Hrushikesh N. Mhaskar

Ryan O'Dowd

Neural Networks, 2025

2024

Inversion of the Laplace Transform of Point Masses.

[BibT_eX]

[DOI]

Michael McKenna

Richard G. Spencer

CoRR, 2024

2023

Tractability of approximation by general shallow networks.

[BibT_eX]

[DOI]

Tong Mao

CoRR, 2023

Approximation by non-symmetric networks for cross-domain learning.

[BibT_eX]

[DOI]

CoRR, 2023

Encoding of data sets and algorithms.

[BibT_eX]

[DOI]

Katarina Doctor

Tong Mao

CoRR, 2023

Numerical solutions to an inverse problem for a non-linear Helmholtz equation.

[BibT_eX]

[DOI]

Quoc Thong Le Gia

CoRR, 2023

Local transfer learning from one data space to another.

[BibT_eX]

[DOI]

Ryan O'Dowd

CoRR, 2023

2022

Theory-Inspired Deep Network for Instantaneous-Frequency Extraction and Subsignals Recovery From Discrete Blind-Source Data.

[BibT_eX]

[DOI]

Ningning Han

IEEE Trans. Neural Networks Learn. Syst., 2022

A manifold learning approach for gesture recognition from micro-Doppler radar measurements.

[BibT_eX]

[DOI]

Eric Mason

Adam Guo

Neural Networks, 2022

Local approximation of operators.

[BibT_eX]

[DOI]

CoRR, 2022

2021

A Function Approximation Approach to the Prediction of Blood Glucose Levels.

[BibT_eX]

[DOI]

Maria D. van der Walt

Frontiers Appl. Math. Stat., 2021

Kernel Distance Measures for Time Series, Random Fields and Other Structured Data.

[BibT_eX]

[DOI]

Srinjoy Das

Alexander Cloninger

Frontiers Appl. Math. Stat., 2021

A manifold learning approach for gesture identification from micro-Doppler radar measurements.

[BibT_eX]

[DOI]

Eric Mason

Adam Guo

CoRR, 2021

2020

An analysis of training and generalization errors in shallow and deep networks.

[BibT_eX]

[DOI]

Neural Networks, 2020

A direct approach for function approximation on data defined manifolds.

[BibT_eX]

[DOI]

Neural Networks, 2020

Dimension independent bounds for general shallow networks.

[BibT_eX]

[DOI]

Neural Networks, 2020

A Witness Function Based Construction of Discriminative Models Using Hermite Polynomials.

[BibT_eX]

[DOI]

Xiuyuan Cheng

Alexander Cloninger

Frontiers Appl. Math. Stat., 2020

Kernel-Based Analysis of Massive Data.

[BibT_eX]

[DOI]

Frontiers Appl. Math. Stat., 2020

A low discrepancy sequence on graphs.

[BibT_eX]

[DOI]

Alex Cloninger

CoRR, 2020

Cautious Active Clustering.

[BibT_eX]

[DOI]

Alexander Cloninger

CoRR, 2020

Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data.

[BibT_eX]

[DOI]

Ningning Han

CoRR, 2020

2019

Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions.

[BibT_eX]

[DOI]

J. Complex., 2019

Data Based Construction of Kernels for Semi-Supervised Learning With Less Labels.

[BibT_eX]

[DOI]

Vasyl Yu. Semenov

Evgeniya V. Semenova

Frontiers Appl. Math. Stat., 2019

Deep Gaussian networks for function approximation on data defined manifolds.

[BibT_eX]

[DOI]

CoRR, 2019

Super-resolution meets machine learning: approximation of measures.

[BibT_eX]

[DOI]

CoRR, 2019

Function approximation by deep networks.

[BibT_eX]

[DOI]

CoRR, 2019

2018

Minimum Sobolev norm interpolation of scattered derivative data.

[BibT_eX]

[DOI]

C. H. Gorman

J. Comput. Phys., 2018

Deep Nets for Local Manifold Learning.

[BibT_eX]

[DOI]

Frontiers Appl. Math. Stat., 2018

Deep Algorithms: designs for networks.

[BibT_eX]

[DOI]

Abhejit Rajagopal

CoRR, 2018

Theory of Deep Learning III: explaining the non-overfitting puzzle.

[BibT_eX]

[DOI]

CoRR, 2018

2017

Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review.

[BibT_eX]

[DOI]

Lorenzo Rosasco

Brando Miranda

Qianli Liao

Int. J. Autom. Comput., 2017

A Deep Learning Approach to Diabetic Blood Glucose Prediction.

[BibT_eX]

[DOI]

Maria D. van der Walt

Frontiers Appl. Math. Stat., 2017

Function approximation with ReLU-like zonal function networks.

[BibT_eX]

[DOI]

CoRR, 2017

A unified method for super-resolution recovery and real exponential-sum separation.

[BibT_eX]

[DOI]

CoRR, 2017

A Fourier-invariant method for locating point-masses and computing their attributes.

[BibT_eX]

[DOI]

CoRR, 2017

When and Why Are Deep Networks Better Than Shallow Ones?

[BibT_eX]

[DOI]

Qianli Liao

Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, 2017

2016

Deep vs. shallow networks : An approximation theory perspective.

[BibT_eX]

[DOI]

CoRR, 2016

Learning Real and Boolean Functions: When Is Deep Better Than Shallow.

[BibT_eX]

[DOI]

Qianli Liao

CoRR, 2016

2015

A minimum Sobolev norm technique for the numerical discretization of PDEs.

[BibT_eX]

[DOI]

J. Comput. Phys., 2015

2014

Smooth function extension based on high dimensional unstructured data.

[BibT_eX]

[DOI]

Math. Comput., 2014

2013

Minimum Sobolev norm interpolation with trigonometric polynomials on the torus.

[BibT_eX]

[DOI]

Karthik Jayaraman Jayaraman

J. Comput. Phys., 2013

Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions.

[BibT_eX]

[DOI]

Valeriya Naumova

Appl. Math. Comput., 2013

2012

Locally Learning Biomedical Data Using Diffusion Frames.

[BibT_eX]

[DOI]

Martin Ehler

Frank Filbir

Karthik Jayaraman Raghuram

J. Comput. Biol., 2012

Higher order numerical discretizations for exterior and biharmonic type PDEs.

[BibT_eX]

[DOI]

Joseph Moffitt

Ming Gu

J. Comput. Appl. Math., 2012

2011

Higher Order Numerical Discretization Methods with Sobolev Norm Minimization.

[BibT_eX]

[DOI]

Shiv Chandrasekaran

K. R. Jayaraman

Ming Gu

J. Mofftt

Proceedings of the International Conference on Computational Science, 2011

A generalized diffusion frame for parsimonious representation of functions on data defined manifolds.

[BibT_eX]

[DOI]

Neural Networks, 2011

Marcinkiewicz-Zygmund measures on manifolds.

[BibT_eX]

[DOI]

Frank Filbir

J. Complex., 2011

2010

L<sup>p</sup> Bernstein estimates and approximation by spherical basis functions.

[BibT_eX]

[DOI]

Math. Comput., 2010

2009

On a filter for exponentially localized kernels based on Jacobi polynomials.

[BibT_eX]

[DOI]

Frank Filbir

J. Approx. Theory, 2009

Preface part 4.

[BibT_eX]

[DOI]

J. Approx. Theory, 2009

Preface part 3.

[BibT_eX]

[DOI]

J. Approx. Theory, 2009

Preface part 2.

[BibT_eX]

[DOI]

J. Approx. Theory, 2009

Preface part 1.

[BibT_eX]

[DOI]

J. Approx. Theory, 2009

Eignets for function approximation on manifolds

[BibT_eX]

[DOI]

CoRR, 2009

2008

Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere.

[BibT_eX]

[DOI]

Quoc Thong Le Gia

SIAM J. Numer. Anal., 2008

2007

Quadrature in Besov spaces on the Euclidean sphere.

[BibT_eX]

[DOI]

Kerstin Hesse

Ian H. Sloan

J. Complex., 2007

Frontiers in Interpolation and Approximation.

[BibT_eX]

[DOI]

Narendra Kumar Govil

Ram N. Mohapatra

Zuhair Nashed

József Szabados

Pure and applied mathematics 282, Chapman & Hall, ISBN: 978-1-58488-636-5, 2007

2006

Matrix-free Interpolation on the Sphere.

[BibT_eX]

[DOI]

Mahadevan Ganesh

SIAM J. Numer. Anal., 2006

Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere.

[BibT_eX]

[DOI]

Quoc Thong Le Gia

Numerische Mathematik, 2006

Weighted quadrature formulas and approximation by zonal function networks on the sphere.

[BibT_eX]

[DOI]

J. Complex., 2006

2004

When is approximation by Gaussian networks necessarily a linear process?

[BibT_eX]

[DOI]

Neural Networks, 2004

Local quadrature formulas on the sphere.

[BibT_eX]

[DOI]

J. Complex., 2004

On the tractability of multivariate integration and approximation by neural networks.

[BibT_eX]

[DOI]

J. Complex., 2004

Polynomial operators and local smoothness classes on the unit interval.

[BibT_eX]

[DOI]

J. Approx. Theory, 2004

A tribute to Géza Freud.

[BibT_eX]

[DOI]

J. Approx. Theory, 2004

On the Representation of Band-Dominant Functions on the Sphere Using Finitely Many Bits.

[BibT_eX]

[DOI]

Adv. Comput. Math., 2004

2003

Zonal function network frames on the sphere.

[BibT_eX]

[DOI]

Neural Networks, 2003

2002

Corrigendum to "Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature''.

[BibT_eX]

[DOI]

Math. Comput., 2002

On the Representation of Band Limited Functions Using Finitely Many Bits.

[BibT_eX]

[DOI]

J. Complex., 2002

2001

Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature.

[BibT_eX]

[DOI]

Math. Comput., 2001

2000

On the detection of singularities of a periodic function.

[BibT_eX]

[DOI]

Adv. Comput. Math., 2000

Polynomial frames on the sphere.

[BibT_eX]

[DOI]

Adv. Comput. Math., 2000

1999

Approximation properties of zonal function networks using scattered data on the sphere.

[BibT_eX]

[DOI]

Adv. Comput. Math., 1999

1997

Neural Networks for Functional Approximation and System Identification.

[BibT_eX]

[DOI]

Nahmwoo Hahm

Neural Comput., 1997

1996

Neural networks and approximation theory.

[BibT_eX]

[DOI]

Neural Networks, 1996

Neural Networks for Optimal Approximation of Smooth and Analytic Functions.

[BibT_eX]

[DOI]

Neural Comput., 1996

Limitations of the approximation capabilities of neural networks with one hidden layer.

[BibT_eX]

[DOI]

Xin Li

Adv. Comput. Math., 1996

Introduction to the theory of weighted polynomial approximation.

[BibT_eX]

Series in approximations and decompositions 7, World Scientific, ISBN: 978-981-02-1312-1, 1996

1994

Dimension-independent bounds on the degree of approximation by neural networks.

[BibT_eX]

[DOI]

Charles A. Micchelli

IBM J. Res. Dev., 1994

1993

Approximation properties of a multilayered feedforward artificial neural network.

[BibT_eX]

[DOI]

Adv. Comput. Math., 1993

How to Choose an Activation Function.

[BibT_eX]

[DOI]