Minimax manifold estimation

被引：0
|
作者：
Genovese, Christopher R. [1 ]
Perone-Pacifico, Marco [2 ]
Verdinelli, Isabella [1 ,2 ]
Wasserman, Larry [1 ,3 ]
机构：
[1] Department of Statistics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, United States
[2] Dipartimento di Scienze Statistiche, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy
[3] Machine Learning Department, Carnegie Mellon University, United States
来源：
Journal of Machine Learning Research | 2012年 / 13卷
关键词：
Hausdorff distance - Manifold learning - Minimax - Minimax estimations - Minimax rates - Optimal rate of convergence;
D O I：
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中图分类号：
学科分类号：
摘要：
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in D given a noisy sample from the manifold. Under certain conditions, we show that the optimal rate of convergence is n-2/(2+d). Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded. © 2012 Christopher Genovese, Marco Perone-Pacifico, Isabella Verdinelli and Larry Wasserman.
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页码：1263 / 1291
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