives, including the linearized ADMM, Nesterov's smoothing, Nemirovski's mirror-prox, and the accelerated hybrid proximal extragradient techniques. Comment: In AISTATS 2016 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1511.05864 |
| رقم الانضمام: | edsarx.1511.05864 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |