Multikernel Regression with Sparsity Constraint

DOI10.1137/20M1318882zbMath1479.46026arXiv1811.00836OpenAlexW3127203349MaRDI QIDQ4999353

Shayan Aziznejad, Michael Unser

Publication date: 6 July 2021

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.00836

zbMATH Keywords

generalized LASSOregularization theoryrepresenter theoremgeneralized total variationmultiple-kernel learning

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Learning and adaptive systems in artificial intelligence (68T05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Spaces of measures (46E27) Linear operators and ill-posed problems, regularization (47A52)

Related Items (4)

Sparse machine learning in Banach spaces ⋮ A duality approach to regularized learning problems in Banach spaces ⋮ TV-based spline reconstruction with Fourier measurements: uniqueness and convergence of grid-based methods ⋮ Understanding neural networks with reproducing kernel Banach spaces

Uses Software

• SimpleMKL
• GlobalBioim
• PRMLT

Cites Work

• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Exact reconstruction using Beurling minimal extrapolation
• Solving support vector machines in reproducing kernel Banach spaces with positive definite functions
• Super-resolution from noisy data
• Concentration estimates for learning with \(\ell ^{1}\)-regularizer and data dependent hypothesis spaces
• Support recovery for sparse super-resolution of positive measures
• Regularized learning in Banach spaces as an optimization problem: representer theorems
• Théorie des distributions à valeurs vectorielles
• Theory of Bessel potentials. I
• Regularization in kernel learning
• Exact support recovery for sparse spikes deconvolution
• Spline solutions to L\(^1\) extremal problems in one and several variables
• Locally adaptive regression splines
• Convex functional analysis
• Sparse kernel learning with LASSO and Bayesian inference algorithm
• A distribution-free theory of nonparametric regression
• An approximation theory approach to learning with \(\ell^1\) regularization
• Optimal regression rates for SVMs using Gaussian kernels
• Regularization networks and support vector machines
• Optimal rates for the regularized least-squares algorithm
• Some results on Tchebycheffian spline functions and stochastic processes
• Learning Theory
• An Introduction to Sparse Stochastic Processes
• Support Vector Machines
• An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels
• Iteratively reweighted least squares minimization for sparse recovery
• Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization
• Super-resolution of point sources via convex programming
• Continuous-Domain Solutions of Linear Inverse Problems With Tikhonov Versus Generalized TV Regularization
• 10.1162/1532443041827925
• Inverse problems in spaces of measures
• Pocket guide to solve inverse problems with GlobalBioIm
• The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy
• B-Spline-Based Exact Discretization of Continuous-Domain Inverse Problems With Generalized TV Regularization
• Breaking the Curse of Dimensionality with Convex Neural Networks
• Distributions and Their Hermite Expansions
• Theory of Reproducing Kernels
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