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ORCIDHrushikesh N. Mhaskar
Hrushikesh Narhar Mhaskar
Person information
- affiliation: Claremont Graduate University, Institute of Mathematical Sciences, CA, USA
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Books and Theses
- 2007
[b2]Narendra Kumar Govil, Hrushikesh Narhar Mhaskar, Ram N. Mohapatra, Zuhair Nashed, József Szabados:
Frontiers in Interpolation and Approximation. Pure and applied mathematics 282, Chapman & Hall 2007, ISBN 978-1-58488-636-5, pp. I-XLIII, 1-431- 1996
- [b1]Hrushikesh Narhar Mhaskar:
Introduction to the theory of weighted polynomial approximation. Series in approximations and decompositions 7, World Scientific 1996, ISBN 978-981-02-1312-1, pp. I-XIV, 1-379
Journal Articles
- 2022
- [j53]Eric Mason, Hrushikesh N. Mhaskar
, Adam Guo:
A manifold learning approach for gesture recognition from micro-Doppler radar measurements. Neural Networks 152: 353-369 (2022) - [j52]Ningning Han, Hrushikesh N. Mhaskar, Charles K. Chui:
Theory-Inspired Deep Network for Instantaneous-Frequency Extraction and Subsignals Recovery From Discrete Blind-Source Data. IEEE Trans. Neural Networks Learn. Syst. 33(8): 3437-3447 (2022) - 2021
- [j51]Hrushikesh N. Mhaskar, Sergei V. Pereverzyev, Maria D. van der Walt:
A Function Approximation Approach to the Prediction of Blood Glucose Levels. Frontiers Appl. Math. Stat. 7: 707884 (2021) - [j50]Srinjoy Das, Hrushikesh N. Mhaskar, Alexander Cloninger:
Kernel Distance Measures for Time Series, Random Fields and Other Structured Data. Frontiers Appl. Math. Stat. 7: 787455 (2021) - 2020
- [j49]Hrushikesh N. Mhaskar:
Kernel-Based Analysis of Massive Data. Frontiers Appl. Math. Stat. 6: 30 (2020) - [j48]Hrushikesh N. Mhaskar, Xiuyuan Cheng, Alexander Cloninger:
A Witness Function Based Construction of Discriminative Models Using Hermite Polynomials. Frontiers Appl. Math. Stat. 6: 31 (2020) - [j47]Hrushikesh N. Mhaskar, Tomaso A. Poggio:
An analysis of training and generalization errors in shallow and deep networks. Neural Networks 121: 229-241 (2020) - [j46]Hrushikesh N. Mhaskar:
Dimension independent bounds for general shallow networks. Neural Networks 123: 142-152 (2020) - [j45]Hrushikesh N. Mhaskar:
A direct approach for function approximation on data defined manifolds. Neural Networks 132: 253-268 (2020) - 2019
- [j44]Hrushikesh N. Mhaskar, Sergei V. Pereverzyev, Vasyl Yu. Semenov, Evgeniya V. Semenova:
Data Based Construction of Kernels for Semi-Supervised Learning With Less Labels. Frontiers Appl. Math. Stat. 5: 21 (2019) - [j43]Hrushikesh N. Mhaskar:
Function approximation with zonal function networks with activation functions analogous to the rectified linear unit functions. J. Complex. 51: 1-19 (2019) - 2018
- [j42]Charles K. Chui, Hrushikesh N. Mhaskar:
Deep Nets for Local Manifold Learning. Frontiers Appl. Math. Stat. 4: 12 (2018) - [j41]Shivkumar Chandrasekaran, C. H. Gorman, Hrushikesh Narhar Mhaskar:
Minimum Sobolev norm interpolation of scattered derivative data. J. Comput. Phys. 365: 149-172 (2018) - 2017
- [j40]Hrushikesh N. Mhaskar, Sergei V. Pereverzyev, Maria D. van der Walt:
A Deep Learning Approach to Diabetic Blood Glucose Prediction. Frontiers Appl. Math. Stat. 3: 14 (2017) - [j39]Tomaso A. Poggio, Hrushikesh N. Mhaskar, Lorenzo Rosasco, Brando Miranda, Qianli Liao:
Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review. Int. J. Autom. Comput. 14(5): 503-519 (2017) - 2015
- [j38]Shivkumar Chandrasekaran, Hrushikesh Narhar Mhaskar:
A minimum Sobolev norm technique for the numerical discretization of PDEs. J. Comput. Phys. 299: 649-666 (2015) - 2014
- [j37]Charles K. Chui, Hrushikesh Narhar Mhaskar:
Smooth function extension based on high dimensional unstructured data. Math. Comput. 83(290): 2865-2891 (2014) - 2013
- [j36]Hrushikesh Narhar Mhaskar, Valeriya Naumova, Sergei V. Pereverzyev:
Filtered Legendre expansion method for numerical differentiation at the boundary point with application to blood glucose predictions. Appl. Math. Comput. 224: 835-847 (2013) - [j35]Shivkumar Chandrasekaran, Karthik Jayaraman Jayaraman, Hrushikesh Narhar Mhaskar:
Minimum Sobolev norm interpolation with trigonometric polynomials on the torus. J. Comput. Phys. 249: 96-112 (2013) - 2012
- [j34]Karthik Jayaraman Raghuram, Shivkumar Chandrasekaran, Joseph Moffitt, Ming Gu, Hrushikesh Narhar Mhaskar:
Higher order numerical discretizations for exterior and biharmonic type PDEs. J. Comput. Appl. Math. 236(18): 4762-4774 (2012) - [j33]Martin Ehler, Frank Filbir, Hrushikesh Narhar Mhaskar:
Locally Learning Biomedical Data Using Diffusion Frames. J. Comput. Biol. 19(11): 1251-1264 (2012) - 2011
- [j32]Frank Filbir, Hrushikesh Narhar Mhaskar:
Marcinkiewicz-Zygmund measures on manifolds. J. Complex. 27(6): 568-596 (2011) - [j31]Hrushikesh N. Mhaskar:
A generalized diffusion frame for parsimonious representation of functions on data defined manifolds. Neural Networks 24(4): 345-359 (2011) - 2010
- [j30]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Jürgen Prestin, Joseph D. Ward:
Lp Bernstein estimates and approximation by spherical basis functions. Math. Comput. 79(271): 1647-1679 (2010) - 2009
- [j29]Charles K. Chui, Hrushikesh Narhar Mhaskar:
Preface part 1. J. Approx. Theory 158(1): 1-2 (2009) - [j28]Charles K. Chui, Hrushikesh Narhar Mhaskar:
Preface part 2. J. Approx. Theory 158(2): 143-144 (2009) - [j27]Charles K. Chui, Hrushikesh Narhar Mhaskar:
Preface part 3. J. Approx. Theory 159(1): 1-2 (2009) - [j26]Charles K. Chui, Hrushikesh Narhar Mhaskar:
Preface part 4. J. Approx. Theory 159(2): 165-166 (2009) - [j25]Frank Filbir, Hrushikesh Narhar Mhaskar, Jürgen Prestin:
On a filter for exponentially localized kernels based on Jacobi polynomials. J. Approx. Theory 160(1-2): 256-280 (2009) - 2008
- [j24]Quoc Thong Le Gia, Hrushikesh N. Mhaskar:
Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere. SIAM J. Numer. Anal. 47(1): 440-466 (2008) - 2007
- [j23]Kerstin Hesse, Hrushikesh N. Mhaskar, Ian H. Sloan:
Quadrature in Besov spaces on the Euclidean sphere. J. Complex. 23(4-6): 528-552 (2007) - 2006
- [j22]Hrushikesh Narhar Mhaskar:
Weighted quadrature formulas and approximation by zonal function networks on the sphere. J. Complex. 22(3): 348-370 (2006) - [j21]Quoc Thong Le Gia, Hrushikesh N. Mhaskar:
Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere. Numerische Mathematik 103(2): 299-322 (2006) - [j20]Mahadevan Ganesh, Hrushikesh N. Mhaskar:
Matrix-free Interpolation on the Sphere. SIAM J. Numer. Anal. 44(3): 1314-1331 (2006) - 2004
- [j19]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward:
On the Representation of Band-Dominant Functions on the Sphere Using Finitely Many Bits. Adv. Comput. Math. 21(1-2): 127-146 (2004) - [j18]Hrushikesh Narhar Mhaskar:
A tribute to Géza Freud. J. Approx. Theory 126(1): 1-15 (2004) - [j17]Hrushikesh Narhar Mhaskar:
Polynomial operators and local smoothness classes on the unit interval. J. Approx. Theory 131(2): 243-267 (2004) - [j16]Hrushikesh Narhar Mhaskar:
On the tractability of multivariate integration and approximation by neural networks. J. Complex. 20(4): 561-590 (2004) - [j15]Hrushikesh Narhar Mhaskar:
Local quadrature formulas on the sphere. J. Complex. 20(5): 753-772 (2004) - [j14]Hrushikesh Narhar Mhaskar:
When is approximation by Gaussian networks necessarily a linear process? Neural Networks 17(7): 989-1001 (2004) - 2003
- [j13]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward:
Zonal function network frames on the sphere. Neural Networks 16(2): 183-203 (2003) - 2002
- [j12]Hrushikesh Narhar Mhaskar:
On the Representation of Band Limited Functions Using Finitely Many Bits. J. Complex. 18(2): 449-478 (2002) - [j11]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward:
Corrigendum to "Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature''. Math. Comput. 71(237): 453-454 (2002) - 2001
- [j10]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward:
Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comput. 70(235): 1113-1130 (2001) - 2000
- [j9]Hrushikesh Narhar Mhaskar, Jürgen Prestin:
On the detection of singularities of a periodic function. Adv. Comput. Math. 12(2-3): 95-131 (2000) - [j8]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Jürgen Prestin, Joseph D. Ward:
Polynomial frames on the sphere. Adv. Comput. Math. 13(4): 387-403 (2000) - 1999
- [j7]Hrushikesh Narhar Mhaskar, Francis J. Narcowich, Joseph D. Ward:
Approximation properties of zonal function networks using scattered data on the sphere. Adv. Comput. Math. 11(2-3): 121-137 (1999) - 1997
- [j6]Hrushikesh Narhar Mhaskar, Nahmwoo Hahm:
Neural Networks for Functional Approximation and System Identification. Neural Comput. 9(1): 143-159 (1997) - 1996
- [j5]Charles K. Chui, Xin Li, Hrushikesh Narhar Mhaskar:
Limitations of the approximation capabilities of neural networks with one hidden layer. Adv. Comput. Math. 5(1): 233-243 (1996) - [j4]Hrushikesh N. Mhaskar:
Neural Networks for Optimal Approximation of Smooth and Analytic Functions. Neural Comput. 8(1): 164-177 (1996) - [j3]Hrushikesh Narhar Mhaskar:
Neural networks and approximation theory. Neural Networks 9(4): 721-722 (1996) - 1994
- [j2]Hrushikesh Narhar Mhaskar, Charles A. Micchelli:
Dimension-independent bounds on the degree of approximation by neural networks. IBM J. Res. Dev. 38(3): 277-284 (1994) - 1993
- [j1]Hrushikesh Narhar Mhaskar:
Approximation properties of a multilayered feedforward artificial neural network. Adv. Comput. Math. 1(1): 61-80 (1993)
Conference and Workshop Papers
- 2017
- [c3]Hrushikesh N. Mhaskar, Qianli Liao, Tomaso A. Poggio:
When and Why Are Deep Networks Better Than Shallow Ones? AAAI 2017: 2343-2349 - 2011
- [c2]Shiv Chandrasekaran, K. R. Jayaraman, Ming Gu, Hrushikesh Narhar Mhaskar, J. Mofftt:
Higher Order Numerical Discretization Methods with Sobolev Norm Minimization. ICCS 2011: 206-215 - 1993
- [c1]Hrushikesh Narhar Mhaskar, Charles A. Micchelli:
How to Choose an Activation Function. NIPS 1993: 319-326
Informal and Other Publications
- 2024
- [i32]Michael McKenna, Hrushikesh N. Mhaskar, Richard G. Spencer:
Inversion of the Laplace Transform of Point Masses. CoRR abs/2402.04348 (2024) - [i31]Hrushikesh N. Mhaskar, Ryan O'Dowd:
Learning on manifolds without manifold learning. CoRR abs/2402.12687 (2024) - 2023
- [i30]Hrushikesh Narhar Mhaskar, Ryan O'Dowd:
Local transfer learning from one data space to another. CoRR abs/2302.00160 (2023) - [i29]Quoc Thong Le Gia, Hrushikesh N. Mhaskar:
Numerical solutions to an inverse problem for a non-linear Helmholtz equation. CoRR abs/2302.01475 (2023) - [i28]Katarina Doctor, Tong Mao, Hrushikesh N. Mhaskar:
Encoding of data sets and algorithms. CoRR abs/2303.00984 (2023) - [i27]Hrushikesh N. Mhaskar:
Approximation by non-symmetric networks for cross-domain learning. CoRR abs/2305.03890 (2023) - [i26]Hrushikesh N. Mhaskar, Tong Mao:
Tractability of approximation by general shallow networks. CoRR abs/2308.03230 (2023) - 2022
- [i25]Hrushikesh N. Mhaskar:
Local approximation of operators. CoRR abs/2202.06392 (2022) - 2021
- [i24]Hrushikesh N. Mhaskar, Sergei V. Pereverzyev, Maria D. van der Walt:
A function approximation approach to the prediction of blood glucose levels. CoRR abs/2105.05893 (2021) - [i23]Srinjoy Das, Hrushikesh N. Mhaskar, Alexander Cloninger:
Kernel distance measures for time series, random fields and other structured data. CoRR abs/2109.14752 (2021) - [i22]Eric Mason, Hrushikesh N. Mhaskar, Adam Guo:
A manifold learning approach for gesture identification from micro-Doppler radar measurements. CoRR abs/2110.01670 (2021) - 2020
- [i21]Charles K. Chui, Ningning Han, Hrushikesh N. Mhaskar:
Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data. CoRR abs/2001.12006 (2020) - [i20]Hrushikesh N. Mhaskar:
Kernel based analysis of massive data. CoRR abs/2003.13226 (2020) - [i19]Alexander Cloninger, Hrushikesh N. Mhaskar:
Cautious Active Clustering. CoRR abs/2008.01245 (2020) - [i18]Alex Cloninger, Hrushikesh N. Mhaskar:
A low discrepancy sequence on graphs. CoRR abs/2010.04227 (2020) - 2019
- [i17]Hrushikesh N. Mhaskar, Alex Cloninger, Xiuyuan Cheng:
A witness function based construction of discriminative models using Hermite polynomials. CoRR abs/1901.02975 (2019) - [i16]Hrushikesh N. Mhaskar, Tomaso A. Poggio:
Function approximation by deep networks. CoRR abs/1905.12882 (2019) - [i15]Hrushikesh N. Mhaskar:
Super-resolution meets machine learning: approximation of measures. CoRR abs/1907.04895 (2019) - [i14]Hrushikesh N. Mhaskar:
Deep Gaussian networks for function approximation on data defined manifolds. CoRR abs/1908.00156 (2019) - [i13]Hrushikesh N. Mhaskar:
Dimension independent bounds for general shallow networks. CoRR abs/1908.09880 (2019) - 2018
- [i12]Tomaso A. Poggio, Kenji Kawaguchi, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Xavier Boix, Jack Hidary, Hrushikesh N. Mhaskar:
Theory of Deep Learning III: explaining the non-overfitting puzzle. CoRR abs/1801.00173 (2018) - [i11]Hrushikesh N. Mhaskar, Tomaso A. Poggio:
An analysis of training and generalization errors in shallow and deep networks. CoRR abs/1802.06266 (2018) - [i10]Abhejit Rajagopal, Shivkumar Chandrasekaran, Hrushikesh Narhar Mhaskar:
Deep Algorithms: designs for networks. CoRR abs/1806.02003 (2018) - 2017
- [i9]Hrushikesh N. Mhaskar, Sergei V. Pereverzyev, Maria D. van der Walt:
A deep learning approach to diabetic blood glucose prediction. CoRR abs/1707.05828 (2017) - [i8]Charles K. Chui, Hrushikesh Narhar Mhaskar:
A Fourier-invariant method for locating point-masses and computing their attributes. CoRR abs/1707.09319 (2017) - [i7]Charles K. Chui, Hrushikesh Narhar Mhaskar:
A unified method for super-resolution recovery and real exponential-sum separation. CoRR abs/1707.09428 (2017) - [i6]Hrushikesh N. Mhaskar:
Function approximation with ReLU-like zonal function networks. CoRR abs/1709.08174 (2017) - 2016
- [i5]Hrushikesh N. Mhaskar, Qianli Liao, Tomaso A. Poggio:
Learning Real and Boolean Functions: When Is Deep Better Than Shallow. CoRR abs/1603.00988 (2016) - [i4]Charles K. Chui, Hrushikesh Narhar Mhaskar:
Deep nets for local manifold learning. CoRR abs/1607.07110 (2016) - [i3]Hrushikesh N. Mhaskar, Tomaso A. Poggio:
Deep vs. shallow networks : An approximation theory perspective. CoRR abs/1608.03287 (2016) - [i2]Tomaso A. Poggio, Hrushikesh N. Mhaskar, Lorenzo Rosasco, Brando Miranda, Qianli Liao:
Why and When Can Deep - but Not Shallow - Networks Avoid the Curse of Dimensionality: a Review. CoRR abs/1611.00740 (2016) - 2009
- [i1]Hrushikesh N. Mhaskar:
Eignets for function approximation on manifolds. CoRR abs/0909.5000 (2009)
Coauthor Index
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