Fetching the paper…
Reading the bibliography…
In this paper we study the concentration properties for the eigenvalues of kernel matrices, which are central objects in a wide range of kernel methods and, more recently, in network analysis.
Functions of positive and negative type and their connection with the theory of integral equations
James Mercer · 1909
Earlier work this paper cites.
Orthogonal polynomials
Gabor Szego · 1939
Earlier work this paper cites.
Distribution of eigenvalues for some sets of random matrices
Vladimit Marchenko and Leonid Pastur · 1967
Earlier work this paper cites.
Stochastic blockmodels:first steps
Paul Holland, Kathryn Laskey, and Samuel Leinhardt · 1983
Earlier work this paper cites.
Decoupling inequalities for the tail probabilities of multivariate U U -statistics
Victor H. De La Pena and Stephen J. Montgomery-Smith · 1995
Earlier work this paper cites.
Relative perturbation results for matrix eigenvalues and singular values
Ilse Ipsen · 1998
Earlier work this paper cites.
Gaussian regression and optimal finite dimensional linear models
Huaiyu Zhu, Christopher Williams, Richard Rohwer, and Michal Morciniec · 1998
Earlier work this paper cites.
Elements of Functional Analysis
Francis Hirsch and Gilles Lacombe · 1999
Earlier work this paper cites.
Exponential and moment inequalities for u-statistics
Evarist Gine, Rafal Latala, and Joel Zinn · 2000
Earlier work this paper cites.
Random approximation of spectra of integral operators
Vladimir Koltchinskii and Evarist Giné · 2000
Earlier work this paper cites.
Jacobi polynomials, weighted Sobolev spaces and approximation results of some singularities
Serge Nicaise · 2000
Earlier work this paper cites.
Latent space approaches to social network analysis
Peter Hoff, Adrian Raftery, and Mark Handcock · 2002
Earlier work this paper cites.
Exponential inequalities, with constants, for U U -statistics of order 2 2
Christian Houdré and Patricia Reynaud-Bouret · 2003
Earlier work this paper cites.
Random geometric graphs
Mathew Penrose · 2003
Earlier work this paper cites.
Learning with non-positive kernels
Cheng Ong, Xavier Mary, Stéphane Canu, and Alexander Smola · 2004
Earlier work this paper cites.
On the eigenspectrum of the Gram matrix and the generalization error of kernel p.c.a
John Shawe-Taylor, Christopher Williams, Nello Cristiani, and Jasvinder Kandola · 2005
Earlier work this paper cites.
Moment inequalities for U U -statistics
Radoslaw Adamczak · 2006
Earlier work this paper cites.
Accurate error bounds for the eigenvalues of the kernel matrix
Mikio L. Braun · 2006
Cited alongside, same era.
Spherical harmonics with maximal L p ( 2 < p ≤ 6 ) L_{p}(2<p\leq 6) norm growth
Xiaolong Han · 2006
Cited alongside, same era.
Limits of dense graph sequences
Lásló Lovász and Balász Szegedy · 2006
Cited alongside, same era.
Statistical properties of kernel principal component analysis
Gilles Blanchard, Olivier Bousquet, and Laurent Zwald · 2007
Cited alongside, same era.
Tracy-Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices
Noureddine El Karoui · 2007
Cited alongside, same era.
Convergent sequences of dense graphs i: subgraph frequencies, metric properties, and testing
Christian Borgs, Jenifer T. Chayes, Lásló Lovász, Vera Sós, and Katalin Vesztergombi · 2008
The spectrum of random kernel matrices:universality results for rough and varying kernels
Yen Do and Van Vu · 2013
Later among the works it cites.
Matrix concentration inequalities via the method of exchangeable pairs
Lester Mckey, Michael Jordan, Richard Chen, Brendan Farrell, and Joel Tropp · 2014
Later among the works it cites.
Testing for high-dimensional geometry in random graphs
Sébastien Bubeck, Jian Ding, Ronen Eldan, and Miklos Racz · 2016
Later among the works it cites.
Efron-Stein inequalities for random matrices
Lester Mckey and Joel Tropp · 2016
Later among the works it cites.
Oracle inequalities for network models and sparse graphon estimation
Olga Klopp, Alexandre Tsybakov, and Nicolas Verzelen · 2017
Later among the works it cites.
Concentration inequalities and moment bounds for sample covariance operators
Vladimir Koltchinskii and Karim Lounici · 2017
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Convergent sequences of dense graphs I. subgraph frequencies, metric properties and testing
Christian Borgs, Jennifer T. Chayes, Lásló Lovász, Vera Sos, and Katalin Vesztergombi · 2008
Cited alongside, same era.
Kernel methods in machine learning
Thomas Hoffman, Bernhard Schölkopf, and Alexander Smola · 2008
Cited alongside, same era.
The spectrum of kernel random matrices
Noureddine El Karoui · 2010
Cited alongside, same era.
On learning with integral operators
Lorenzo Rosasco, Mikhail Belkin, and Ernesto De Vito · 2010
Cited alongside, same era.
Positive definite kernels: past, present and future
Gregory E. Fasshauer · 2011
Cited alongside, same era.
Matrix analysis
Roger Horn and Charles Johnson · 2012
Cited alongside, same era.
Later among the works it cites.
Structured random matrices
Ramon Van Handel · 2017
Later among the works it cites.
Rate of convergence of spectral methods for graphon estimation
Jiaming Xu · 2017
Later among the works it cites.
Approximation beats concentration?
Mikhail Belkin · 2018
Closest in time.
Latent distance estimation for random geometric graph
Ernesto Araya and Yohann De Castro · 2019
Closest in time.
Towards understanding the spectral bias of deep learning
Yuan Cao, Zhiying Fang, Yue Wu, Ding-Xuan Zhou, and Quanquan Gu · 2019
Closest in time.
An inequality for Hermite polynomials
Jack Indritz · 2019
Closest in time.
Perturbation bounds for eigenspaces under a relative gap condition
Moritz Jirak and Martin Wahl · 2019
Closest in time.
High-dimensional covariance matrix estimation with missing observations
Karim Lounici · 2019
Closest in time.
Affine invariant covariance estimation for heavy-tailed distributions
Dmitrii Ostovskii and Alessandro Rudi · 2019
Closest in time.
Adaptive estimation of nonparametric geometric graphs
Yohann De Castro, Claire Lacour, and Thanh Mai Pham Ngoc · 2020
Closest in time.