Professor Shahar Mendelson
Areas of expertise
- Probability Theory 010404
- Operator Algebras And Functional Analysis 010108
- Statistical Theory 010405
Publications
- Mendelson, S 2021, 'Extending the scope of the small-ball method', Studia Mathematica, vol. 256, no. 2, pp. 147-167.
- Mendelson, S 2021, 'Learning bounded subsets of Lp', IEEE Transactions on Information Theory, vol. 67, no. 8, pp. 5269 - 5282.
- Lugosi, G & Mendelson, S 2021, 'Robust multivariate mean estimation: The optimality of trimmed mean', Annals of Statistics, vol. 49, no. 1, pp. 393-410.
- Mendelson, S & Zhivotovskiy, N 2020, 'Robust covariance estimation under L4 - L2 norm equivalence', Annals of Statistics, vol. 48, no. 3, pp. 1648-1664.
- Lugosi, G, Mendelson, S & Zhivotovskiy, N 2020, 'Concentration of the spectral norm of Erdős-Rényi random graphs', Bernoulli, vol. 26, no. 3, pp. 2253-2274.
- Lugosi, G & Mendelson, S 2020, 'Risk minimization by median-of-means tournaments', European Mathematical Society Journal, vol. 22, no. 3, pp. 925-965.
- Mendelson, S 2020, 'On the Geometry of Random Polytopes', in Bo’az Klartag, Emanuel Milman (ed.), Geometric Aspects of Functional Analysis, Springer International Publishing AG, Cham, Switzerland, pp. 187-198.
- Lugosi, G & Mendelson, S 2019, 'Sub-Gaussian estimators of the mean of a random vector', Annals of Statistics, vol. 47, no. 2, pp. 783-794.
- Lugosi, G & Mendelson, S 2019, 'Near-optimal mean estimators with respect to general norms', Probability Theory and Related Fields, vol. 175, pp. 957-973.
- Lugosi, G & Mendelson, S 2019, 'Mean Estimation and Regression Under Heavy-Tailed Distributions: A Survey', Foundations of Computational Mathematics, vol. 19, pp. 1145-1190.
- Lugosi, G & Mendelson, S 2019, 'Regularization, sparse recovery, and median-of-means tournaments', Bernoulli, vol. 25, no. 3, pp. 2075-2106.
- Mendelson, S, Milman, E & Paouris, G 2019, 'Generalized dual Sudakov minoration via dimension-reduction-a program', Studia Mathematica, vol. 244, no. 2, pp. 159-202.
- Mendelson, S 2019, 'An unrestricted learning procedure', Journal of the ACM, vol. 66, no. 6, pp. 1-42.
- Lecue, G & Mendelson, S 2018, 'Regularization and the small-ball method I: sparse recovery', Annals of Statistics, vol. 46, no. 2, pp. 611-641.
- Lecue, G & Mendelson, S 2018, 'Regularization and the small-ball method II: complexity dependent error rates', Journal of Machine Learning Research, vol. 18, no. 1, pp. 5356-5403.
- Mendelson, S 2018, 'Learning without concentration for general loss functions', Probability Theory and Related Fields, vol. 171, no. 1-2, pp. 459-502.
- Mendelson, S 2018, 'Column normalization of a random measurement matrix', Electronic Communications in Probability, vol. 23, no. 13, pp. 1-8.
- Mendelson, S, Rauhut, H & Ward, R 2018, 'Improved Bounds for Sparse Recovery from Subsampled Random Convolutions', Annals of Applied Probability, vol. 28, no. 6, pp. 3491-3527.
- Mendelson, S 2017, 'On Multiplier Processes Under Weak Moment Assumptions', in Bo'az Klartag and Emanuel Milman (ed.), Geometric Aspects of Functional Analysis: Israel Seminar (GAFA) 2014–2016, Springer, Cham, pp. 301-308.
- Mendelson, S 2017, 'On aggregation for heavy-tailed classes', Probability Theory and Related Fields, vol. 168, no. 3-4, pp. 641-674.
- Mendelson, S 2017, ''local' vs. 'global' parameters_breaking the Gaussian complexity barrier', Annals of Statistics, vol. 45, no. 5, pp. 1835-1862.
- Mendelson, S & Lecue, G 2017, 'Sparse recovery under weak moment assumptions', European Mathematical Society Journal, vol. 19, no. 3, pp. 881-904.
- Mendelson, S 2016, 'Upper bounds on product and multiplier empirical processes', Stochastic Processes and their Applications, vol. 126, no. 12, pp. 3652-3680pp.
- Lecue, G & Mendelson, S 2016, 'Performance of empirical risk minimization in linear aggregation', Bernoulli, vol. 22, no. 3, pp. 1520-1534.
- Mendelson, S 2016, 'Dvoretzky Type Theorems for Subgaussian Coordinate Projections', Journal of Theoretical Probability, vol. 29, no. 4, pp. 1644-1660.
- Koltchinskii, V & Mendelson, S 2015, 'Bounding the Smallest Singular Value of a Random Matrix Without Concentration', International Mathematics Research Notices, vol. 2015, no. 23, pp. 12991-13008.
- Mendelson, S 2015, 'Learning without concentration', Journal of the ACM, vol. 62, no. 3, pp. 1-25.
- Mendelson, S & Lecue, G 2015, 'Minimax rate of convergence and the performance of empirical risk minimization in phase retrieval', Electronic Journal of Probability, vol. 20, no. 57, pp. 1-27.
- Mendelson, S 2014, 'A remark on the diameter of random sections of convex bodies', in Bo’az Klartag, Emanuel Milman (ed.), Geometric Aspects of Functional Analysis, Springer International Publishing AG, Cham, Switzerland, pp. 395-404.
- Mendelson, S & Paouris, G 2014, 'On the singular values of random matrices', European Mathematical Society Journal, vol. 16, no. 4, pp. 823-834.
- Krahmer, F, Mendelson, S & Rauhut, H 2014, 'Suprema of Chaos Processes and the Restricted Isometry Property', Communications on Pure and Applied Mathematics, vol. 67, no. 11, pp. 1877-1904.
- Eldar, Y & Mendelson, S 2014, 'Phase retrieval: Stability and recovery guarantees', Applied and Computational Harmonic Analysis, vol. 36, no. 3, pp. 473-494.
- Lecue, G & Mendelson, S 2013, 'On the optimality of the aggregate with exponential weights for low temperatures', Bernoulli, vol. 19, no. 2, pp. 646-675.
- Lecue, G & Mendelson, S 2013, 'On the optimality of the empirical risk minimization procedure for the convex aggregation problem', Annales de l Institut Henri Poincare B: Probability and Statistics, vol. 49, no. 1, pp. 288-306.
- Lecue, G & Mendelson, S 2012, 'General nonexact oracle inequalities for classes with a subexponential envelope', Annals of Statistics, vol. 40, no. 2, pp. 832-860.
- Mendelson, S & Paouris, G 2012, 'On generic chaining and the smallest singular value of random matrices with heavy tails', Journal of Functional Analysis, vol. 262, no. 9, pp. 3775-3811.
- Bartlett, P, Mendelson, S & Neeman, J 2012, 'â„“1-regularised linear regression: persistence and oracle inequalities', Probability Theory and Related Fields, vol. 154, no. 1-2, pp. 193-224.
- Mendelson, S 2011, 'Discrepancy, chaining and subgaussian processes', The Annals of Probability, vol. 39, no. 3, pp. 985-1026.
- Lecue, G & Mendelson, S 2010, 'Sharper lower bounds on the performance of the empirical risk minimization algorithm', Bernoulli, vol. 16, no. 3, pp. 605-613.
- Mendelson, S 2010, 'Empirical Processes with a Bounded Ψ1 Diameter', Geometric and Functional Analysis, vol. 20, no. 4, pp. 988-1027.
- Mendelson, S & Neeman, J 2010, 'Regularization in kernel learning', Annals of Statistics, vol. 38, no. 1, pp. 526-565.
- Bartlett, P, Mendelson, S & Phillips, P 2010, 'On the optimality of sample-based estimates of the expectation of the empirical minimize', ESAIM - Probability and Statistics, vol. 14, no. 4, pp. 315-337.
- Mendelson, S & Lecue, G 2009, 'Aggregation via Empirical risk minimization', Probability Theory and Related Fields, vol. 145, pp. 591-613.
- Mendelson, S 2008, 'Lower Bounds for the Empirical Minimization Algorithm', IEEE Transactions on Information Theory, vol. 54, no. 8, pp. 3797-3803.
- Mendelson, S & Tomczak-Jaegermann, N 2008, 'A subgaussian embedding theorem', Israel Journal of Mathematics, vol. 164, no. 1, pp. 349-364.
- Mendelson, S, Pajor, A & Tomczak-Jaegermann, N 2008, 'Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles', Constructive Approximation, vol. 28, no. 3, pp. 277-289.
- Mendelson, S 2008, 'Obtaining fast error rates in nonconvex situations', Journal of Complexity, vol. 24, pp. 380-397.
- Mendelson, S 2008, 'On weakly bounded empirical processes', Mathematische Annalen, vol. 340, no. 2, pp. 293-314.
- Guedon, O, Mendelson, S, Pajor, A et al 2008, 'Majorizing measures and proprtional subsets of bounded orthonormal systems', Revista Matematica Iberoamericana, vol. 24, no. 3, pp. 1075-1095.
- Mendelson, S, Pajor, A & Tomczak-Jaegermann, N 2007, 'Reconstruction and Subgaussian Operators in Asymptotic Geometric Analysis', Geometric and Functional Analysis, vol. 17, no. 4, pp. 1248-1282.
- Guedon, O, Mendelson, S, Pajor, A et al 2007, 'Subspaces and orthogonal decompositions generated by bounded orthogonal systems', Positivity, vol. 11, no. 2, pp. 269-283.
- Mendelson, S 2007, 'Lipschitz representations of subsets of the cube', Proceedings of the American Mathematical Society, vol. 135, no. 5, pp. 1455-1463.
- Linial, N, Mendelson, S, Schechtman, G et al 2007, 'Complexity measures of sign matrices', Combinatorica, vol. 27, no. 4, pp. 439-463.
- Gordon, Y, Litvak, A, Mendelson, S et al 2007, 'Gaussian averages of interpolated bodies and applications to approximate reconstruction', Journal of Approximation Theory, vol. 149, no. 1, pp. 59-73.
- Bartlett, P & Mendelson, S 2006, 'Local Rademacher complexities and oracle inequalities in risk minimization', Annals of Statistics, vol. 34, no. 6, pp. 2657-2663.
- Bartlett, P & Mendelson, S 2006, 'Empirical minimization', Probability Theory and Related Fields, vol. 135, pp. 311-334.
- Mendelson, S & Pajor, A 2006, 'On singular values of matrices with independent rows', Bernoulli, vol. 12, no. 5, pp. 761.773.
- Mendelson, S & Zinn, J 2006, 'Modified Empirical CLT's under only pre-Gaussian conditions', in Evarist Gine, Vladimir Koltchinskii, Wenbo Li, Joel Zinn (ed.), High Dimensional Probability: Proceedings of the Fourth International Conference, Institute of Mathematical Statistics, Beachwood, Ohio, pp. 173-184.
- Bartlett, P, Bousquet, O & Mendelson, S 2005, 'Local Rademacher complexitites', Annals of Statistics, vol. 33, no. 4, pp. 1497-1537.
- Mendelson, S 2005, 'On the limitations of embedding methods', Lecture Notes in Computer Science (LNCS), vol. 3559, pp. 353-365.
- Mendelson, S & Pajor, A 2005, 'Ellipsoid approximation using random vectors', Lecture Notes in Computer Science (LNCS), vol. 3559, pp. 429-443.
- Mendelson, S, Pajor, A & Tomczak-Jaegermann, N 2005, 'Reconstruction and subgaussian processes', Academie des Sciences Comptes Rendus: Mathematique, vol. 340, no. 12, pp. 885-888.
- Klartag, B & Mendelson, S 2005, 'Empirical processes and random projections', Journal of Functional Analysis, vol. 225, no. 1, pp. 229-245.
- Mendelson, S 2005, 'Embedding with a Lipschitz Function', Random Structures and Algorithms, vol. 27, no. 1, pp. 25-45.
- Barthe, F, Guedon, O, Mendelson, S et al 2005, 'A Probabilistic Approach to the Geometry of the lnp-Ball', The Annals of Probability, vol. 33, no. 2, pp. 480-513.
- Mendelson, S, Pajor, A & Rudelson, M 2005, 'The Geometry of Random {-1,1}-Polytopes', Discrete and Computational Geometry, vol. 34, no. 3, pp. 365-379.
- Bartlett, P, Mendelson, S & Philips, P 2004, 'Local Complexities for Empirical Risk Minimization', Annual Conference on Computational Learning Theory (COLT 2004), ed. J. Shawe-Taylor, Y. Singer, Springer, Germany, pp. 270-284.
- Mendelson, S & Philips, P 2004, 'On the Importance of Small Coordinate Projections', Journal of Machine Learning Research, vol. 5, pp. 219-238.
- Mendelson, S & Vershynin, R 2004, 'Remarks on the geometry of coordinate projections in R^n', Israel Journal of Mathematics, vol. 140, pp. 203-220.
- Mendelson, S & Schechtman, G 2004, 'The shattering dimension of sets of linear functionals', The Annals of Probability, vol. 32, no. 3A, pp. 1746-1770.
- Mendelson, S & Philips, P 2003, 'Random subclass bounds', 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, ed. Bernhard Schoelkopf, Manfred Warmuth, Springer, Berlin, pp. 1-17.
- Mendelson, S 2003, 'On the Performance of Kernel Classes', Journal of Machine Learning Research, vol. 4, pp. 759-771.
- Mendelson, S & Vershynin, R 2003, 'Entropy and the Combinatorial Dimension', Inventiones Mathematicae, vol. 152, pp. 37-55.
- Mendelson, S 2003, 'A Few Notes on Statistical Learning Theory', in Shahar Mendelson and Alexander J. Smola (ed.), Advanced Lectures on Machine Learning, Springer, Germany, pp. 1-40.
- Lugosi, G, Mendelson, S & Koltchinskii, V 2003, 'A Note on the Richness of Convex Hulls of VC Classes', Electronic Communications in Probability, vol. 8, pp. 167-169.
- Mendelson, S & Williamson, R 2002, 'Agnostic learning nonconvex function classes', Annual Conference on Computational Learning Theory (COLT 2002), ed. J. Kivinen, R.H. Sloan, Springer, Berlin, pp. 1-13.
- Mendelson, S 2002, 'Geometric parameters of kernel machines', Annual Conference on Computational Learning Theory (COLT 2002), ed. J. Kivinen, R.H. Sloan, Springer, Berlin, pp. 29-43.
- Mendelson, S & Vershynin, R 2002, 'Entropy, combinatorial dimensions and random averages', Annual Conference on Computational Learning Theory (COLT 2002), ed. J. Kivinen, R.H. Sloan, Springer, Berlin, pp. 14-28.
- Bartlett, P, Bousquet, O & Mendelson, S 2002, 'Localized Rademacher complexities', Annual Conference on Computational Learning Theory (COLT 2002), ed. J. Kivinen, R.H. Sloan, Springer, Berlin, pp. 44-58.
- Mendelson, S 2002, 'Improving the sample complexity using global data', IEEE Transactions on Information Theory, vol. 48, no. 7, pp. 1977-1991.
- Mendelson, S 2001, 'e-norm and its application to learning theory', Positivity, vol. 5, no. 2, pp. 177-191.
- Bartlett, P & Mendelson, S 2001, 'Rademacher and Gaussian complexities: risk bonds and structural results', in D Helmbold & B Williamson (ed.), Computational Learning Theory: Proceedings of COLT and EuroCOLT 2001, Springer, Germany, pp. 224-240.
- Mendelson, S 2001, 'Learning relatively small classes', in D Helmbold & B Williamson (ed.), Computational Learning Theory: Proceedings of COLT and EuroCOLT 2001, Springer, Germany, pp. 273-288.
- Mendelson, S 2001, 'On the size of convex hulls of small sets', Journal of Machine Learning Research, vol. 2, pp. 1-18.
- Mendelson, S 2001, 'Geometric methods in the analysis of Glivenko-Cantelli classes', in D Helmbold & B Williamson (ed.), Computational Learning Theory: Proceedings of COLT and EuroCOLT 2001, Springer, Germany, pp. 256--272.
