Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

DOI10.1016/j.jmva.2015.08.009zbMath1327.41004OpenAlexW1912937467MaRDI QIDQ893175

Raúl Tempone, Fabio Nobile, Giovanni Migliorati

Publication date: 13 November 2015

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmva.2015.08.009

zbMATH Keywords

convergence rateslearning theoryerror analysislarge deviationsapproximation theorydiscrete least squaresmultivariate polynomial approximationnoisy evaluations

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Best approximation, Chebyshev systems (41A50) Multidimensional problems (41A63) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25)

Related Items (9)

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension ⋮ Convergence bounds for empirical nonlinear least-squares ⋮ Boosted optimal weighted least-squares ⋮ Multilevel weighted least squares polynomial approximation ⋮ Multivariate Approximation in Downward Closed Polynomial Spaces ⋮ Stability of Discrete Empirical Interpolation and Gappy Proper Orthogonal Decomposition with Randomized and Deterministic Sampling Points ⋮ Convergence rates for a class of estimators based on Stein's method ⋮ Optimal weighted least-squares methods ⋮ Adaptive Approximation by Optimal Weighted Least-Squares Methods

Cites Work

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• On the stability and accuracy of least squares approximations
• Analysis of discrete \(L^2\) projection on polynomial spaces with random evaluations
• Multivariate Markov-type and Nikolskii-type inequalities for polynomials associated with downward closed multi-index sets
• User-friendly tail bounds for sums of random matrices
• A distribution-free theory of nonparametric regression
• Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets
• Approximation in learning theory
• Universal algorithms for learning theory. II: Piecewise polynomial functions
• On the mathematical foundations of learning
• Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces
• Multivariate Discrete Least-Squares Approximations with a New Type of Collocation Grid
• Learning Theory
• Spectral Methods for Uncertainty Quantification
• Strong converse for identification via quantum channels
• Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
• Large deviations

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