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结构化稀疏诱导范数的有效集算法

Active Set Algorithm for Structured Sparsity-Inducing Norm
课程网址: http://videolectures.net/nipsworkshops09_jenatton_asa/  
主讲教师: Rodolphe Jenatton
开课单位: 法国国家信息与自动化研究所
开课时间: 2010-01-19
课程语种: 英语
中文简介:
研究了线性监督学习的经验风险最小化问题,利用结构稀疏诱导规范进行了正则化。这些定义为某些变量子集上欧几里德范数的总和,通过允许子集重叠扩展了通常的_1-范数和_1-范数组。这将导致一组特定的允许非零模式来解决此类问题。我们首先探讨了定义范数的组与产生的非零模式之间的关系。特别地,我们展示了如何通过正则化对变量的几何信息进行编码。最后提出了一种有效求解相应的最小化问题的主动集算法。
课程简介: We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual ℓ1-norm and the group ℓ1-norm by allowing the subsets to overlap. This leads to a specific set of allowed nonzero patterns for the solutions of such problems. We first explore the relationship between the groups defining the norm and the resulting nonzero patterns. In particular, we show how geometrical information about the variables can be encoded by our regularization. We finally present an active set algorithm to efficiently solve the corresponding minimization problem.
关 键 词: 结构化稀疏; 诱导规范; 非零模式; 最小化问题
课程来源: 视频讲座网
最后编审: 2021-01-15:yumf
阅读次数: 135