References
Recommended References
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- [W] High-dimensional statistics: A non-asymptotic viewpoint (2019), by M.
Wainwright.
- Concentration Inequalities: A Nonasymptotic Theory of Independencei, by S.
Boucheron, G. Lugosi and P. Massart, Oxford University Press, 2013.
- High-Dimensional Probability, An Introduction with Applications in Data
Science, by R. Vershynin, 2019, available here.
- Probability in High Dimension, 2016, by R. VCan Handel, 2016, available here.
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Good references on ULLNs:
- Devroye, L., Gyorfi, L. and Lugosi, G. (1997). A Probabilistic Theory of
Pattern Recognition, Springer.
- Koltchinskii, V. (2011). Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery
Problems, Springer Lecture Notes in Mathematics, 2033.
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Laszlo Gyorfi, Michael Kohler, Adam Krzyzak, Harro Walk (2002). A
Distribution-Free Theory of Nonparametric Regression, Springer.
For relative VC deviations see:
- M. Anthony and J. Shawe-Taylor, "A result of Vapnik with applications," Discrete Applied Mathematics, vol. 47, pp. 207-217, 1993.
- V. N. Vapnik and A. Y. Chervonenkis, "On the uniform convergence of
relative frequencies of events to their probabilities," Theory of
Probability and its Applications, vol. 16, pp. 264-280, 1971.
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