图 书 馆
套索和支持向量机之间的联系Connections between the Lasso and Support Vector Machines |
|
| 课程网址: | http://videolectures.net/roks2013_jaggi_connections/ |
| 主讲教师: | Martin Jaggi |
| 开课单位: | 巴黎高等理工学院 |
| 开课时间: | 2013-08-26 |
| 课程语种: | 英语 |
| 中文简介: |  我们研究了机器学习和信号处理中两个基本工具的关系，即用于分类的支持向量机（SVM）和用于回归的套索技术。我们从以下意义上证明[7]，所产生的优化问题是等效的：给定两个问题之一的任何实例，我们构造另一个问题的实例，并具有相同的最优解。 因此，许多针对SVM和套索的现有优化算法也可以应用于各自的其他问题实例。同样，等效性允许在两个设置之间转换SVM和Lasso的许多已知理论见解。一个这样的含义给出了套索的简单内核化版本，类似于SVM设置中使用的内核。另一个结果是，套索解决方案的稀疏性等于相应SVM实例的支持向量的数量，并且可以使用筛选规则来修剪支持向量集。此外，我们可以将亚线性时间算法与这两个问题联系起来，并为套索给出一种新的此类算法。 |
| 课程简介: | We investigate the relation of two fundamental tools in machine learning and signal processing, that is the support vector machine (SVM) for classification, and the Lasso technique used in regression. We show [7] that the resulting optimization problems are equivalent, in the following sense: Given any instance of one of the two problems, we construct an instance of the other, having the same optimal solution. In consequence, many existing optimization algorithms for both SVMs and Lasso can also be applied to the respective other problem instances. Also, the equivalence allows for many known theoretical insights for SVM and Lasso to be translated between the two settings. One such implication gives a simple kernelized version of the Lasso, analogous to the kernels used in the SVM setting. Another consequence is that the sparsity of a Lasso solution is equal to the number of support vectors for the corresponding SVM instance, and that one can use screening rules to prune the set of support vectors. Furthermore, we can relate sublinear time algorithms for the two problems, and give a new such algorithm variant for the Lasso. |
| 关 键 词: | 信号处理; 线性时间算法 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-12：zyk |
| 最后编审: | 2021-05-14：yumf |
| 阅读次数: | 27 |