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关于凸凹过程的收敛性

On the Convergence of the Convex-Concave Procedure
课程网址: http://videolectures.net/nipsworkshops09_sriperumbudur_ccc/  
主讲教师: Bharath K. Sriperumbudur
开课单位: 圣地亚哥大学
开课时间: 2010-01-19
课程语种: 英语
中文简介:
凹凸程序(CCCP)是一种优化最小化算法,它将D.C(凸函数差)程序作为一系列凸程序来求解。在机器学习中,CCCP被广泛应用于稀疏支持向量机(SVMS)、转导SVMS、稀疏主成分分析等多种学习算法中,虽然在许多应用中得到了广泛的应用,但CCCP的收敛行为并没有得到足够的重视。在本文中,我们通过解决这些问题,对CCCP的收敛性进行了严格的分析:(i)CCCP在什么时候找到所考虑的直流程序的局部极小点或平稳点?*(ii)CCCP生成的序列什么时候收敛?我们还提出了一个关于CCCP局部收敛问题的开放性问题。
课程简介: The concave-convex procedure (CCCP) is a majorization-minimization algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms like sparse support vector machines (SVMs), transductive SVMs, sparse principal component analysis, etc. Though widely used in many applications, the convergence behavior of CCCP has not gotten a lot of specific attention. In this paper, we provide a rigorous analysis of the convergence of CCCP by addressing these questions: *(i) When does CCCP find a local minimum or a stationary point of the d.c. program under consideration? *(ii) When does the sequence generated by CCCP converge? We also present an open problem on the issue of local convergence of CCCP.
关 键 词: 计算机科学; 机器学习; 核方法; 支持向量机
课程来源: 视频讲座网
最后编审: 2020-06-11:liush
阅读次数: 111