An introduction

I study high dimensional phenomena and mathematical aspects of data science, focusing mainly on the (surprising) connections between Statistical Learning Theory, Empirical Processes Theory and Asymptotic Geometric Analysis.

Statistical recovery problems are, fundamentally, questions on preservation of structure. Recovery from given data is possible because randomness – even at minimal levels – preserves and exposes structure; and structure preservation is the real reason why recovery algorithms perform well. 

As it happens, key problems in Data Science may be recast as challenging geometric questions on preservation of structure in high dimension, touching diverse areas of pure mathematics, such as asymptotic geometric analysis, probability theory, harmonic analysis and combinatorics. My work is devoted to the study of these questions.

Editorships

I am the Managing Editor of Mathematical Statistics and Learning, a journal that publishes research articles of the highest quality on all aspects of mathematics of Data Science.

Selected publications 

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

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

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

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

  • 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.

  • S. Mendelson, Learning without concentration, Journal of the ACM, 62(3), Article No. 21, 1-25, 2015.

  • G. Lecue, S. Mendelson, Sparse recovery under weak moment assumptions, Journal of the European Mathematical Society, 19(3), 881-904, 2017.

  •  G. Lugosi, S. Mendelson, Sub-Gaussian estimators of the mean of a random vector, Annals of Statistics, 47(2) 783-794, 2019.

  • G. Lugosi, S. Mendelson, Near-optimal mean estimators with respect to general norms, Probability Theory and Related Fields, 175(3-4), 957-973, 2019.

  • G. Lugosi, S. Mendelson, Risk minimization by median-of-means tournaments Journal of the European Mathematical Society, 22(3) 925-965, 2020.

  • S. Mendelson, An unrestricted learning procedure, Journal of the ACM, 66(6) article 42, 2019.

  • S. Dirksen, S. Mendelson, Robust one-bit compressed sensing with non-gaussian measurements, Journal of the European Mathematical Society 23(9), 2913-2947, 2021.

  • D. Bartl, S. Mendelson, Random embeddings with an almost gaussian distortion, Advances in Mathematics, 400, article 108261, 2022.

  • G. Lugosi, S. Mendelson, Multivariate mean estimation with direction-dependent accuracy, Journal of the European Mathematical Society, 26(6),  2211–2247, 2024. 

Contact: 

[email protected]

In the 2024-2025 academic year I will be in Zurich, visiting FIM - Institute for Mathematical Research, ETH Zurich.