图 书 馆
k-NN回归适应于局部固有维数k-NN Regression Adapts to Local Intrinsic Dimension |
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| 课程网址: | http://videolectures.net/nips2011_kpotufe_intrinsic/ |
| 主讲教师: | Samory Kpotufe |
| 开课单位: | 普林斯顿大学 |
| 开课时间: | 2012-01-25 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that $k$-NN regression is also adaptive to intrinsic dimension. In particular our rates are local to a query $x$ and depend only on the way masses of balls centered at $x$ vary with radius. Furthermore, we show a simple way to choose $k = k(x)$ locally at any $x$ so as to nearly achieve the minimax rate at $x$ in terms of the unknown intrinsic dimension in the vicinity of $x$. We also establish that the minimax rate does not depend on a particular choice of metric space or distribution, but rather that this minimax rate holds for any metric space and doubling measure. |
| 关 键 词: | 非参数回归量; 高维数据; 内在维度 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-09-06：lxf |
| 阅读次数: | 73 |