Search Results - "MHASKAR, H. N."

Super-Resolution Meets Machine Learning: Approximation of Measures by Mhaskar, H. N.

“…The problem of super-resolution in general terms is to recuperate a finitely supported measure μ given finitely many of its coefficients μ ^ ( k ) with respect…”
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A Low Discrepancy Sequence on Graphs by Cloninger, A., Mhaskar, H. N.

“…Many applications such as election forecasting, environmental monitoring, health policy, and graph based machine learning require taking expectation of…”
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A generalized diffusion frame for parsimonious representation of functions on data defined manifolds by Mhaskar, H.N.

“…One of the now standard techniques in semi-supervised learning is to think of a high dimensional data as a subset of a low dimensional manifold embedded in a…”
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Dimension independent bounds for general shallow networks by Mhaskar, H.N.

“…This paper proves an abstract theorem addressing in a unified manner two important problems in function approximation: avoiding curse of dimensionality and…”
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A direct approach for function approximation on data defined manifolds by Mhaskar, H.N.

“…In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere…”
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Learning on manifolds without manifold learning by Mhaskar, H.N., O’Dowd, Ryan

“…Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes…”
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Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature by Mhaskar, H. N., Narcowich, F. J., Ward, J. D.

“…Geodetic and meteorological data, collected via satellites for example, are genuinely scattered and not confined to any special set of points. Even so, known…”
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Theory-Inspired Deep Network for Instantaneous-Frequency Extraction and Subsignals Recovery From Discrete Blind-Source Data by Han, Ningning, Mhaskar, H. N., Chui, Charles K.

“…In the mathematical and engineering literature on signal processing and time-series analysis, there are two opposite points of view concerning the extraction…”
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An analysis of training and generalization errors in shallow and deep networks by Mhaskar, H.N., Poggio, T.

“…This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows…”
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When is approximation by Gaussian networks necessarily a linear process? by Mhaskar, H.N.

“…Let s≥1 be an integer. A Gaussian network is a function on R s of the form g( x )= ∑ k=1 N a k exp(−‖ x − x k‖ 2). The minimal separation among the centers,…”
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A manifold learning approach for gesture recognition from micro-Doppler radar measurements by Mason, E.S., Mhaskar, H.N., Guo, Adam

“…A recent paper (Mhaskar (2020)) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of…”
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A minimum Sobolev norm technique for the numerical discretization of PDEs by Chandrasekaran, S., Mhaskar, H.N.

“…Partial differential equations (PDEs) are discretized into an under-determined system of equations and a minimum Sobolev norm solution is shown to be efficient…”
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Locally learning biomedical data using diffusion frames by Ehler, M, Filbir, F, Mhaskar, H N

“…Diffusion geometry techniques are useful to classify patterns and visualize high-dimensional datasets. Building upon ideas from diffusion geometry, we outline…”
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Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere by LE GIA, Q. T, MHASKAR, H. N

“…We study the solutions of an equation of the form Lu=f, where L is a pseudo-differential operator defined for functions on the unit sphere embedded in a…”
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Minimum Sobolev norm interpolation with trigonometric polynomials on the torus by Chandrasekaran, S., Jayaraman, K.R., Mhaskar, H.N.

“…Let q⩾1 be an integer, y1,…,yM∈[-π,π]q, and η be the minimal separation among these points. Given the samples {f(yj)}j=1M of a smooth target function f of q…”
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A Function Approximation Approach to the Prediction of Blood Glucose Levels by Mhaskar, H. N., Pereverzyev, S. V., van der Walt, M. D.

“…The problem of real time prediction of blood glucose (BG) levels based on the readings from a continuous glucose monitoring (CGM) device is a problem of great…”
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LOCALIZED LINEAR POLYNOMIAL OPERATORS AND QUADRATURE FORMULAS ON THE SPHERE by LE GIA, Q. T., MHASKAR, H. N.

“…The purpose of this paper is to construct universal, auto-adaptive, localized, linear, polynomial (-valued) operators based on scattered data on the (hyper)…”
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Smooth function extension based on high dimensional unstructured data by CHUI, CHARLES K., MHASKAR, H. N.

“…, but have similar geometric properties, can be arranged to be close neighbors on the manifold. The objective of this paper is to incorporate the consideration…”
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Neural networks for functional approximation and system identification by Mhaskar, H N, Hahm, N

“…We construct generalized translation networks to approximate uniformly a class of nonlinear, continuous functionals defined on Lp ([-1, 1]s) for integer s > or…”
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Wiener type theorems for Jacobi series with nonnegative coefficients by MHASKAR, H. N., TIKHONOV, S.

“…This paper gives three theorems regarding functions integrable on [-1,1]-integrability (with respect to the Jacobi weight) on an interval near 1-integrability…”
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