Fetching the paper…
Reading the bibliography…
We consider best approximation problems in a nonlinear subset $\mathcal{M}$ of a Banach space of functions $(\mathcal{V},\|\bullet\|)$.
Joseph Jr., Armenak Petrosyan, Hoang Tran and Clayton. Webster · 1909
Earlier work this paper cites.
“The Expression of a Tensor or a Polyadic as a Sum of Products”
Frank. Hitchcock · 1927
Earlier work this paper cites.
“Necessary and Sufficient Conditions for the Uniform Convergence of Means to their Expectations”
V.. Vapnik and A.. Chervonenkis · 1982
Earlier work this paper cites.
“Extension theorems for Sobolev spaces”
Victor Burenkov · 1999
Earlier work this paper cites.
“On the mathematical foundations of learning”
Felipe Cucker and Steve Smale · 2001
Earlier work this paper cites.
“A Distribution-Free Theory of Nonparametric Regression”
László Györfi, Michael Kohler, Adam Krzyżak and Harro Walk · 2002
Earlier work this paper cites.
“Tensor network approaches for learning non-linear dynamical laws”, 2020
A. Goeßmann, M. Götte, I. Roth, R. Sweke, G. Kutyniok and J. Eisert · 2002
Earlier work this paper cites.
“New tight frames of curvelets and optimal representations of objects with piecewiseC2singularities”
Emmanuel. Candès and David. Donoho · 2003
Earlier work this paper cites.
“Stable signal recovery from incomplete and inaccurate measurements”
Emmanuel. Candès, Justin. Romberg and Terence Tao · 2006
Earlier work this paper cites.
“Learning Theory: An Approximation Theory Viewpoint”, Cambridge Monographs on Applied and Computational Mathematics
Felipe Cucker and Ding Zhou · 2007
Earlier work this paper cites.
“On the role of sparsity in Compressed Sensing and random matrix theory”
Roman Vershynin · 2009
Earlier work this paper cites.
“Compressive sensing and structured random matrices”
Holger Rauhut · 2010
Earlier work this paper cites.
“The Power of Convex Relaxation: Near-Optimal Matrix Completion”
E.. Candes and T. Tao · 2010
Earlier work this paper cites.
“Pointwise bounds for orthonormal basis elements in Hilbert spaces”, 2011
E. Kowalski · 2011
Earlier work this paper cites.
“An introduction to hierarchical (H-) rank and TT-rank of tensors with examples”
Lars Grasedyck and Wolfgang Hackbusch · 2011
Cited alongside, same era.
“Compressed sensing: theory and applications”
Yonina Eldar and Gitta Kutyniok · 2012
Cited alongside, same era.
“User-Friendly Tail Bounds for Sums of Random Matrices”
Joel. Tropp · 2012
Cited alongside, same era.
“Tensor spaces and numerical tensor calculus”
Wolfgang Hackbusch · 2012
Cited alongside, same era.
“Analysis of Discrete L 2 L^{2} Projection on Polynomial Spaces with Random Evaluations”
G. Migliorati, F. Nobile, E. von Schwerin and R. Tempone · 2014
Cited alongside, same era.
“Interpolation via weighted ℓ \ell 1 minimization”
Holger Rauhut and Rachel Ward · 2015
Cited alongside, same era.
“Optimal weighted least-squares methods”
Albert Cohen and Giovanni Migliorati · 2017
Later among the works it cites.
“Low rank tensor recovery via iterative hard thresholding”
Holger Rauhut, Reinhold Schneider and Željka Stojanac · 2017
Later among the works it cites.
“Infinite-Dimensional Compressed Sensing and Function Interpolation”
Ben Adcock · 2017
Later among the works it cites.
“Iterative methods based on soft thresholding of hierarchical tensors”
Markus Bachmayr and Reinhold Schneider · 2017
Later among the works it cites.
“Manifold Constrained Low-Rank Decomposition”
C. Chen, B. Zhang, A. Del Bue and V. Murino · 2017
Later among the works it cites.
“Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations”, 2018
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
“On Tensor Completion via Nuclear Norm Minimization”
Ming Yuan and Cun-Hui Zhang · 2015
Cited alongside, same era.
“Discrete least squares polynomial approximation with random evaluations - application to parametric and stochastic elliptic PDEs”
Abdellah Chkifa, Albert Cohen, Giovanni Migliorati, Fabio Nobile and Raul Tempone · 2015
Cited alongside, same era.
“Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points”
Giovanni Migliorati, Fabio Nobile and Raúl Tempone · 2015
Cited alongside, same era.
“On the Minimax Risk of Dictionary Learning”, 2015
Alexander Jung, Yonina. Eldar and Norbert Görtz · 2015
Cited alongside, same era.
“Tail bounds via generic chaining”
Sjoerd Dirksen · 2015
Cited alongside, same era.
“Breaking the coherence barrier: A new theory for compressed sensing”
Ben Adcock, Anders. Hansen, Clarice Poon and Bogdan Roman · 2016
Cited alongside, same era.
Julius Berner, Philipp Grohs and Arnulf Jentzen · 2018
Later among the works it cites.
“On the convergence rate of sparse grid least squares regression”
Bastian Bohn · 2018
Later among the works it cites.
“Reproducing kernels of Sobolev spaces on ℝ d \mathbb{R}^{d} and applications to embedding constants and tractability”
Erich Novak, Mario Ullrich, Henryk Woźniakowski and Shun Zhang · 2018
Later among the works it cites.
“Variational Monte Carlo—bridging concepts of machine learning and high-dimensional partial differential equations”
Martin Eigel, Reinhold Schneider, Philipp Trunschke and Sebastian Wolf · 2019
Later among the works it cites.
“Stable ALS approximation in the TT-format for rank-adaptive tensor completion”
Lars Grasedyck and Sebastian Krämer · 2019
Later among the works it cites.
“A Theoretical Analysis of Deep Neural Networks and Parametric PDEs”, 2019
Gitta Kutyniok, Philipp Petersen, Mones Raslan and Reinhold Schneider · 2019
Later among the works it cites.
“Compressed Sensing and Dictionary Learning”
Ke-Lin Du and M… Swamy · 2019
Later among the works it cites.
“Compressive Hermite Interpolation: Sparse, High-Dimensional Approximation from Gradient-Augmented Measurements”
Ben Adcock and Yi Sui · 2019
Later among the works it cites.
“Manifold Constrained Low-Rank and Joint Sparse Learning for Dynamic Cardiac MRI”
Q. Meng, X. Xiu and Y. Li · 2020
Closest in time.