Optimization with Sparsity-Inducing Penalties
Optimization with Sparsity-Inducing Penalties
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DOI：
10.1561/2200000015
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发表时间：
2012-01-01
影响因子：
32.8
通讯作者：
Obozinski, Guillaume
中科院分区：
文献类型：
--
作者：
Bach, Francis;Jenatton, Rodolphe;Obozinski, Guillaume
稀疏估计方法旨在使用或获得数据或模型的简洁表示。它们最初致力于线性变量选择，但现在出现了许多扩展，例如结构化稀疏性或核选择。结果表明，通过使用适当的非光滑范数对经验风险进行正则化，可以将许多相关的估计问题转化为凸优化问题。本专著的目标是从一般的角度介绍专门用于这种稀疏性诱导惩罚的优化工具和技术。我们涵盖了近端方法，块坐标下降，重加权l(2)惩罚技术，工作集和同伦方法，以及非凸公式和扩展，并提供了一组广泛的实验，从计算的角度比较各种算法。
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. The goal of this monograph is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted l(2)-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view.