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SIAM Journal on Scientific Computing, ISSN 1064-8275, 2018, Volume 40, Issue 2, pp. A629 - A652
Journal Article
Constructive Approximation, ISSN 0176-4276, 10/2011, Volume 34, Issue 2, pp. 257 - 280
In the present paper, we discuss the novel concept of super-compressed tensor-structured data formats in high-dimensional applications. We describe the... 
65N35 | Mathematics | FEM | 65F50 | Rank-structured tensor approximation | 65F10 | Analysis | Numerical Analysis | High-dimensional problems | 65F30 | Material sciences | Matrix-valued functions | Quantics folding of vectors | Stochastic modeling | DECOMPOSITION | ALGORITHMS | PRODUCT APPROXIMATION | MATHEMATICS | ELLIPTIC PROBLEMS | OPERATORS | Finite element method
Journal Article
Annals of Statistics, ISSN 0090-5364, 10/2017, Volume 45, Issue 5, pp. 1895 - 1919
Journal Article
IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2016, Volume 62, Issue 6, pp. 3702 - 3720
Journal Article
Physics Reports, ISSN 0370-1573, 02/2018, Volume 732, pp. 1 - 102
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf... 
HIGH-DIMENSIONAL INTEGRATION | SOURCE GALERKIN METHOD | PHYSICS, MULTIDISCIPLINARY | ALTERNATING LEAST-SQUARES | MULTIVARIATE INTERPOLATION | ORTHOGONAL FUNCTIONALS | PROBABILITY DENSITY-FUNCTION | GENERALIZED POLYNOMIAL CHAOS | VARIATIONAL FORMULATION | WIENER-HERMITE EXPANSION | STOCHASTIC COLLOCATION
Journal Article
Artificial Intelligence in Medicine, ISSN 0933-3657, 05/2019, Volume 96, pp. 134 - 141
Omics data usually have ultra-high dimension (p)and small sample size (n). Standard support vector machines (SVMs), which minimize the L norm for the primal... 
Ultra-high dimensional data | Feature selection | approximation | Metagenomics sequencing | SVM | Classification | L-0 approximation | PENALTY | MEDICAL INFORMATICS | ENGINEERING, BIOMEDICAL | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Journal Article
SIAM JOURNAL ON NUMERICAL ANALYSIS, ISSN 0036-1429, 2019, Volume 57, Issue 5, pp. 2217 - 2245
Given any domain X subset of R-d and a probability measure rho on X, we study the problem of approximating in L-2(X, rho) a given function u : X -> R, using... 
approximation theory | MATHEMATICS, APPLIED | weighted least squares | adaptive approximation | wavelets | convergence rates | high dimensional approximation | multivariate polynomials
Journal Article
Journal of Machine Learning Research, ISSN 1532-4435, 2010, Volume 11, pp. 411 - 450
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 02/2015, Volume 103, Issue 2, pp. 400 - 428
The numerical approximation of parametric partial differential equations is a computational challenge when the dimension of the parameter vector is large, due... 
Sparse high dimensional interpolation | Parametric PDEs | Curse of dimensionality | Sparse Legendre series | MATHEMATICS | MATHEMATICS, APPLIED | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | ANALYTIC REGULARITY | CONVERGENCE | Anisotropy | Analysis | Numerical Analysis | Mathematics
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 10/2012, Volume 18, Issue 5, pp. 915 - 953
Journal Article
BERNOULLI, ISSN 1350-7265, 05/2019, Volume 25, Issue 2, pp. 1326 - 1354
We consider the famous Rasch model, which is applied to psychometric surveys when n persons under test answer m questions. The score is given by a realization... 
item response model | ASYMPTOTIC EQUIVALENCE | Le Cam distance | high-dimensional central limit theorem | DENSITY-ESTIMATION | psychometrics | NONPARAMETRIC REGRESSION | WHITE-NOISE | STATISTICS & PROBABILITY | PARAMETERS | asymptotic equivalence of statistical experiments
Journal Article
IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 02/2018, Volume 29, Issue 2, pp. 500 - 508
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2016, Volume 54, Issue 4, pp. 2282 - 2301
The ability to efficiently and accurately approximate an inverse frame operator is critical for establishing the utility of numerical frame approximations.... 
Numerical frame approximation | High-dimensional frames | Localized frames | Fourier frames | Inverse frame operator | Nonuniform fourier data | MATHEMATICS, APPLIED | MRI | high-dimensional frames | RECONSTRUCTION | ALGORITHM | ROSETTE TRAJECTORIES | inverse frame operator | localized frames | numerical frame approximation | nonuniform Fourier data
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2018, Volume 87, Issue 311, pp. 1415 - 1450
Journal Article
by Dung, D
SBORNIK MATHEMATICS, ISSN 1064-5616, 04/2019, Volume 210, Issue 4, pp. 565 - 588
Consider the parametric elliptic problem - div (a(y)(x)del u(y)(x)) = f(x), x is an element of D, y is an element of I-infinity, u vertical bar(partial... 
MATHEMATICS | HYPERBOLIC CROSS APPROXIMATION | parametric and stochastic elliptic PDEs | POLYNOMIAL-APPROXIMATION | affine dependence of the diffusion coefficients | PARTIAL-DIFFERENTIAL-EQUATIONS | linear collective collocation approximation | high-dimensional problems
Journal Article
Artificial Intelligence In Medicine, ISSN 0933-3657, 05/2019, Volume 96, pp. 134 - 141
Omics data usually have ultra-high dimension ( ) and small sample size ( ). Standard support vector machines (SVMs), which minimize the norm for the primal... 
Ultra-high dimensional data | Feature selection | Metagenomics sequencing | SVM | L0 approximation | Classification
Journal Article
Structural and Multidisciplinary Optimization, ISSN 1615-147X, 5/2019, Volume 59, Issue 5, pp. 1439 - 1454
Journal Article
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