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We study the generalization error of functions that interpolate prescribed data points and are selected by minimizing a weighted norm.
Theory of reproducing kernels
Nachman Aronszajn · 1950
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L ∞ {L}^{\infty} multivariate approximation theory
Martin H. Schultz · 1969
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Local error estimates for radial basis function interpolation of scattered data
Zong-min Wu and Robert Schaback · 1993
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On the mathematical foundations of learning
Felipe Cucker and Steve Smale · 2002
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Approximation in Sobolev spaces by kernel expansions
Francis J. Narcowich, Robert Schaback, and Joseph D. Ward · 2002
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Scattered data interpolation on spheres: error estimates and locally supported basis functions
Francis J. Narcowich and Joseph D. Ward · 2002
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A few notes on statistical learning theory
Shahar Mendelson · 2003
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Scattered-data interpolation on ℝ n \mathbb{R}^{n} : Error estimates for radial basis and band-limited functions
Francis J. Narcowich and Joseph D. Ward · 2004
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Scattered Data Approximation
Holger Wendland · 2004
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Recent developments in error estimates for scattered-data interpolation via radial basis functions
Francis J. Narcowich · 2005
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Mercer theorem for RKHS on noncompact sets
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Modern Fourier Analysis
Loukas Grafakos · 2009
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Minimum Sobolev norm interpolation with trigonometric polynomials on the torus
Shivkumar Chandrasekaran, Karthik R. Jayaraman, and Hrushikesh N. Mhaskar · 2013
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Spherical Harmonics in p p Dimensions
Efthimiou Costas and Frye Christopher · 2014
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Deep vs. shallow networks: An approximation theory perspective
Hrushikesh N. Mhaskar and Tomaso Poggio · 2016
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Interpolation via weighted ℓ 1 \ell^{1} minimization
Holger Rauhut and Rachel Ward · 2016
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Overfitting or perfect fitting? risk bounds for classification and regression rules that interpolate
Mikhail Belkin, Daniel Hsu, and Partha Mitra · 2018
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To understand deep learning we need to understand kernel learning
Mikhail Belkin, Siyuan Ma, and Soumik Mandal · 2018
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Gradient descent provably optimizes over-parameterized neural networks
Surprises in high-dimensional ridgeless least squares interpolation
Trevor Hastie, Andrea Montanari, Saharon Rosset, and Ryan J. Tibshirani · 2019
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The generalization error of random features regression: Precise asymptotics and double descent curve
Song Mei and Andrea Montanari · 2019
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Andrea Montanari, Feng Ruan, Youngtak Sohn, and Jun Yan · 2019
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Double descent in the condition number
Tomaso Poggio, Gil Kur, and Andrzej Banburski · 2019
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Failures of model-dependent generalization bounds for least-norm interpolation
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