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：

暂无

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.

引用

页码：1263 / 1291

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