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自适应套索的一些结果Some results for the adaptive Lasso |
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| 课程网址: | http://videolectures.net/smls09_geer_srftal/ |
| 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: | 2009-05-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider the high-dimensional linear regression model, with n observations, and p > > n variables. The adaptive Lasso uses least squares loss with a weighted l_1-penalty, where the weights are proportional to the inverse of an initial estimator of the coefficients. We e.g. show for the case that the initial estimator is obtained from the standard Lasso, then, under the restricted eigenvalue condition as given in Bickel et al. (2007), with large probability, there will be no false positives, and adaptive Lasso will detect all coefficients larger than a certain value c_n, provided the number of coefficients smaller than c_n is small. If we assume a (perhaps) stronger version of the restricted eigenvalue condition, the adaptive Lasso will in fact detect even smaller coefficients. In the limiting case, under the irrepresentable condition (Zhao and Yu (2006)), coefficients of order at least (log (p)/n)^{1/2} will be detected. These results can be obtained from an oracle inequality for Lasso with general weights. We will present the results in an non-asymptotic form. |
| 关 键 词: | 高维线性回归; 自适应套索; 预言不等式 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-09-21：cwx |
| 阅读次数: | 102 |