Capturing ridge functions in high dimensions from point queries
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Publication:2428577
DOI10.1007/s00365-011-9147-6zbMath1318.62286OpenAlexW1991143958MaRDI QIDQ2428577
Ronald A. DeVore, Gérard Kerkyacharian, Dominique Picard, Ingrid Daubechies, Albert Cohen
Publication date: 26 April 2012
Published in: Constructive Approximation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00365-011-9147-6
Nonparametric regression and quantile regression (62G08) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical interpolation (65D05) Neural nets and related approaches to inference from stochastic processes (62M45)
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Cites Work
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- Convergence rates of best \(N\)-term Galerkin approximations for a class of elliptic SPDEs
- The Gelfand widths of \(\ell_p\)-balls for \(0 < p \leq 1\)
- Approximation of functions of few variables in high dimensions
- Instance-optimality in probability with an \(\ell _1\)-minimization decoder
- Nonparametric estimation of composite functions
- A simple proof of the restricted isometry property for random matrices
- Estimating high-dimensional intervention effects from observational data
- Additive regression and other nonparametric models
- Optimal rates and adaptation in the single-index model using aggregation
- Diffusion wavelets
- Compressed sensing and best 𝑘-term approximation
- Sliced Inverse Regression for Dimension Reduction
- Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
- Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting
- Distilled Sensing: Adaptive Sampling for Sparse Detection and Estimation
- Stable signal recovery from incomplete and inaccurate measurements
