Fetching the paper…
Reading the bibliography…
We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size.
Harish-Chandra, Differential operators on a semisimple lie algebra, American Journal of Mathematics , 87 (1957)
1957
Earlier work this paper cites.
N. Rosenzweig and C. E. Porter, ” repulsion of energy levels” in complex atomic spectra, Physical Review 120
1960
Earlier work this paper cites.
C. Itzykson and J.-B. Zuber, The planar approximation. ii, Journal of Mathematical Physics 21
1980
Earlier work this paper cites.
S. Chadha, G. Mahoux, and M. L. Mehta, A method of integration over matrix variables: 2, Journal of Physics A: Mathematical and General 14
1981
Earlier work this paper cites.
M. Mézard, G. Parisi, and M. A. Virasoro, Spin-Glass Theory and Beyond , Lecture Notes in Physics, Vol. 9 (World Scientific, Singapore, 1987)
1987
Earlier work this paper cites.
E. Brézin and S. R. Wadia, The large N expansion in quantum field theory and statistical physics (World scientific, 1993)
1993
Earlier work this paper cites.
M. L. Mehta, A method of integration over matrix variables, in The large N Expansion In Quantum Field Theory And Statistical Physics: From Spin Systems to 2-Dimensional Gravity (World Scientific, 1993) pp. 616–629
1993
Earlier work this paper cites.
V. Kazakov and A. Migdal, Induced gauge theory at large N, Nuclear Physics B 397
1993
Earlier work this paper cites.
V. Kazakov, D-dimensional induced gauge theory as a solvable matrix model, Nuclear Physics B-Proceedings Supplements 30
1993
Earlier work this paper cites.
A. Matytsin, On the large-n limit of the Itzykson-Zuber integral, Nuclear Physics B 411
1994
Earlier work this paper cites.
B. A. Olshausen and D. J. Field, Emergence of simple-cell receptive field properties by learning a sparse code for natural images, Nature 381
1996
Earlier work this paper cites.
E. Brézin and S. Hikami, Correlations of nearby levels induced by a random potential, Nuclear Physics B 479
1996
Earlier work this paper cites.
B. A. Olshausen and D. J. Field, Sparse coding with an overcomplete basis set: A strategy employed by v1?, Vision research 37
1997
Earlier work this paper cites.
A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines, A blind source separation technique using second-order statistics, IEEE Transactions on signal processing 45
1997
Earlier work this paper cites.
A. Zvonkin, Matrix integrals and map enumeration: an accessible introduction, Mathematical and Computer Modelling 26
1997
Earlier work this paper cites.
A. Matytsin and P. Zaugg, Kosterlitz-Thouless phase transitions on discretized random surfaces, Nuclear Physics B 497
1997
Earlier work this paper cites.
G. B. Arous and A. Guionnet, Large deviations for wigner’s law and voiculescu’s non-commutative entropy, Probability theory and related fields 108
1997
Earlier work this paper cites.
G. B. Arous and O. Zeitouni, Large deviations from the circular law, ESAIM: Probability and Statistics 2
1998
Earlier work this paper cites.
V. A. Kazakov, Solvable matrix models, arXiv preprint hep-th/0003064 (2000)
2000
Earlier work this paper cites.
P. Zinn-Justin, The dilute potts model on random surfaces, Journal of Statistical Physics 98
2000
Earlier work this paper cites.
F. Hiai and D. Petz, A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices, in Annales de l’Institut Henri Poincare (B) Probability and Statistics , Vol. 36 (Elsevier, 2000) pp. 71–85
2000
Earlier work this paper cites.
I. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, The Annals of statistics 29
2001
Earlier work this paper cites.
P. Bleher and A. Its, Random matrix models and their applications , Vol. 40 (Cambridge university press, 2001)
2001
Earlier work this paper cites.
K. J. Johansson, Universality of the local spacing distribution in certain ensembles of hermitian Wigner matrices, Communications in Mathematical Physics 215
2001
Earlier work this paper cites.
A. Guionnet and O. Zeitouni, Large deviations asymptotics for spherical integrals, Journal of functional analysis 188
2002
Earlier work this paper cites.
K. Kreutz-Delgado, J. F. Murray, B. D. Rao, K. Engan, T.-W. Lee, and T. J. Sejnowski, Dictionary learning algorithms for sparse representation, Neural computation 15
2003
Earlier work this paper cites.
B. Collins, Moments and cumulants of polynomial random variables on unitarygroups, the Itzykson-Zuber integral, and free probability, International Mathematics Research Notices 2003
2003
Earlier work this paper cites.
P. Zinn-Justin and J.-B. Zuber, On some integrals over the U(N) unitary group and their large N limit, Journal of Physics A: Mathematical and General 36
2003
Earlier work this paper cites.
B. Schlittgen and T. Wettig, Generalizations of some integrals over the unitary group, Journal of Physics A: Mathematical and General 36
2003
Earlier work this paper cites.
E. Gudowska-Nowak, R. A. Janik, J. Jurkiewicz, and M. A. Nowak, Infinite products of large random matrices and matrix-valued diffusion, Nuclear Physics B 670
2003
Earlier work this paper cites.
M. L. Mehta, Random matrices , Vol. 142 (Academic press, 2004)
2004
Earlier work this paper cites.
I. Johnstone and A. Lu, Sparse principal components analysis, Unpublished manuscript 7
2004
Earlier work this paper cites.
A. Guionnet, First order asymptotics of matrix integrals; a rigorous approach towards the understanding of matrix models, Communications in mathematical physics 244
2004
Earlier work this paper cites.
J. Baik, G. B. Arous, and S. Péché, Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices, Annals of Probability , 1643 (2005)
2005
Earlier work this paper cites.
M. Stephanov, J. Verbaarschot, and T. Wettig, Random matrices, arXiv preprint hep-ph/0509286 (2005)
2005
Earlier work this paper cites.
D. Guo, S. Shamai, and S. Verdú, Mutual information and minimum mean-square error in gaussian channels, IEEE Trans. on Inf. Theory 51
2005
Earlier work this paper cites.
The factor 4 4 that differs from the 2 2 in the usual I-MMSE relation Guo et al. 2005 comes from the fact that the Wigner matrix to denoise has only a fraction N ( N + 1 ) / ( 2 N 2 ) = 1 / 2 + O ( 1 / N ) N(N+1)/(2N^{2})=1/2+O(1/N) of independent entries. The O ( 1 / N ) O(1/N) correction comes from the diagonal terms in matrix 𝑺 {\bm{S}} for which the signal-to-noise ratio is different than the one of the off-diagonal entries. The complex noise case of the I-MMSE relation is discussed in Section V.D of Guo et al. 2005
2005
Earlier work this paper cites.
A. Edelman and N. R. Rao, Random matrix theory, Acta numerica 14
2005
Earlier work this paper cites.
H. Zou, T. Hastie, and R. Tibshirani, Sparse principal component analysis, Journal of computational and graphical statistics 15
2006
Earlier work this paper cites.
J. Baik and J. W. Silverstein, Eigenvalues of large sample covariance matrices of spiked population models, Journal of multivariate analysis 97
2006
Earlier work this paper cites.
Y. V. Fyodorov and I. Williams, Replica symmetry breaking condition exposed by random matrix calculation of landscape complexity, Journal of Statistical Physics 129
2007
Earlier work this paper cites.
W. Bryc, Computing moments of free additive convolution of measures, Applied mathematics and computation 194
2007
Cited alongside, same era.
J.-B. Zuber, The large-n limit of matrix integrals over the orthogonal group, Journal of Physics A: Mathematical and Theoretical 41
2008
Cited alongside, same era.
A. Ghaderipoor and C. Tellambura, Generalization of some integrals over unitary matrices by character expansion of groups, Journal of mathematical physics 49
2008
Cited alongside, same era.
J. Mairal, F. Bach, J. Ponce, and G. Sapiro, Online dictionary learning for sparse coding, in Proceedings of the 26th annual international conference on machine learning (2009) pp. 689–696
2009
Cited alongside, same era.
E. Candès and B. Recht, Exact matrix completion via convex optimization, Foundations of Computational mathematics 9
2009
P. J. Forrester and D.-Z. Liu, Singular values for products of complex Ginibre matrices with a source: hard edge limit and phase transition, Communications in Mathematical Physics 344
2016
Later among the works it cites.
M. Kieburg, A. B. Kuijlaars, and D. Stivigny, Singular value statistics of matrix products with truncated unitary matrices, International Mathematics Research Notices 2016
2016
Later among the works it cites.
D.-Z. Liu, D. Wang, and L. Zhang, Bulk and soft-edge universality for singular values of products of Ginibre random matrices, in Annales de l’Institut Henri Poincaré, Probabilités et Statistiques , Vol. 52 (Institut Henri Poincaré, 2016) pp. 1734–1762
2016
Later among the works it cites.
B. Hajek, Y. Wu, and J. Xu, Information limits for recovering a hidden community, IEEE Transactions on Information Theory 63
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…
Cited alongside, same era.
S. B. Korada and N. Macris, Exact solution of the gauge symmetric p-spin glass model on a complete graph, Journal of Statistical Physics 136
2009
Cited alongside, same era.
M. Mézard and A. Montanari, Information, Physics and Computation (Oxford Press, 2009)
2009
Cited alongside, same era.
We note that this assumption is reminiscent of results in Benaych-Georges 2009 (see also Belinschi et al. 2009 ) for the addition of two large random matrices with at least one being bi-unitary invariant
2009
Cited alongside, same era.
F. Benaych-Georges, Rectangular random matrices, related convolution, Probability Theory and Related Fields 144
2009
Cited alongside, same era.
2009
Cited alongside, same era.
G. W. Anderson, A. Guionnet, and O. Zeitouni, An introduction to random matrices , 118 (Cambridge university press, 2010)
2010
Cited alongside, same era.
E. J. Candès and T. Tao, The power of convex relaxation: Near-optimal matrix completion, IEEE Transactions on Information Theory 56
2010
Cited alongside, same era.
E. Abbe, Community detection and stochastic block models: recent developments, The Journal of Machine Learning Research 18
2017
Later among the works it cites.
F. Caltagirone, M. Lelarge, and L. Miolane, Recovering asymmetric communities in the stochastic block model, IEEE Transactions on Network Science and Engineering 5
2017
Later among the works it cites.
T. Lesieur, F. Krzakala, and L. Zdeborová, Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications, Journal of Statistical Mechanics: Theory and Experiment 2017
2017
Later among the works it cites.
Y. Deshpande, E. Abbe, and A. Montanari, Asymptotic mutual information for the balanced binary stochastic block model, Information and Inference: A Journal of the IMA 6
2017
Later among the works it cites.
2017
Later among the works it cites.
T. Lesieur, L. Miolane, M. Lelarge, F. Krzakala, and L. Zdeborová, Statistical and computational phase transitions in spiked tensor estimation, in IEEE International Symposium on Information Theory (ISIT), 2017
2017
Later among the works it cites.
2017
Later among the works it cites.
2017
Later among the works it cites.
J. A. Mingo and R. Speicher, Free probability and random matrices , Vol. 35 (Springer, 2017)
2017
Later among the works it cites.
G. Menon, The complex Burgers equation, the HCIZ integral and the Calogero-Moser system (2017)
2017
Later among the works it cites.
G. Livan, M. Novaes, and P. Vivo, Introduction to random matrices: theory and practice , Vol. 26 (Springer, 2018)
2018
Later among the works it cites.
A. Perry, A. S. Wein, A. S. Bandeira, and A. Moitra, Optimality and sub-optimality of PCA I: Spiked random matrix models, Annals of Statistics 46
2018
Later among the works it cites.
2018
Later among the works it cites.
A. El Alaoui and F. Krzakala, Estimation in the spiked Wigner model: a short proof of the replica formula, in 2018 IEEE International Symposium on Information Theory (ISIT) (IEEE, 2018) pp. 1874–1878
2018
Later among the works it cites.
J.-C. Mourrat, Hamilton-Jacobi equations for mean-field disordered systems, arXiv:1811.01432 (2018)
2018
Later among the works it cites.
H. C. Schmidt, Statistical physics of sparse and dense models in optimization and inference (2018)
2018
Later among the works it cites.
J.-C. Mourrat, Hamilton-Jacobi equations for finite-rank matrix inference, arXiv:1904.05294 (2019)
2019
Later among the works it cites.
S. S. Mannelli, G. Biroli, C. Cammarota, F. Krzakala, and L. Zdeborová, Who is afraid of big bad minima? analysis of gradient-flow in spiked matrix-tensor models, in Advances in Neural Information Processing Systems (2019) pp. 8676–8686
2019
Later among the works it cites.
S. S. Mannelli, F. Krzakala, P. Urbani, and L. Zdeborova, Passed & spurious: Descent algorithms and local minima in spiked matrix-tensor models, in international conference on machine learning (PMLR, 2019) pp. 4333–4342
2019
Later among the works it cites.
A. Maillard, L. Foini, A. L. Castellanos, F. Krzakala, M. Mézard, and L. Zdeborová, High-temperature expansions and message passing algorithms, Journal of Statistical Mechanics: Theory and Experiment 2019
2019
Later among the works it cites.
J. Barbier, Overlap matrix concentration in optimal Bayesian inference, Information and Inference: A Journal of the IMA (2019)
2019
Later among the works it cites.
J. Barbier, N. Macris, and C. Rush, All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimation, in Advances in Neural Information Processing Systems (2020)
2020
Later among the works it cites.
G. Reeves, Information-theoretic limits for the matrix tensor product, IEEE Journal on Selected Areas in Information Theory (2020)
2020
Later among the works it cites.
2020
Later among the works it cites.
M. Potters and J.-P. Bouchaud, A First Course in Random Matrix Theory: For Physicists, Engineers and Data Scientists (Cambridge University Press, 2020)
2020
Later among the works it cites.
M. Potters and J.-P. Bouchaud, A first course in random matrix theory (Cambridge University Press, 2021)
2021
Closest in time.
2021
Closest in time.
2021
Closest in time.
2021
Closest in time.
2021
Closest in time.
2021
Closest in time.
It is now known that the estimator proposed in paper Bun et al. 2016 is Bayes-optimal in certain settings, see Maillard et al. 2021
2021
Closest in time.
G. Biroli and M. Tarzia, Lévy-Rosenzweig-Porter random matrix ensemble, Physical Review B 103
2021
Closest in time.
J. Leake, C. McSwiggen, and N. K. Vishnoi, Sampling matrices from Harish-Chandra–Itzykson–Zuber densities with applications to quantum inference and differential privacy, in Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (2021) pp. 1384–1397
2021
Closest in time.
2021
Closest in time.