Optimal Rates for the Regularized Least-Squares Algorithm
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Summary
A complete minimax analysis of the problem is described, showing that the convergence rates obtained by regularized least-squares estimators are indeed optimal over a suitable class of priors defined by the considered kernel.
- Type
- article
- Published
- 2007-07-01
- Cited by
- 972
- References
- 42
- Access
- Open access
- OpenAlex
- https://openalex.org/W2012501405
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:207063850
Keywords
Mathematics, Minimax, Reproducing kernel Hilbert space, Prior probability, Estimator
References
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- Reproducing kernel Hilbert spaces and Mercer theorem
- Regularization of Inverse Problems
- CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS
- Learning Theory Estimates via Integral Operators and Their Approximations
- Theory of Reproducing Kernels.
- Sous-espaces hilbertiens d’espaces vectoriels topologiques et noyaux associés (Noyaux reproduisants)
- Approximation in Learning Theory
- Weak Convergence and Empirical Processes: With Applications to Statistics
- Shannon sampling II: Connections to learning theory
- Leave-One-Out Bounds for Kernel Methods
- On the mathematical foundations of learning
- Remarks on Inequalities for Large Deviation Probabilities
- Nonlinear Methods of Approximation
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- Non-parametric Stochastic Approximation with Large Step sizes
- Linear regression through PAC-Bayesian truncation
- Stability of Multi-Task Kernel Regression Algorithms
- Ship efficiency forecast based on sensors data collection: Improving numerical models through data analytics
- Optimal Rates for Regularization Operators in Learning Theory
- Adaptation for Regularization Operators in Learning Theory
- Density Estimation in Infinite Dimensional Exponential Families
- Conditional mean embeddings as regressors
- Gradient-based kernel dimension reduction for supervised learning
- Sharp Convergence Rate and Support Consistency of Multiple Kernel Learning with Sparse and Dense Regularization
- Learning with Incremental Iterative Regularization
- Iterative Regularization for Learning with Convex Loss Functions
- Risk bounds in linear regression through PAC-Bayesian truncation
- Spectral Analysis of Symmetric and Anti-Symmetric Pairwise Kernels
- Filtering with State-Observation Examples via Kernel Monte Carlo Filter
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