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The problem of extending a function $f$ defined on a training data $\mathcal{C}$ on an unknown manifold $\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper.
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Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
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Neural networks for localized approximation
C. K. Chui, X. Li, and H. N. Mhaskar · 1994
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Regularization theory and neural networks architectures
F. Girosi, M. B. Jones, and T. Poggio · 1995
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Neural networks for function approximation
H. N. Mhaskar and L. Khachikyan · 1995
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Limitations of the approximation capabilities of neural networks with one hidden layer
C. K. Chui, X. Li, and H. N. Mhaskar · 1996
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Constructive approximation: advanced problems
G. G. Lorentz, M. von Golitschek, and Y. Makovoz · 1996
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Neural networks for optimal approximation of smooth and analytic functions
H. N. Mhaskar · 1996
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Localized linear polynomial operators and quadrature formulas on the sphere
Q. T. Le Gia and H. N. Mhaskar · 2008
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Diffusion polynomial frames on metric measure spaces
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Polynomial operators and local smoothness classes on the unit interval, ii
H. N. Mhaskar · 2009
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Minimum sobolev norm schemes and applications in image processing
S. Chandrasekaran, K. R. Jayaraman, J. Moffitt, H. N. Mhaskar, and S. Pauli · 2010
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A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel
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Universal local parametrizations via heat kernels and eigenfunctions of the Laplacian
P. W. Jones, M. Maggioni, and R. Schul · 2010
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Statistical learning theory
V. N. Vapnik and V. Vapnik · 1998
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H. N. Mhaskar · 1999
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Quasi-interpolation in shift invariant spaces
H. N. Mhaskar, F. J. Narcowich, and J. D. Ward · 2000
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Bounds on rates of variable basis and neural network approximation
V. Kurková and M. Sanguineti · 2001
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Comparison of worst case errors in linear and neural network approximation
V. Kurková and M. Sanguineti · 2002
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Forecasting box-office receipts of motion pictures using neural networks, 2002
R. Sharda and D. Delen · 2002
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Eignets for function approximation on manifolds
H. N. Mhaskar · 2010
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Higher order numerical discretization methods with sobolev norm minimization
S. Chandrasekaran, K. R. Jayaraman, M. Gu, H. N. Mhaskar, and J. Mofftt · 2011
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Marcinkiewicz–Zygmund measures on manifolds
F. Filbir and H. N. Mhaskar · 2011
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A generalized diffusion frame for parsimonious representation of functions on data defined manifolds
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Locally learning biomedical data using diffusion frames
M. Ehler, F. Filbir, and H. N. Mhaskar · 2012
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A meta-learning approach to the regularized learning—case study: Blood glucose prediction
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Minimum sobolev norm interpolation with trigonometric polynomials on the torus
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Filtered legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions
H. N. Mhaskar, V. Naumova, and S. V. Pereverzyev · 2013
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The nature of statistical learning theory
V. Vapnik · 2013
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Representation of functions on big data: graphs and trees
C. K. Chui, F. Filbir, and H. N. Mhaskar · 2014
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Smooth function extension based on high dimensional unstructured data
C. K. Chui and H. N. Mhaskar · 2014
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Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
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G. Mishne, U. Shaham, A. Cloninger, and I. Cohen · 2015
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Notes on hierarchical splines, dclns, convolutional kernels and i-theory
L. Rosasco, A. Shashua, N. Cohen, and T. Poggio · 2015
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