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This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in random features regression.
Earle, C. J
1968
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[author] Helton, J. WilliamJ. W., McCullough, Scott A.S. A. and Vinnikov, VictorV. (2006). Noncommutative convexity arises from linear matrix inequalities. Journal of Functional Analysis 240 105-191. https://doi.org/10.1016/j.jfa.2006.03.018
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[author] Helton, J. WilliamJ. W., Far, Reza RashidiR. R. and Speicher, RolandR. (2007). Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints. International Mathematics Research Notices. 10.1093/imrn/rnm086
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Rahimi, A
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[author] Krizhevsky, AlexA. (2009). Learning multiple layers of features from tiny images Technical Report, University of Toronto
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[author] Deng, LiL. (2012). The mnist database of handwritten digit images for machine learning research. IEEE Signal Processing Magazine 29 141–142
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[author] Tao, TerenceT. (2012). Topics in Random Matrix Theory. Graduate Studies in Mathematics 132. American Mathematical Society
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[author] Anderson, Greg W.G. W. (2013). Convergence of the largest singular value of a polynomial in independent Wigner matrices. The Annals of Probability 41. 10.1214/11-aop739
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[author] Belinschi, Serban T.S. T., Mai, TobiasT. and Speicher, RolandR. (2017). Analytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem. Journal für die reine und angewandte Mathematik (Crelles Journal) 2017 21–53. doi:10.1515/crelle-2014-0138
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[author] Anderson, Greg W.G. W. (2015). A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices. Annales de l’I.H.P. Probabilités et statistiques 51 809-841. 10.1214/14-AIHP602
2015
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[author] Ajanki, Oskari H.O. H., Erdős, LászlóL. and Krüger, TorbenT. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields 169. 10.1007/s00440-016-0740-2
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[author] Ajanki, Oskari H.O. H., Krüger, TorbenT. and Erdős, LászlóL. (2017). Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half-Plane. Communications on Pure and Applied Mathematics 70 1672-1705. https://doi.org/10.1002/cpa.21639
2017
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[author] Helton, J. WilliamJ. W., Mai, TobiasT. and Speicher, RolandR. (2018). Applications of realizations (aka linearizations) to free probability. Journal of Functional Analysis 274 1-79. https://doi.org/10.1016/j.jfa.2017.10.003
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[author] Luger, AnnemarieA. and Nedic, MitjaM. (2017). A characterization of Herglotz–Nevanlinna functions in two variables via integral representations. Arkiv för Matematik 55 199–216. 10.4310/arkiv.2017.v55.n1.a10
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Cited alongside, same era.
Pennington, J
2017
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[author] Xiao, HanH., Rasul, KashifK. and Vollgraf, RolandR. (2017). Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
2017
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[author] Alt, JohannesJ. (2018). Dyson equation and eigenvalue statistics of random matrices, PhD thesis, IST Austria
2018
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[author] Alt, JohannesJ., Erdős, LászlóL. and Krüger, TorbenT. (2018). The Dyson equation with linear self-energy: spectral bands, edges and cusps. Documenta Mathematica 25 1421-1539. 10.25537/dm.2020v25.1421-1539
2018
Tripuraneni, N
2021
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2021
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Adlam, B
2022
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[author] Benigni, LucasL. and Péché, SandrineS. (2022). Largest Eigenvalues of the Conjugate Kernel of Single-Layered Neural Networks
2022
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[author] Chouard, ClémentC. (2022). Quantitative deterministic equivalent of sample covariance matrices with a general dependence structure
2022
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Goldt, S
2022
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[author] Louart, CosmeC., Liao, ZhenyuZ. and Couillet, RomainR. (2018). A random matrix approach to neural networks. The Annals of Applied Probability 28 1190 – 1248. 10.1214/17-AAP1328
2018
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[author] Vershynin, RomanR. (2018). High-Dimensional Probability: An Introduction with Applications in Data Science. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press. 10.1017/9781108231596
2018
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[author] Alt, JohannesJ., Erdős, LászlóL., Krüger, TorbenT. and Nemish, YuriyY. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 661 – 696. 10.1214/18-AIHP894
2019
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[author] Belkin, MikhailM., Hsu, DanielD., Ma, SiyuanS. and Mandal, SoumikS. (2019). Reconciling modern machine-learning practice and the classical bias-variance trade-off. Proceedings of the National Academy of Sciences 116 15849-15854. 10.1073/pnas.1903070116
2019
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[author] Erdős, LászlóL. (2019). The matrix Dyson equation and its applications for random matrices
2019
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[author] Erdős, LászlóL., Krüger, TorbenT. and Schröder, DominikD. (2019). Random Matrices With Slow Correlation Decay. Forum of Mathematics, Sigma 7. 10.1017/fms.2019.2
2019
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[author] Alt, JohannesJ., Erdős, LászlóL., Krüger, TorbenT. and Schröder, DominikD. (2020). Correlated random matrices: Band rigidity and edge universality. The Annals of Probability 48. 10.1214/19-aop1379
2020
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[author] Hastie, TrevorT., Montanari, AndreaA., Rosset, SaharonS. and Tibshirani, Ryan J.R. J. (2022). Surprises in high-dimensional ridgeless least squares interpolation. The Annals of Statistics 50 949 – 986. 10.1214/21-AOS2133
2022
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[author] Hu, HongH. and Lu, Yue M.Y. M. (2023). Universality Laws for High-Dimensional Learning With Random Features. IEEE Transactions on Information Theory 69 1932-1964. 10.1109/TIT.2022.3217698
2022
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[author] Loureiro, BrunoB., Gerbelot, CédricC., Cui, HugoH., Goldt, SebastianS., Krzakala, FlorentF., Mézard, MarcM. and Zdeborová, LenkaL. (2022). Learning curves of generic features maps for realistic datasets with a teacher-student model*. Journal of Statistical Mechanics: Theory and Experiment 2022 114001. 10.1088/1742-5468/ac9825
2022
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[author] Mei, SongS. and Montanari, AndreaA. (2022). The Generalization Error of Random Features Regression: Precise Asymptotics and the Double Descent Curve. Communications on Pure and Applied Mathematics 75 667-766. https://doi.org/10.1002/cpa.22008
2022
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[author] Bosch, DavidD., Panahi, AshkanA. and Hassibi, BabakB. (2023). Precise Asymptotic Analysis of Deep Random Feature Models
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2023
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