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This article studies the Gram random matrix model $G=\frac1T\Sigma^{\rm T}\Sigma$, $\Sigma=\sigma(WX)$, classically found in the analysis of random feature maps and random neural networks, where $X=[x_1,\ldots,x_T]\in{\mathbb R}^{p\times T}$ is a (data) matrix of bounded norm, $W\in{\mathbb R}^{n\times p}$ is a matrix of independent zero-mean unit variance entries, and $\sigma:{\mathbb R}\to{\mathbb R}$ is a Lipschitz continuous (activation) function --- $\sigma(WX)$ being understood entry-wise.
[author] Titchmarsh, E. C.E. C. (1939). The Theory of Functions. Oxford University Press, New York, NY, USA. \endbibitem
1939
Earlier work this paper cites.
[author] Rosenblatt, FrankF. (1958). The perceptron: a probabilistic model for information storage and organization in the brain. Psychological review 65 386. \endbibitem
1958
Earlier work this paper cites.
[author] Loubaton, P.P. and Vallet, P.P. (2010). Almost sure localization of the eigenvalues in a Gaussian information plus noise model. Application to the spiked models. Electronic Journal of Probability 16 1934–1959. \endbibitem
1959
Earlier work this paper cites.
[author] Marc̆enko, V. A.V. A. and Pastur, L. A.L. A. (1967). Distribution of eigenvalues for some sets of random matrices. Math USSR-Sbornik 1 457-483. \endbibitem
1967
Earlier work this paper cites.
[author] Hornik, KurtK., Stinchcombe, MaxwellM. and White, HalbertH. (1989). Multilayer feedforward networks are universal approximators. Neural networks 2 359–366. \endbibitem
1989
Earlier work this paper cites.
[author] Akhiezer, N. I.N. I. and Glazman, I. M.I. M. (1993). Theory of linear operators in Hilbert space. Courier Dover Publications. \endbibitem
1993
Earlier work this paper cites.
[author] Silverstein, J. W.J. W. and Bai, Z. D.Z. D. (1995). On the empirical distribution of eigenvalues of a class of large dimensional random matrices. Journal of Multivariate Analysis 54 175-192. \endbibitem
1995
Earlier work this paper cites.
[author] Silverstein, J. W.J. W. and Choi, S.S. (1995). Analysis of the limiting spectral distribution of large dimensional random matrices. Journal of Multivariate Analysis 54 295-309. \endbibitem
1995
Earlier work this paper cites.
[author] Yates, R. D.R. D. (1995). A framework for uplink power control in cellular radio systems. IEEE Journal on Selected Areas in Communications 13 1341-1347. \endbibitem
1995
Earlier work this paper cites.
[author] Bai, Z. D.Z. D. and Silverstein, J. W.J. W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large dimensional sample covariance matrices. The Annals of Probability 26 316-345. \endbibitem
1998
Earlier work this paper cites.
[author] LeCun, Y.Y., Cortes, C.C. and Burges, C.C. (1998). The MNIST database of handwritten digits. \endbibitem
1998
Earlier work this paper cites.
[author] Williams, Christopher K. I.C. K. I. (1998). Computation with infinite neural networks. Neural Computation 10 1203–1216. \endbibitem
1998
Earlier work this paper cites.
[author] Jaeger, H.H. and Haas, H.H. (2004). Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science 304 78–80. \endbibitem
2004
Earlier work this paper cites.
[author] Ledoux, MichelM. (2005). The concentration of measure phenomenon 89. American Mathematical Soc. \endbibitem
2005
Earlier work this paper cites.
[author] Huang, Guang-BinG.-B., Zhu, Qin-YuQ.-Y. and Siew, Chee-KheongC.-K. (2006). Extreme learning machine: theory and applications. Neurocomputing 70 489–501. \endbibitem
2006
Cited alongside, same era.
[author] Bai, Z. D.Z. D. and Silverstein, J. W.J. W. (2007). On the signal-to-interference-ratio of CDMA systems in wireless communications. Annals of Applied Probability 17 81-101. \endbibitem
2007
Cited alongside, same era.
{binproceedings}
2007
Cited alongside, same era.
[author] Bai, Z. D.Z. D. and Silverstein, J. W.J. W. (2009). Spectral analysis of large dimensional random matrices, second ed. Springer Series in Statistics, New York, NY, USA. \endbibitem
2009
Cited alongside, same era.
[author] Kammoun, A.A., Kharouf, M.M., Hachem, W.W. and Najim, J.J. (2009). A central limit theorem for the sinr at the lmmse estimator output for large-dimensional signals. IEEE Transactions on Information Theory 55 5048–5063. \endbibitem
[author] Hoydis, J.J., Couillet, R.R. and Debbah, M.M. (2013). Random beamforming over quasi-static and fading channels: a deterministic equivalent approach. IEEE Transactions on Information Theory 58 6392-6425. \endbibitem
2013
Later among the works it cites.
2013
Later among the works it cites.
[author] Rudelson, MarkM., Vershynin, RomanR. et al. (2013). Hanson-Wright inequality and sub-Gaussian concentration. Electron. Commun. Probab 18 1–9. \endbibitem
2013
Later among the works it cites.
2014
Later among the works it cites.
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2009
Cited alongside, same era.
[author] El Karoui, N.N. (2009). Concentration of measure and spectra of random matrices: applications to correlation matrices, elliptical distributions and beyond. The Annals of Applied Probability 19 2362–2405. \endbibitem
2009
Cited alongside, same era.
[author] El Karoui, N.N. (2010). The spectrum of kernel random matrices. The Annals of Statistics 38 1–50. \endbibitem
2010
Cited alongside, same era.
[author] Pastur, L.L. and Ŝerbina, M.M. (2011). Eigenvalue distribution of large random matrices. American Mathematical Society. \endbibitem
2011
Cited alongside, same era.
{binproceedings}
2011
Cited alongside, same era.
[author] Benaych-Georges, F.F. and Nadakuditi, R. R.R. R. (2012). The singular values and vectors of low rank perturbations of large rectangular random matrices. Journal of Multivariate Analysis 111 120–135. \endbibitem
2012
Cited alongside, same era.
[author] Huang, Guang-BinG.-B., Zhou, HongmingH., Ding, XiaojianX. and Zhang, RuiR. (2012). Extreme learning machine for regression and multiclass classification. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 42 513–529. \endbibitem
2012
Cited alongside, same era.
{binproceedings}
2012
Cited alongside, same era.
[author] Cambria, ErikE., Gastaldo, PaoloP., Bisio, FedericaF. and Zunino, RodolfoR. (2015). An ELM-based model for affective analogical reasoning. Neurocomputing 149 443–455. \endbibitem
2015
Later among the works it cites.
{binproceedings}
2015
Later among the works it cites.
[author] Couillet, R.R., Pascal, F.F. and Silverstein, J. W.J. W. (2015). The random matrix regime of Maronna’s M-estimator with elliptically distributed samples. Journal of Multivariate Analysis 139 56–78. \endbibitem
2015
Later among the works it cites.
[author] Giryes, RajaR., Sapiro, GuillermoG. and Bronstein, Alex M.A. M. (2015). Deep Neural Networks with Random Gaussian Weights: A Universal Classification Strategy? IEEE Transactions on Signal Processing 64 3444-3457. \endbibitem
2015
Later among the works it cites.
[author] Schmidhuber, JürgenJ. (2015). Deep learning in neural networks: An overview. Neural Networks 61 85–117. \endbibitem
2015
Later among the works it cites.
[author] Couillet, R.R. and Benaych-Georges, F.F. (2016). Kernel spectral clustering of large dimensional data. Electronic Journal of Statistics 10 1393–1454. \endbibitem
2016
Later among the works it cites.
{binproceedings}
2016
Later among the works it cites.
{binproceedings}
2017
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[author] Zhenyu Liao, Romain CouilletR. C. (2017). A Large Dimensional Analysis of Least Squares Support Vector Machines. (submitted to) Journal of Machine Learning Research. \endbibitem
2017
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