图 书 馆
加性模型中的不相干条件The incoherence condition in additive models |
|
| 课程网址: | http://videolectures.net/sip08_geer_ticiam/ |
| 主讲教师: | Sara van de Geer |
| 开课单位: | 苏黎世联邦理工学院 |
| 开课时间: | 2008-12-18 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We extend the idea of regularization using the Lasso, to the case of an additive model with p components, p being larger than the sample size n. Our method has a group Lasso type structure, and penalizes non-smoothness of the components in the additive model. To arrive at a sparsity oracle in- equality, we need an incoherence condition which generalizes the incoherence conditions used for the Lasso. Bickel et al. (2008) impose the “restricted eigenvalue assumption”, which is closely related to the “compatibility con- dition” in van de Geer (2007), which we simply call “Condition C”. We will formulate a version of such a “Condition C” for additive models. To verify it, we discuss the case of random design. We prove new results for weighted empirical processes, which make the transition from random to fixed design possible, and which only requires a population version of “Condition C”. A consequence is that the sparsity oracle property of our procedure holds when the variables are independent,andthatalsovariousdependencystructuresare allowed. |
| 关 键 词: | 正则化; 加性模型; 非平滑性 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-09-21：cwx |
| 阅读次数: | 148 |