Kernel regression, minimax rates and effective dimensionality: Beyond the regular case
| Autor: | Gilles Blanchard, Nicole Mücke |
|---|---|
| Přispěvatelé: | Institute of Mathematics, University of Potsdam, Université Paris-Saclay, Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Understanding the Shape of Data (DATASHAPE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), Institut für Mathematik [Potsdam], Universität Potsdam, Technische Universität Berlin (TU) |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Applied Mathematics Machine Learning (stat.ML) 010103 numerical & computational mathematics Minimax 01 natural sciences Regularization (mathematics) [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] 010101 applied mathematics [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] Statistics - Machine Learning [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Kernel regression Applied mathematics 0101 mathematics ComputingMilieux_MISCELLANEOUS Analysis Curse of dimensionality Mathematics |
| Zdroj: | Analysis and Applications Analysis and Applications, World Scientific Publishing, 2020, 18 (4), pp.683-696. ⟨10.1142/S0219530519500258⟩ Analysis and Applications, World Scientific Publishing, 2020, 18 (04), pp.683-696. ⟨10.1142/S0219530519500258⟩ |
| ISSN: | 1793-6861 0219-5305 |
| DOI: | 10.1142/s0219530519500258 |
| Popis: | International audience; We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kernel mapping covariance operator. In the perspective of distribution-free results, we investigate this issue under much weaker assumption on the eigenvalue decay, allowing for more complex behavior that can reflect different structure of the data at different scales. |
| Databáze: | OpenAIRE |
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