Learning without concentration

Journal of Machine Learning Research

Volumn 35, Issue , 2014, Pages 25-39

  Mendelson, Shahar ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; SOFTWARE ENGINEERING;

BOUNDEDNESS; CONVERGENCE RATES; EMPIRICAL RISK MINIMIZATION; HEAVY-TAILED; NOISE LEVELS; SHARP BOUNDS;

RISK PERCEPTION;

EID: 84939623358     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (20)

1. P. L. Bartlett, O. Bousquet, and S. Mendelson. Local rademacher complexities. Annals of Statistics, 33(4):1497-1537, 2005.
2. P. L. Bartlett, S. Mendelson, and J. Neeman. l1-regularized linear regression: Persistence and oracle inequalities. Probability Theory and Related Fields, 154:193-224, 2012.
3. S. Boucheron, G. Lugosi, and P. Massart. Concentration Inequalities: A Nonasymptotic Theory of Independence. Oxford University Press, 2013.
4. D. Chafaï, O. Guédon, G. Lecué, and A. Pajor. Interacrions between compressed sensing, random matrices and high dimensional geometry, volume 37. SMF, 2012.
5. V. De La Peña and E. Giné. Decoupling: From Dependence to Independence. Springer-Verlag, 1999.
6. A. W. Van Der Vaart and J. A. Wellner. Weak convergence and empirical processes. Springer Verlag, 1996.
7. E. Giné and J. Zinn. Some limit theorems for empirical processes. Annals of Probability, 12(4):929-989, 1984.
8. V. Koltchinskii. Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems, volume 2033 of Lecture notes in Matehmatics. Springer, 2011.
9. V. Koltchinskii and S. Mendelson. Bounding the smallest singular value of a random matrix without concentration. preprint, arXiv:1312.3580.
10. G. Lecué and S. Mendelson. Learning subgaussian classes: Upper and minimax bounds. preprint, arXiv:1305.4825, a.
11. G. Lecué and S. Mendelson. Compressed sensing under weak moment assumptions. preprint, arXiv:1401.2188, b.
12. G. Lecué and S. Mendelson. Necessary moment conditions for exact reconstruction via basis pursuit. preprint, arXiv:1404.3116, c.
13. M. Ledoux and M. Talagrand. Probability in Banach spaces. Isoperimetry and processes, volume 23 of Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, 1991.
14. S. Mendelson. Learning without concentration, extended version. preprint, arXiv:1401.0304, a.
15. S. Mendelson. Learning without concentration for general loss functions. preprint, b.
16. S. Mendelson. A remark on the diameter of random sections of convex bodies. preprint, arXiv:1312.3608, c.
17. S. Mendelson. Empirical processes with a bounded Ψ1 diameter. Geometric and Functional Analysis, 20(4):988-1027, 2010.
18. S. Mendelson and G. Paouris. On generic chaining and the smallest singular values of random matrices with heavy tails. Journal of Functional Analysis, 262(9):3775-3811, 2012.
19. S. Mendelson and G. Paouris. On the singular values of random matrices. Journal of the European Mathematics Society, 2014.
20. S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann. Reconstruction and subgaussian operators. Geometric and Functional Analysis, 17(4):1248-1282, 2007.