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A. Thesis and Books

  1. M.Sc. thesis: On the farthest point problem.

  2. Ph.D. thesis: Mathematical aspects of learning in Neural Networks.

  3. Advanced Lectures in Machine Learning, (S. Mendelson, A.J. Smola Eds), LNCS 2600, Springer 2003. 

  4. Geometric Aspects of Functional Analysis, Israel Seminar 2006-2010, Bo'az Klartag, Shahar Mendelson and Vitali D. Milman Editors, Lecture notes in Mathematics 2050, Springer 2012.

     

B. Original Papers (accepted)

  1. S. Mendelson, On the size of convex hulls of small sets, Journal of Machine Learning Research 2, 1-18, 2001.

  2. S. Mendelson, l-norm and its application to Learning Theory, Positivity, 5, 177-191, 2001.

  3. S. Mendelson, A new on-line learning model, Neural Computation 13(4), 935-957, April 2001.

  4. S. Mendelson and I. Nelken, Recurrence techniques in the analysis of neural networks, Neural Computation 13(8) 1839-1861, August 2001.

  5. S. Mendelson, Rademacher averages and phase transitions in Glivenko-Cantelli classes, IEEE Transactions on Information Theory, 48(1), 251-263, 2002.

  6. S. Mendelson, Improving the sample complexity using global data, IEEE Transactions on Information Theory 48(7), 1977-1991, 2002.

  7. S. Mendelson, Learnability in Hilbert spaces with Reproducing Kernels, Journal of Complexity, 18(1), 152-170, 2002.

  8. P.L. Bartlett, S. Mendelson, Rademacher and Gaussian complexities: risk bounds and structural results (extended version of conference paper (5)), Journal of Machine Learning Research 3, 463-482, 2002

  9. S. Mendelson, R. Vershynin, Entropy and the combinatorial dimension, Inventiones Mathematicae, 152(1), 37-55, 2003.

  10. S. Mendelson, A few notes on Statistical Learning Theory,In Advanced Lectures in Machine Learning, (S. Mendelson, A.J. Smola Eds), LNCS 2600, 1-40, Springer 2003.

  11. S. Mendelson, Estimating the performance of kernel classes, Journal of Machine Learning Research, 4, 759-771, 2003.

  12. G. Lugosi, S. Mendelson, V. Koltchinskii, A note on the richness of convex hulls of VC classes, Electronic communications in Probability, 8, 167-169, 2003.

  13. S. Mendelson, G. Schechtman, The shattering dimension of sets of linear functionals, Annals of Probability, 32(3A), 1746-1770, 2004.

  14. S. Mendelson, Geometric parameters in Learning Theory. GAFA lecture notes, LNM 1850, 193-236, 2004.

  15. S. Mendelson, P. Philips, On the importance of "small" coordinate projections, Journal of Machine Learning Research, 5(Mar), 219-238, 2004.

  16. S. Mendelson, R. Vershynin, Remarks on the geometry of coordinate projections in R^n, Israel Journal of Mathematics, 140, 203-220, 2004.

  17. F. Barthe, O. Guedon, S. Mendelson, A. Naor, A probabilistic approach to the geometry of the $\ell_p^n$ ball, Annals of Probability, 33(2), 480-513, 2005.

  18. S. Mendelson, Embeddings with a Lipschitz function, Random Structures and Algorithms, 27(1) 25-45, 2005.

  19. S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Reconstruction and subgaussian processes, CRAS 340(12) 885-888, 2005.

  20. P.L. Bartlett, O. Bousquet, S. Mendelson, Local Rademacher Complexities, Annals of Statistics, 33(4) 1497-1537, 2005.

  21. B. Klartag, S. Mendelson, Empirical Processes and Random Projections, Journal of Functional Analysis, 225(1) 229-245, 2005.

  22. S. Mendelson, A. Pajor, M. Rudelson, On the Geometry of random {-1,1}-polytopes, Discrete and Computational Geometry, 33(3) 365-379, 2005.

  23. P.L. Bartlett, S. Mendelson, Empirical minimization, Probability Theory and Related Fields, 135, 311-334, 2006.

  24. S. Mendelson, A. Pajor, On singular values of matrices with independent rows, Bernoulli, 12(5), 761-773, 2006.

  25. P.L. Bartlett, S. Mendelson, Local Rademacher complexities and empirical minimization, Annals of Statistics, 34, 2657-2663, 2006.

  26. S. Mendelson, J. Zinn, Modified Empirical CLT's under only pre-Gaussian conditions, High Dimensional Probability, in IMS lecture notes monograph series, vol 51, 173-184, 2006.

  27. N. Linial, S. Mendelson, G. Schechtman, A. Schraibman, Complexity measures of sign matrices, Combinatorica, 27(4) 439-463, 2007.

  28. S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Reconstruction and subgaussian operators in Asymptotic Geometric Analysis, Geometric and Functional Analysis, 17(4), 1248-1282, 2007.

  29. S. Mendelson, Lipschitz representations of subsets of the cube, Proceedings of the AMS, 135, 1455-1463, 2007.

  30. S. Mendelson, N. Tomczak-Jaegermann, A subgaussian embedding theorem, Israel Journal of Mathematics, 164, 349-364, 2008.

  31. O. Guedon, S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Subspaces and orthogonal decompositions generated by bounded orthogonal systems, Positivity, 11(2), 269-283, 2008.

  32. S. Mendelson, On weakly bounded empirical processes, Math. Annalen, 340(2), 293-314, 2008.

  33. S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Uniform uncertainty principle for Bernoulli and subgaussian ensembles, Constructive Approximation, 28, 277-289, 2008.

  34. Y. Gordon, A. Litvak, S. Mendelson, A. Pajor, Gaussian averages of interpolated bodies, Journal of Approximation Theory, 149, 59-73, 2008.

  35. S. Mendelson, Obtaining fast error rates in nonconvex situations, Journal of Complexity, 24(3), 380-397, 2008.

  36. S. Mendelson, Lower bounds for the empirical minimization algorithm, IEEE Transactions on Information Theory, 54(8) 3797-3803, 2008.

  37. O. Guedon, S. Mendelson, A. Pajor, N. Tomczak-Jaegermann, Majorizing measures and proportional subsets of bounded orthonormal systems, Revista Mathematica Iberoamricana, 24(3). 1075-1095, 2008.

  38. G. Lecue, S. Mendelson, Aggregation via Empirical risk minimization, Probability Theory and related Fields, 145, 591-613, 2009.

  39. S. Mendelson, J. Neeman, Regularization in Kernel Learning, Annals of Statistics, 38(1), 526-565, 2010.

  40. G. Lecue, S. Mendelson, Sharper bounds on the performance of the empirical minimization algorithm, Bernoulli, 16(3), 605-613, 2010.

  41. S. Mendelson, Empirical processes with a bounded \psi_1 diameter, Geometric and Functional Analysis, 20(4) 988-1027, 2010.

  42. P.L. Bartlett, S. Mendelson, P. Philips, Optimal sample based estimates of the expectation of the empirical minimizer, ESAIM Probability and Statistics, 14, 315-337, 2010.

  43. S. Mendelson, Discrepancy, Chaining and Subgaussian processes, Annals of Probability, 39(3) 985-1026, 2011.

  44. P. Bartlett, S. Mendelson, J. Neeman, \ell_1-regularized linear regression: Persistence and oracle inequalities, Probability Theory and Related Fields, 154, 193-224, 2012.

  45. G. Lecue, S. Mendelson, General non-exact oracle inequalities in the unbounded case, Annals of Statistics, 40(2), 832-860, 2012.

  46. S. Mendelson, 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.

  47. G. Lecue, S. Mendelson, Optimality of the aggregate with exponential weights for low temperatures, Bernoulli, 19(2) 646-675, 2013.

  48. G. Lecue, S. Mendelson, On the optimality of the empirical risk minimization procedure for the convex aggregation problem, Annales dIHP, 49(1), 288-306, 2013.

  49. S. Mendelson, G. Paouris, On the singular values of random matrices, Journal of the European Mathematical Society, 16, 823-834, 2014.

  50. F. Krahmer, S. Mendelson, H. Rauhut, Suprema of chaos processes and the restricted isometry property, Communications on Pure and Applied Mathematics, 67(11) 1877-1904, 2014.

  51. Y.C. Eldar, S. Mendelson, Phase Retrieval: Stability and Recovery Guarantees, Applied and computational Harmonic Analysis, 26(3), 473-494, 2014.

  52. S. Mendelson, A remark on the diameter of random sections of convex bodies, Geometric Aspects of Functional Analysis (GAFA Seminar Notes, B. Klartag and E. Milman Eds.), Lecture notes in Mathematics 2116, 395-404, 2014.

  53. S. Mendelson, Learning without concentration, Journal of the ACM, 62(3), Article No. 21, 1-25, 2015. doi:10.1145/2699439.

  54. V. Koltchinskii, S. Mendelson, Bounding the smallest singular value of a random matrix without concentration, International Mathematics Research Notices, doi:10.1093/imrn/rnv096.

  55. G. Lecue, S. Mendelson, Minimax rate of convergence and the performance of ERM in phase recovery, Electronic Journal of Probability 20(57), 1-29, 2015.

  56. G. Lecue, S. Mendelson, Performance of empirical risk minimization in linear aggregation, Bernoulli, 23(3) 1520-1534, 2016.

  57. S. Mendelson, Upper bounds on product and multiplier empirical processes, Stochastic Processes and their Applications, 126(12), 3652–3680, 2016.

  58. S. Mendelson, Dvoretzky type theorems for subgaussian coordinate projections, Journal of Theoretical Probability, 29(4), 1644-1660, 2016.

  59. G. Lecue, S. Mendelson, Learning subgaussian classes: Upper and minimax bounds, Topics in Learning Theory - Societe Mathematique de France, (S. Boucheron and N. Vayatis Eds.), to appear (37 pages).

  60. G. Lecue, S. Mendelson, Sparse recovery under weak moment assumptions, Journal of the European Mathematical Society, to appear (24 pages).

  61. S. Mendelson, On multiplier processes under weak moment assumptions, Geometric aspects of Functional Analysis, Lecture notes in Mathematics, to appear, (19 pages).

  62. S. Mendelson, On aggregation for heavy-tailed classes, Probability Theory and related fields, DOI 10.1007/s00440-016-0720-6, (34 pages).

  63. S. Mendelson, Local vs. global parameters - breaking the gaussian complexity barrier, Annals of Statistics, to appear, (28 pages).

  64. G. Lecue, S. Mendelson, Regularization and the small-ball method I: sparse recovery, Annals of Statistics, to appear, (29 pages).

C. Original Conference Papers (accepted)

  1. S. Mendelson, N. Tishby, Statistical Sufficiency for classes in empirical L2 spaces, Proceedings of the 13th annual conference on Computational Learning Theory COLT00, 81-89, 2000.

  2. S. Mendelson, Geometric Methods in the Analysis of Glivenko-Cantelli Classes, Proceedings of the 14th annual conference on Computational Learning Theory COLT01, 256-272, 2001.

  3. S. Mendelson, Learning Relatively Small Classes, Proceedings of the 14th annual conference on Computational Learning Theory COLT01, 273-288, 2001.

  4. P. L. Bartlett, S. Mendelson, Rademacher and gaussian complexities: risk bounds and structural results, Proceedings of the 14th annual conference on Computational Learning Theory COLT01, 224-240, 2001.

  5. S. Mendelson, R.C. Williamson, Agnostic learning of non-convex classes of functions, Proceedings of the 15th annual conference on Computational Learning Theory COLT02, 1-13, 2002.

  6. S. Mendelson, R. Vershynin, Entropy, combinatorial dimensions and random averages, Proceedings of the 15th annual conference on Computational Learning Theory COLT02, 14-28, 2002.

  7. S. Mendelson, Geometric parameters of kernel machines, Proceedings of the 15th annual conference on Computational Learning Theory COLT02, 29-43, 2002.

  8. P.L. Bartlett, O. Bousquet, S. Mendelson, Localized Rademacher Averages, Proceedings of the 15th annual conference on Computational Learning Theory COLT02, 44-58, 2002.

  9. S. Mendelson, P. Philips, Random subclass bounds, Proceedings of the 16th annual conference on Learning Theory COLT03, Lecture Notes in Computer Sciences 2777, Springer, 329-343, 2003.

  10. P.L. Bartlett, S. Mendelson, P. Philips, Local complexities for empirical risk minimization, Proceedings of the 17th annual conference on Learning Theory COLT04, Lecture Notes in Computer Sciences 3120, Springer, 270-284, 2004.

  11. S. Mendelson, A. Pajor, Ellipsoid approximation with random vectors, Proceedings of the 18th annual conference on Learning Theory COLT05, Lecture Notes in Computer Sciences 3559, Springer, 429-433, 2005.

  12. S. Mendelson, On the limitations of embedding methods,Proceedings of the 18th annual conference on Learning Theory COLT05, Lecture Notes in Computer Sciences 3559, Springer, 353-365, 2005.

  13. S. Mendelson, Learning without Concentration,Proceedings of the 27th annual conference on Learning Theory COLT14, Journal of Machine Learning Research – Workshop and Conference Proceedings, 35, 25-39, 2014.


D. Original Journal Papers (submitted)

  1. S. Mendelson, Learning without concentration for a general loss function, (61 pages).

  2. G. Lugosi, S. Mendelson, Risk minimization by median-of-means tournaments, (40 pages).

  3. G. Lecue, S. Mendelson, Regularization and the small-ball method II: complexity dependent error rates, (41 pages).

  4. S. Mendelson, H. Rauhut, R. Ward, Improved bounds for sparse recovery from subsampled random convolutions, (45 pages).

  5. S. Mendelson, E. Milman, G. Paouris, Generalized Sudakov via Dimension Reduction - A Program, (44 pages).

  6. G. Lugosi, S. Mendelson, Regularization, sparse recovery and median-of-means tournaments, (28 pages).

  7. G. Lugosi, S. Mendelson, Sub-Gaussian estimators of the mean of a random vector, (12 pages).

  8. S. Mendelson, Column normalization of a random measurement matrix, (12 pages).