Fetching the paper…
Reading the bibliography…
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a Gaussian mixture distribution.
——, “Some inequalities for gaussian processes and applications,” Israel Journal of Mathematics , vol. 50, no. 4, pp. 265–289, Dec. 1985
1985
Earlier work this paper cites.
Y. Gordon, On Milman’s inequality and random subspaces which escape through a mesh in ℝ n \mathbb{R}^{n} . Springer, 1988
1988
Earlier work this paper cites.
P. McCullagh and J. A. Nelder, Generalized Linear Models, Second Edition . London: Chapman & Hall, 1989
1989
Earlier work this paper cites.
W. K. Newey and D. L. McFadden, “Large sample estimation and hypothesis testing,” in Handbook of Econometrics , D. L. McFadden and R. F. Engle, Eds. Elsevier, 1994, vol. 4, pp. 2111–2245
1994
Earlier work this paper cites.
R. K. Sundaram, A first course in optimization theory . Cambridge University Press, 1996
1996
Earlier work this paper cites.
Y. Freund and R. E. Schapire, “A decision-theoretic generalization of on-line learning and an application to boosting,” J. Comput. Syst. Sci. , vol. 55, no. 1, pp. 119–139, Aug. 1997
1997
Earlier work this paper cites.
V. Vapnik, Statistical learning theory . New York: John Wiley and Sons, 1998
1998
Earlier work this paper cites.
S. Boyd and L. Vandenberghe, Convex Optimization . Cambridge University Press, 2003
2003
Earlier work this paper cites.
C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics) . Springer-Verlag New York, Inc., 2006
2006
Earlier work this paper cites.
H. Funaya and K. Ikeda, “A Statistical Analysis of Soft-margin Support vector machines for non-separable problems,” in IEEE World Congress on Computational Intelligence , Brisbane, Australia, 2012
2012
Cited alongside, same era.
M. Stojnic, “A framework to characterize performance of LASSO algorithms,” 2013
2013
Cited alongside, same era.
2013
Cited alongside, same era.
C. Thrampoulidis, S. Oymak, and B. Hassibi, “Regularized linear regression: A precise analysis of the estimation error,” in Proceedings of the 28th conference on learning theory , vol. 40, Paris, France, 2015, pp. 1683–1709
2015
Cited alongside, same era.
C. Thrampoulidis, S. Oymak, and B. Hassibi, “Regularized linear regression: A precise analysis of the estimation error,” in Conference on Learning Theory , 2015, pp. 1683–1709
K. Elkhalil, A. Kammoun, R. Couillet, T.-Y. Naffouri, and M.-S. Alouini, “A Large Dimensional Study of Regularized Discriminant Analysis Classifiers,” 2017
2017
Later among the works it cites.
K. Elkhalil, A. Kammoun, R. Couillet, T. Y. Al-Naffouri, and M.-S. Alouini, “A Large Dimensional Study of Regularized Discriminant Analysis Classifiers,” 2018, submitted to IEEE Transactions on information theory
2018
Later among the works it cites.
C. Thrampoulidis, E. Abbasi, and B. Hassibi, “Precise Error Analysis of Regularized M-Estimators in High Dimensions,” IEEE Transactions on Information Theory , vol. 64, no. 8, Aug. 2018
2018
Later among the works it cites.
X. Mai and R. Couillet, “Statistical Analysis and Improvement of Large Dimensional SVM,” 2018, romaincouillet.hebfree.org/docs/conf/SVM_ICML18.pdf
2018
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2015
Cited alongside, same era.
R. Couillet and F. Benyach-Georges, “Kernel Spectral Clustering of Large Dimensional Data,” Electronic Journal of Statistics , 2016
2016
Cited alongside, same era.
D. Donoho and A. Montanari, “High dimensional robust M-estimation: asymptotic variance via approximate message passing,” Probability Theory and Related Fields , vol. 166, no. 3, pp. 935–969, Dec. 2016
2016
Cited alongside, same era.
——, “Asymptotic Performance of Regularized Quadratic Discriminant Analysis based Classifiers,” in Internation Workshop on Machine Learning for Signal Processing , Sep. 2017
2017
Cited alongside, same era.
H. Huang, “Asymptotic behavior of support vector machine for spiked population model,” Journal of Machine Learning Research , vol. 18, pp. 45:1–45:21, 2017
2017
Cited alongside, same era.
N. E. Karoui, “Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators: rigorous results,” arXiv preprint arxiv 1311.2445
Cited in the paper.
H. Sifaou, A. Kammoun, and M.-S. Alouini, “Improved LDA classifier based on spiked models,” in 19th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2018, Kalamata, Greece, June 25-28, 2018 , 2018, pp. 1–5
2018
Later among the works it cites.
C. Thrampoulidis, W. Xu, and B. Hassibi, “Symbol error rate performance of Box-relaxation decoders in Massive MIMO ,” IEEE Transactions on Signal Processing , vol. 66, no. 13, Jul. 2018
2018
Later among the works it cites.
2018
Later among the works it cites.
Z. Liao and R. Couillet, “A large dimensional analysis of least squares support vector machines,” IEEE Trans. Signal Processing , vol. 67, no. 4, pp. 1065–1074, 2019
2019
Later among the works it cites.