图 书 馆
通过模块功能结构稀疏诱导规范Structured sparsity-inducing norms through submodular functions |
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| 课程网址: | http://videolectures.net/nips2010_bach_ssi/ |
| 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: | 2011-01-12 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization problem by replacing the cardinality function by its convex envelope (tightest convex lower bound), in this case the L1-norm. In this paper, we investigate more general set-functions than the cardinality, that may incorporate prior knowledge or structural constraints which are common in many applications: namely, we show that for nondecreasing submodular set-functions, the corresponding convex envelope can be obtained from its Lovasz extension, a common tool in submodular analysis. This defines a family of polyhedral norms, for which we provide generic algorithmic tools (subgradients and proximal operators) and theoretical results (conditions for support recovery or high-dimensional inference). By selecting specific submodular functions, we can give a new interpretation to known norms, such as those based on rank-statistics or grouped norms with potentially overlapping groups; we also define new norms, in particular ones that can be used as non-factorial priors for supervised learning. |
| 关 键 词: | 计算机科学; 机器学习; 监督学习 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-06-03：王淑红(课程编辑志愿者) |
| 阅读次数: | 168 |