图 书 馆
仿射估计的最优集结Optimal aggregation of affine estimators |
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| 课程网址: | http://videolectures.net/colt2011_salmon_optimal/ |
| 主讲教师: | Joseph Salmon |
| 开课单位: | 丹尼斯狄德罗大学 |
| 开课时间: | 2011-08-02 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads to sharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures—such as the least square regression, the kernel ridge regression, the shrinkage estimators, etc.—used in the literature on statistical inverse problems. As a consequence, we show that the proposed aggregate provides an adaptive estimator in the exact minimax sense without neither discretizing the range of tuning parameters nor splitting the set of observations. We also illustrate numerically the good performance achieved by the exponentially weighted aggregate. |
| 关 键 词: | 非参数回归模型; 异方差高斯噪声; 仿射估计; 指数加权集; 最小二乘回归; 核脊回归; 收缩估计值 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2020-06-29：cxin |
| 阅读次数: | 68 |