Alexandre TSYBAKOV

Grade : Professeur des Universités (CMC-ENSAE)

Mail : alexandre.tsybakov[arrowbase]

ResearchJobsBooksJournal articlesTeachingWork in progressOther

Research Interests



Nonparametric estimation, high-dimensional inference and sparsity, learning theory, statistics of inverse problems, classification, image analysis





Head of the Laboratory of Statistics of CREST 

Professor, Université Paris 6 

Professor, Ecole Polytechnique (2009-2015)

Editorial work:

Associate Editor of Annals of Statistics, Electronic Journal of Statistics, Journal de l'Ecole Polytechnique, Statistica Neerlandica, Automation and Remote Control, Statistical Science, Mathematical Statistics and Learning (Editor)





Tsybakov, A.B. (2009) Introduction to Nonparametric Estimation. Springer, New York e.a.    Errata

Tsybakov, A.B. (2004) Introduction à l'estimation non-paramétrique. Springer, Berlin-Heidelberg e.a. 

Härdle, W., Kerkyacharian, G., Picard, D.,Tsybakov, A.B. (1998) Wavelets, Approximation and Statistical Applications. Lecture Notes in Statistics, v.129, Springer, New York e.a.

Korostelev, A.P., Tsybakov, A.B. (1993) Minimax Theory of Image Reconstruction. Lecture Notes in Statistics, v.82, Springer, New York e.a.

Journal articles

Belomestny, D., Trabs, M., Tsybakov A.B. (2017) Sparse covariance matrix estimation in high-dimensional deconvolution. arxiv 1710.10870 PDF

Belloni, A., Chernozhukov, V., Kaul, A., Rosenbaum, M., Tsybakov A.B. (2017) Pivotal estimation via self-normalization for high-dimensional linear models with error in variables. arxiv 1708.08353

Klopp, O., Lu, Y., Tsybakov, A.B., Zhou, H. (2017) Structured matrix estimation and completion. arxiv1707.02090 PDF

Bellec, P.C., Lecué, G., Tsybakov, A.B. (2017) Towards the study of least squares estimators with convex penalty. arxiv1701.09120 PDF

Belloni, A., Rosenbaum, M., Tsybakov, A.B. (2017) Linear and convex programming estimators in high-dimensional errors-in-variables models. JRSS (B), v.79, n.3, 939-956. PDF

Rakhlin, A., Sridharan, K., Tsybakov, A.B. (2017) Empirical entropy, minimax regret and minimax risk.  Bernoulli, v.23, n.2,789-824.  PDF

Klopp O., Tsybakov A.B., Verzelen N. (2017) Oracle inequalities for network models and sparse graphon estimation. Annals of Statisticsv.45, n.1, 316-354 PDF

Collier, O., Comminges, L., Tsybakov, A.B. (2017) Minimax estimation of linear and quadratic functionals on sparsity classes. Annals of Statistics, v.45, n.3, 923-958.  PDF

Collier, O., Comminges, L., Tsybakov, A.B., Verzelen, N. (2016) Optimal adaptive  estimation of linear functionals under sparsity. arxiv1611.09744 PDF

Bellec, P.C., Tsybakov, A.B. (2016) Bounds on the prediction error of penalized least squares estimators with convex penalty. arxiv1609.06675 PDF

Bellec, P.C., Lecué, G., Tsybakov, A.B. (2016) Slope meets Lasso: improved oracle bounds and optimality. arxiv1605.08651 PDF

Belloni, A., Rosenbaum, M., Tsybakov, A.B. (2016) An $l_1,l_2,l_\infty$ approach to high-dimensional errors-in-variables models. Electronic J. of Statistics, v.10, n.2, 1729-1750. PDF

Koltchinskii, V., Lounici, K., Tsybakov, A.B. (2016) Estimation of low-rank covariance function. Stochastic Processes and their Applications, v.126, n.12, 3952-3967.  PDF

Butucea, C., Stepanova, N., Tsybakov, A.B. (2015) Variable selection with Hamming loss. Annals of Statistics, to appear. arxiv1512.01832 PDF

Klopp, O., Lounici, K., Tsybakov, A.B. (2014) Robust matrix completion. PTRF,  to appear. arxiv1412.8132 PDF

Klopp, O., Tsybakov, A.B. (2015) Estimation of matrices with row sparsity. Problems of Information Transmission, v.51, n.4, 335-348. PDF

Bellec, P.C., Tsybakov A.B. (2015) Sharp oracle bounds for isotonic and convex regression through aggregation. Journal of Machine Learning Research, v.16, 1879-1892. PDF

Tsybakov, A.B. (2014) Aggregation and minimax optimality in high-dimensional estimation. In: Proceedings of the International Congress of Mathematicians (Seoul, August 2014), v.3, 225-246. PDF

Kerkyacharian, G., Tsybakov, A.B., Temlyakov, V., Picard, D., Koltchinskii, V. (2014) Optimal exponential bounds on the accuracy of classification. Constructive Approximation, v.39, 421-444. PDF

Dalalyan, A., Ingster, Y., Tsybakov, A.B. (2014) Statistical inference in compound functional models. Probability Theory and Related Fields, v.158, n.3-4, 513-532. PDF

Gautier, E., Tsybakov, A.B. (2013) Pivotal estimation in high-dimensional regression via linear programming. In: Empirical Inference -- Festschrift in Honor of Vladimir N. Vapnik, B.Schölkopf, Z. Luo, V. Vovk eds., 195 - 204. Springer, New York e.a. PDF

Rosenbaum, M., Tsybakov, A.B. (2013) Improved matrix uncertainty selector. In: From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, M.Banerjee et al. eds. IMS Collections, v.9, 276-290. Institute of Mathematical Statistics. PDF

Tsybakov, B.S., Tsybakov, A.B. (2012) On Walsh code assignment. Problems of Information Transmission, v.48, 334-341. PDF

Rigollet, P., Tsybakov, A.B. (2012) Estimation of covariance matrices under sparsity constraints. Statistica Sinica, v.22, 1358-1365. PDF

Dalalyan, A., Tsybakov, A.B. (2012) Sparse Regression Learning by Aggregation and Langevin Monte-Carlo. Journal of Computer and System Sciences, v.78, 1423-1443. PDF

Dalalyan, A., Tsybakov, A.B.  (2012) Mirror averaging with sparsity priors. Bernoulli,  v.18, 914-944. PDF

Giraud, C., Tsybakov, A.B. (2012) Discussion of "Latent variable graphical model selection via convex optimization". Annals of Statistics, v.40, 1984-1988. PDF

Rigollet, P., Tsybakov, A.B. (2012) Sparse estimation by exponential weighting. Statistical Science, v. 27, 558–575 PDF

Gautier, E., Tsybakov, A.B. (2011) High-dimensional instrumental variables regression and confidence sets. PDF

Koltchinskii,V., Lounici,K., Tsybakov, A.B. (2011) Nuclear norm penalization and optimal rates for noisy low rank matrix completion. Annals of Statistics, v.39, 2302-2329. PDF

Lounici, K., Pontil, M., Tsybakov, A.B., Van de Geer, S.A. (2011) Oracle Inequalities and Optimal Inference under Group Sparsity. Annals of Statistics, v.39, 2164-2204. PDF 

Rigollet, P., Tsybakov, A.B. (2011) Exponential Screening and optimal rates of sparse estimation. Annals of Statistics, v.39, 731-771. PDF

Rohde, A., Tsybakov, A.B. (2011) Estimation of high-dimensional low rank matrices. Annals of Statistics, v.39, 887-930. PDF

Ingster,Yu.I., Tsybakov, A.B., Verzelen, N. (2010) Detection boundary in sparse regression. Electronic Journal of Statistics, v. 4, 1476-1526. PDF

Bickel, P.J., Ritov, Y, Tsybakov, A.B.  Hierarchical selection of variables in sparse high-dimensional regression. In: Borrowing Strength: Theory Powering Applications - A Festschrift for Lawrence D. Brown. IMS Collections, v. 6, 56-69 (2010), Institute of Mathematical Statistics. PDF

Amato, U., Antoniadis, A., Samarov, A., Tsybakov, A.B.  Noisy independent factor analysis model for density estimation and classification. Electronic Journal of Statistics, v.4, 707-736 (2010) PDF

Bunea, F., Tsybakov, A.B., Wegkamp, M.H. SPADES and mixture models. Annals of Statistics, v.38, n.4, 2525-2558 (2010) PDF

Rosenbaum, M., Tsybakov, A.B. Sparse recovery under matrix uncertainty. Annals of Statistics, v.38, n.5, 2620-2651 (2010) PDF

Bickel, P.J., Ritov, Y, Tsybakov, A.B. Simultaneous analysis of Lasso and Dantzig selector. Annals of Statistics, v.37, n.4, 1705-1732 (2009)   PDF (corrected version)

Ingster, Yu.I., Pouet,C., Tsybakov, A.B. Classification of sparse high-dimensional vectors. Royal Society Philosophical Transactions A, v.367, 4427-4448 (2009) Full version with extended proofs available on arXiv:  PDF

Dalalyan, A., Tsybakov, A.B.  Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity. Machine Learning, v.72, 39-61 (2008).  PDF

Dalalyan, A., Tsybakov, A.B.  Aggregation by exponential weighting and sharp oracle inequalities. Proceedings of COLT-2007, Lecture Notes in Artificial Intelligence, v.4539, 97-111 (2007).  PDF

Tsybakov, A.B.  Optimal rates of aggregation. Proceedings of COLT-2003,  Lecture Notes in Artificial Intelligence, v.2777, 303-313 (2003). PDF

Tsybakov, A.B. On the best rate of adaptive estimation in some inverse problems. C.R. de l'Académie des Sciences, sér. I - Mathématiques. v. 330, 835-840 (2000). Full version with extended proofs: Adaptive estimation for inverse problems: a logarithmic effect in L_2. Preprint LPMA n.579 (May 2000) 

Earlier published papers: (2005-2009)  (2004) (1980-2008)









Cours Apprentissage statistique, Ecole Polytechnique (2014)

Projet 1

Projet 1, matériel supplémentaire: Chapitre 15 de [1]

Projet 2

Projet 3

Projet 4

Projet 5

Saint Flour Lecture Notes (2013)  PDF



PhD students:

Simo Ndaoud (Ecole Polytechnique)

Alexis Derumigny (ENSAE)


 Former PhD students: 

Ghislaine Gayraud, Professor, Université Technologique de Compiegne

Laurent Cavalier, Professor, Université de Provence (deceased)

Cristina Butucea, Professor, Université de Marne-la-Vallée et ENSAE

Christophe Pouet, Professor, Ecole Centrale de Marseille

Karine Bertin, Professor, University of Valparaiso, Chili

Guillaume Lecué, Chargé de Recherche, CNRS et ENSAE

Philippe Rigollet, Associate Professor, MIT, USA

Karim Lounici, Professor, Université de Nice Sophia-Antipolis 

Victor-Emmanuel Brunel, Assistant Professor, MIT, USA

Pierre Bellec, Assistant Professor, Rutgers University, USA





Work in progress


Recent preprints can be downloaded from :






Fellow of the Institute of Mathematical Statistics (2004)

Miller Professor, University of California, Berkeley (2006)

IMS Medallion Lecture, Bernoulli Congress (Istanbul, 2012) 

Gay-Lussac -- Humboldt Prize (2013)

Invited Lecture, International Congress of Mathematicians (Seoul, 2014)















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