We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R-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.
Minimax Manifold Estimation / C. R., Genovese; PERONE PACIFICO, Marco; Verdinelli, Isabella; L., Wasserman. - In: JOURNAL OF MACHINE LEARNING RESEARCH. - ISSN 1532-4435. - STAMPA. - 13:(2012), pp. 1263-1291.
Minimax Manifold Estimation
PERONE PACIFICO, Marco;VERDINELLI, Isabella;
2012
Abstract
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R-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.File allegati a questo prodotto
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