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Article overview
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Fast Saddle-Point Algorithm for Generalized Dantzig Selector and FDR Control with the Ordered $ell_1$-Norm | | Sangkyun Lee
; Damian Brzyski
; Malgorzata Bogdan
; | | Date: |
18 Nov 2015 | | Abstract: | In this paper we propose a primal-dual proximal extragradient algorithm to
solve the generalized Dantzig selector (GDS) estimation, based on a new
convex-concave saddle-point (SP) formulation of the GDS and a simple gradient
extrapolation technique. Our reformulation makes it possible to adapt 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
acceleration 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. | | Source: | arXiv, 1511.5864 | | Services: | Forum | Review | PDF | Favorites | |
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