Minimax Manifold Estimation
| Autor: | Genovese, C. R., PERONE PACIFICO, Marco, Verdinelli, Isabella, Wasserman, L. |
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| Rok vydání: | 2010 |
| Předmět: |
FOS: Computer and information sciences
Mathematics - Statistics Theory Machine Learning (stat.ML) Statistics Theory (math.ST) Mathematics::Geometric Topology Machine Learning (cs.LG) Computer Science - Learning Statistics - Machine Learning manifold learning FOS: Mathematics Mathematics::Differential Geometry minimax estimation Mathematics::Symplectic Geometry |
| DOI: | 10.48550/arxiv.1007.0549 |
| Popis: | 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. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. 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. Comment: journal submission, revision with some errors corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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