Optimization with Sparsity-Inducing Penalties (Foundations and Trends(R) in Machine Learning)
Optimization with Sparsity-Inducing Penalties (Foundations and Trends(R) in Machine Learning)
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发表时间：
2011-12
影响因子：
6.4
通讯作者：
F. Bach;Rodolphe Jenatton;J. Mairal
中科院分区：
文献类型：
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作者：
F. Bach;Rodolphe Jenatton;J. Mairal
稀疏估计方法旨在使用或获得数据或模型的简约表示。它们最初致力于线性变量选择，但现在已经出现了许多扩展，例如结构化稀疏或内核选择。事实证明，许多相关的估计问题可以通过用适当的非光滑范数正则化经验风险来转化为凸优化问题。具有稀疏诱导惩罚的优化从一般角度介绍了专用于这种稀疏诱导惩罚的优化工具和技术。它涵盖了近似方法，块坐标下降，重新加权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，从计算的角度来比较各种算法。稀疏诱导惩罚优化的介绍基本上是基于现有的文献，但构建一个一般框架的过程自然会导致新的结果，连接和观点。对于任何从事机器学习和相关领域工作的人来说，这是一个理想的参考。
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. Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective. It covers proximal methods, block-coordinate descent, reweighted 2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provides an extensive set of experiments to compare various algorithms from a computational point of view. The presentation of Optimization with Sparsity-Inducing Penalties is essentially based on existing literature, but the process of constructing a general framework leads naturally to new results, connections and points of view. It is an ideal reference on the topic for anyone working in machine learning and related areas.