Error guarantees for least squares approximation with noisy samples in domain adaptation
DOI10.5802/smai-jcm.96arXiv2204.04436OpenAlexW4385430012MaRDI QIDQ6071903
Publication date: 29 November 2023
Published in: SMAI Journal of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.04436
polynomial approximationleast squaressampling theoryunit cubetransfer learningdomain adaptationindividual function approximation
Ill-posedness and regularization problems in numerical linear algebra (65F22) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Multidimensional problems (41A63) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Algorithms for approximation of functions (65D15) Sampling theory in information and communication theory (94A20) Numerical analysis (65-XX) Numerical methods in Fourier analysis (65Txx)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Tent-transformed lattice rules for integration and approximation of multivariate non-periodic functions
- A mathematical introduction to compressive sensing
- Regularization theory for ill-posed problems. Selected topics
- On the stability and accuracy of least squares approximations
- Analysis of discrete \(L^2\) projection on polynomial spaces with random evaluations
- Sparse Legendre expansions via \(\ell_1\)-minimization
- Spectral and high order methods for partial differential equations. Selected papers from the 8th ICOSAHOM '09 conference, Trondheim, Norway, June 22--26, 2009
- User-friendly tail bounds for sums of random matrices
- Hanson-Wright inequality and sub-Gaussian concentration
- Fast cross-validation in harmonic approximation
- Tractability of multivariate approximation over a weighted unanchored Sobolev space
- Multivariate modified Fourier series and application to boundary value problems
- Theory of function spaces
- Theory of function spaces II
- Coherence motivated sampling and convergence analysis of least squares polynomial chaos regression
- Numerical Fourier analysis
- A distribution-free theory of nonparametric regression
- Optimal pointwise sampling for \(L^2\) approximation
- \(L_2\)-norm sampling discretization and recovery of functions from RKHS with finite trace
- On a regularization of unsupervised domain adaptation in RKHS
- Concentration inequalities for cross-validation in scattered data approximation
- A new upper bound for sampling numbers
- On sampling discretization in \(L_2\)
- Optimal sampling and Christoffel functions on general domains
- Function values are enough for \(L_2\)-approximation
- Worst-case recovery guarantees for least squares approximation using random samples
- Balancing principle in supervised learning for a general regularization scheme
- On approximate recovery of functions with bounded mixed derivative
- Lattice rules for nonperiodic smooth integrands
- Learning multivariate functions with low-dimensional structures using polynomial bases
- A sharp upper bound for sampling numbers in \(L_2\)
- A Christoffel function weighted least squares algorithm for collocation approximations
- Spectral Methods
- From high oscillation to rapid approximation II: expansions in Birkhoff series
- Model selection for regression on a random design
- Support Vector Machines
- From high oscillation to rapid approximation I: modified Fourier expansions
- Optimal weighted least-squares methods
- Function integration, reconstruction and approximation using rank-$1$ lattices
- Boosted optimal weighted least-squares
- A Note on Sampling Recovery of Multivariate Functions in the Uniform Norm
- Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
- Reconstruction and collocation of a class of non-periodic functions by sampling along tent-transformed rank-1 lattices
- Constructive subsampling of finite frames with applications in optimal function recovery
- A Note on Transformed Fourier Systems for the Approximation of Non-periodic Signals
