图 书 馆
子模函数学习：凸优化的一个视角Learning with Submodular Functions: A Convex Optimization Perspective |
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| 课程网址: | http://videolectures.net/nipsworkshops2011_bach_optimization/ |
| 主讲教师: | Francis R. Bach |
| 开课单位: | 法国国家信息与自动化研究所 |
| 开课时间: | 2012-01-25 |
| 课程语种: | 英语 |
| 中文简介: |  子模块函数与机器学习有关，主要有两个原因：（1）一些问题可能直接表示为子模块函数的优化；（2）子模块函数的Lovasz扩展为监督和改进的函数提供了有用的正则化函数无监督学习。在本次演讲中，我将从凸分析的角度介绍子模函数的理论，并提出某些多面体，组合优化和凸优化问题之间的紧密联系。特别是，我将展示子模函数最小化如何等效于解决各种各样的凸优化问题。这允许在理论上保证和良好的实用性能的情况下，推导用于近似亚模函数最小化的新有效算法。通过列出子模块函数的示例，我还将回顾机器学习的各种应用，例如聚类或子集选择，以及可以从子模块函数中导出和使用的一系列结构化稀疏性归纳规范。 |
| 课程简介: | Submodular functions are relevant to machine learning for mainly two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the Lovasz extension of submodular functions provides a useful set of regularization functions for supervised and unsupervised learning. In this talk, I will present the theory of submodular functions from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems. In particular, I will show how submodular function minimization is equivalent to solving a wide variety of convex optimization problems. This allows the derivation of new efficient algorithms for approximate submodular function minimization with theoretical guarantees and good practical performance. By listing examples of submodular functions, I will also review various applications to machine learning, such as clustering or subset selection, as well as a family of structured sparsity-inducing norms that can be derived and used from submodular functions. |
| 关 键 词: | 机器学习; 凸优化 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2020-11-22：zyk |
| 最后编审: | 2021-01-15：yumf |
| 阅读次数: | 160 |