Fetching the paper…
Reading the bibliography…
The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems.
Mean width and volume of convex bodies in an n n -dimensional space
P.S. Urysohn · 1924
Earlier work this paper cites.
Some problems in multivariate analysis, Part I
C. Stein · 1956
Earlier work this paper cites.
ε \varepsilon -entropy and ε \varepsilon -capacity of sets in function spaces
A.N. Kolmogorov and V.M. Tikhomirov · 1959
Earlier work this paper cites.
Some matrix inequalities and metrization of matric-space
J. von Neumann · 1962
Earlier work this paper cites.
Some problems in covariance estimation
M.L. Eaton · 1970
Earlier work this paper cites.
Convergence of estimates under dimensionality restrictions
L. Le Cam · 1973
Earlier work this paper cites.
Statistical Estimation: Asymptotic Theory
I.A. Ibragimov and R.Z. Has’minskii · 1981
Earlier work this paper cites.
Approximation dans les espaces métriques et théorie de l’estimation
L. Birgé · 1983
Earlier work this paper cites.
Asymptotic theory of finite dimensional normed spaces
V.D. Milman and G. Schechtman · 1986
Earlier work this paper cites.
Group invariance applications in statistics
M.L. Eaton · 1989
Earlier work this paper cites.
Matrix Analysis
R.A. Horn and C.R. Johnson · 1990
Earlier work this paper cites.
Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data
D.L. Donoho · 1993
Earlier work this paper cites.
Minimax risk over l p l_{p} -balls for l q l_{q} -error
D.L. Donoho and I.M. Johnstone · 1994
Earlier work this paper cites.
Stein estimation in high dimensions: a retrospective
R. Beran · 1996
Earlier work this paper cites.
Matrix analysis
R. Bhatia · 1997
Earlier work this paper cites.
Mutual information, metric entropy and cumulative relative entropy risk
D. Haussler and M. Opper · 1997
Earlier work this paper cites.
Assouad, Fano, and Le Cam
Bin Yu · 1997
Cited alongside, same era.
Finding a large hidden clique in a random graph
N. Alon, M. Krivelevich, and B. Sudakov · 1998
Cited alongside, same era.
The volume of convex bodies and Banach space geometry
G. Pisier · 1999
Cited alongside, same era.
Information-theoretic determination of minimax rates of convergence
Y. Yang and A.R. Barron · 1999
Cited alongside, same era.
The expected norm of random matrices
Y. Seginer · 2000
Cited alongside, same era.
Handbook on the Geometry of Banach Spaces , volume 1, chapter Local operator theory, random matrices and Banach spaces, pages 317–366
K.R. Davidson and S. Szarek · 2001
Cited alongside, same era.
Optimal rates of convergence for covariance matrix estimation
T.T. Cai, C.-H. Zhang, and H.H. Zhou · 2010
Later among the works it cites.
Optimal selection of reduced rank estimators of high-dimensional matrices
F. Bunea, Y. She, and M.H. Wegkamp · 2011
Later among the works it cites.
Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
E.J. Candés and Y. Plan · 2011
Later among the works it cites.
Lower bounds for the minimax risk using f f -divergences, and applications
A. Guntuboyina · 2011
Later among the works it cites.
Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
V. Koltchinskii, K. Lounici, and A.B. Tsybakov · 2011
Later among the works it cites.
Oracle inequalities and optimal inference under group sparsity
K. Lounici, M. Pontil, S. Van De Geer, and A. B. Tsybakov · 2011
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Platelets: a multiscale approach for recovering edges and surfaces in photon-limited medical imaging
R.M. Willett and R.D. Nowak · 2003
Cited alongside, same era.
Some estimates of norms of random matrices
R. Latała · 2005
Cited alongside, same era.
Model selection and estimation in regression with grouped variables
M. Yuan and Y. Lin · 2006
Cited alongside, same era.
Concentration of mass on the schatten classes
O. Guédon and G. Paouris · 2007
Cited alongside, same era.
Operator norm consistent estimation of large-dimensional sparse covariance matrices
N. El Karoui · 2008
Cited alongside, same era.
From the Mahler conjecture to Gauss linking integrals
G. Kuperberg · 2008
Cited alongside, same era.
Later among the works it cites.
Estimation of (near) low-rank matrices with noise and high-dimensional scaling
S. Negahban and M.J. Wainwright · 2011
Later among the works it cites.
Exponential Screening and optimal rates of sparse estimation
P. Rigollet and A.B. Tsybakov · 2011
Later among the works it cites.
Estimation of high-dimensional low-rank matrices
A. Rohde and A.B. Tsybakov · 2011
Later among the works it cites.
Lectures in Geometric Funtional Analysis
R. Vershynin · 2011
Later among the works it cites.
Detection of a sparse submatrix of a high-dimensional noisy matrix
C. Butucea and Y. I. Ingster · 2012
Later among the works it cites.
Optimal rates of convergence for sparse covariance matrix estimation
T.T. Cai and H.H Zhou · 2012
Later among the works it cites.
Minimax-optimal rates for sparse additive models over kernel classes via convex programming
G. Raskutti, M.J. Wainwright, and B. Yu · 2012
Later among the works it cites.
Community detection in random networks
E. Arias-Castro and N. Verzelen · 2013
Closest in time.
On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix
X. Sun and A.B. Nobel · 2013
Closest in time.