Fetching the paper…
Reading the bibliography…
We determine statistical and computational limits for estimation of a rank-one matrix (the spike) corrupted by an additive gaussian noise matrix, in a sparse limit, where the underlying hidden vector (that constructs the rank-one matrix) has a number of non-zero components that scales sub-linearly with the total dimension of the vector, and the signal-to-noise ratio tends to infinity at an appropriate speed.
Envelope theorems for arbitrary choice sets
P. Milgrom and I. Segal · 2002
Earlier work this paper cites.
A CDMA multiuser detection algorithm on the basis of belief propagation
Y. Kabashima · 2003
Earlier work this paper cites.
Learning intrinsic dimension and intrinsic entropy of high-dimensional datasets
J. Costa and A. Hero · 2004
Earlier work this paper cites.
Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
J. Baik, G. B. Arous, and S. Péché · 2005
Earlier work this paper cites.
Mutual information and minimum mean-square error in gaussian channels
D. Guo, S. Shamai, and S. Verdu · 2005
Earlier work this paper cites.
Stable signal recovery from incomplete and inaccurate measurements
E. J. Candès, J. K. Romberg, and T. Tao · 2006
Earlier work this paper cites.
Compressed sensing
D. L. Donoho · 2006
Earlier work this paper cites.
The largest eigenvalue of small rank perturbations of hermitian random matrices
S. Péché · 2006
Earlier work this paper cites.
The largest eigenvalue of rank one deformation of large wigner matrices
D. Féral and S. Péché · 2007
Earlier work this paper cites.
A Wavelet Tour of Signal Processing (Third Edition): The Sparse Way
S. Mallat · 2009
Earlier work this paper cites.
Exact matrix completion via convex optimization
E. Candès and B. Recht · 2009
Earlier work this paper cites.
The elements of statistical learning: data mining, inference and prediction
T. Hastie, R. Tibshirani, and J. Friedman · 2009
Earlier work this paper cites.
Message-passing algorithms for compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2009
Earlier work this paper cites.
High-dimensional analysis of semidefinite relaxations for sparse principal components
A. A. Amini and M. J. Wainwright · 2009
Earlier work this paper cites.
Information, physics and computation
M. Mezard and A. Montanari · 2009
Earlier work this paper cites.
Exact solution of the gauge symmetric p-spin glass model on a complete graph
S. B. Korada and N. Macris · 2009
Earlier work this paper cites.
The dynamics of message passing on dense graphs, with applications to compressed sensing
M. Bayati and A. Montanari · 2011
Earlier work this paper cites.
Generalized approximate message passing for estimation with random linear mixing
S. Rangan · 2011
Earlier work this paper cites.
Estimation in gaussian noise: Properties of the minimum mean-square error
D. Guo, Y. Wu, S. S. Shitz, and S. Verdú · 2011
Earlier work this paper cites.
Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices
F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborová · 2012
Earlier work this paper cites.
Graphical models concepts in compressed sensing
A. Montanari · 2012
Earlier work this paper cites.
Complexity theoretic lower bounds for sparse principal component detection
Q. Berthet and P. Rigollet · 2013
Earlier work this paper cites.
State evolution for general approximate message passing algorithms, with applications to spatial coupling
A. Javanmard and A. Montanari · 2013
Cited alongside, same era.
Concentration inequalities: A nonasymptotic theory of independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
Cited alongside, same era.
Sparse Modeling: Theory, Algorithms, and Applications
I. Rish and G. Grabarnik · 2014
Cited alongside, same era.
Information-theoretically optimal sparse pca
Y. Deshpande and A. Montanari · 2014
Cited alongside, same era.
Bilinear generalized approximate message passing. part i: Derivation
J. T. Parker, P. Schniter, and V. Cevher · 2014
Cited alongside, same era.
An iterative construction of solutions of the tap equations for the sherrington–kirkpatrick model
Statistical and computational phase transitions in spiked tensor estimation
T. Lesieur, L. Miolane, M. Lelarge, F. Krzakala, and L. Zdeborová · 2017
Later among the works it cites.
The Layered Structure of Tensor Estimation and its Mutual Information
J. Barbier, N. Macris, and L. Miolane · 2017
Later among the works it cites.
High dimensional regression with binary coefficients. estimating squared error and a phase transtition
D. Gamarnik and I. Zadik · 2017
Later among the works it cites.
Estimation of low-rank matrices via approximate message passing
A. Montanari and R. Venkataramanan · 2017
Later among the works it cites.
Constrained low-rank matrix estimation: phase transitions, approximate message passing and applications
T. Lesieur, F. Krzakala, and L. Zdeborová · 2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
E. Bolthausen · 2014
Cited alongside, same era.
Statistical Learning with Sparsity: The Lasso and Generalizations
T. Hastie, R. Tibshirani, and M. Wainwright · 2015
Cited alongside, same era.
Finding hidden cliques of size N / e \sqrt{N/e} in nearly linear time
Y. Deshpande and A. Montanari · 2015
Cited alongside, same era.
Hyperspectral unmixing via turbo bilinear approximate message passing
J. Vila, P. Schniter, and J. Meola · 2015
Cited alongside, same era.
Non-negative principal component analysis: Message passing algorithms and sharp asymptotics
A. Montanari and E. Richard · 2015
Cited alongside, same era.
Optimal estimation and rank detection for sparse spiked covariance matrices
T. Cai, Z. Ma, and Y. Wu · 2015
Cited alongside, same era.
Do semidefinite relaxations solve sparse pca up to the information limit?
R. Krauthgamer, B. Nadler, and D. Vilenchik · 2015
Cited alongside, same era.
A. E. Alaoui, F. Krzakala, and M. I. Jordan · 2017
Later among the works it cites.
Fundamental limits of symmetric low-rank matrix estimation
M. Lelarge and L. Miolane · 2018
Later among the works it cites.
The adaptive interpolation method: a simple scheme to prove replica formulas in bayesian inference
J. Barbier and N. Macris · 2018
Later among the works it cites.
Iterative reconstruction of rank-one matrices in noise
A. K. Fletcher and S. Rangan · 2018
Later among the works it cites.
Reducibility and computational lower bounds for problems with planted sparse structure
M. Brennan, G. Bresler, and W. Huleihel · 2018
Later among the works it cites.
Estimation in the spiked wigner model: a short proof of the replica formula
A. El Alaoui and F. Krzakala · 2018
Later among the works it cites.
Optimality and sub-optimality of pca i: Spiked random matrix models
A. Perry, A. S. Wein, A. S. Bandeira, A. Moitra, et al · 2018
Later among the works it cites.
Detection limits in the high-dimensional spiked rectangular model
A. E. Alaoui and M. I. Jordan · 2018
Later among the works it cites.
Finite sample analysis of approximate message passing algorithms
C. Rush and R. Venkataramanan · 2018
Later among the works it cites.
High-Dimensional Statistics: A Non-Asymptotic Viewpoint
M. Wainwright · 2019
Later among the works it cites.
Optimal errors and phase transitions in high-dimensional generalized linear models
J. Barbier, F. Krzakala, N. Macris, L. Miolane, and L. Zdeborová · 2019
Later among the works it cites.
The adaptive interpolation method for proving replica formulas. applications to the curie–weiss and wigner spike models
J. Barbier and N. Macris · 2019
Later among the works it cites.
Hamilton-jacobi equations for finite-rank matrix inference
J.-C. Mourrat · 2019
Later among the works it cites.
The all-or-nothing phenomenon in sparse linear regression
G. Reeves, J. Xu, and I. Zadik · 2019
Later among the works it cites.
The overlap gap property in principal submatrix recovery
D. Gamarnik, A. Jagannath, and S. Sen · 2019
Later among the works it cites.
Mutual information for low-rank even-order symmetric tensor factorization
J. Barbier, C. Luneau, and N. Macris · 2019
Later among the works it cites.
Mutual information and optimality of approximate message-passing in random linear estimation
J. Barbier, N. Macris, M. Dia, and F. Krzakala · 2020
Closest in time.