Mohamed Hebiri
Université Paris-Est, France

Short Syllabus

High-dimensional data can be used for a variety of different objectives. Recently, prediction-type objectives have received particular attention. We focus on linear regression models of the from Y = Xβ + ξ, where (X, Y) ∈ Rn×p × Rn is the data, β ∈ Rp the unknown regression vector, and ξ is a noise vector in Rn.
Our first objective is standard prediction, that is, uncovering Xβ from data. We especially cover recent developments in the understanding of the prediction performances and limitations of lasso-type estimators.
Our second objective is prediction in a supervised/transductive settings. Observing (X,Y) and additional sets of covariates Z ∈ Rm×p, the goal is to estimate Zβ. Available for this are the original labeled data (X, Y) as well as the additional unlabeled set of predictors Z. We especially highlight how the correlations in X and Z are connected to the performance of lasso-type estimators


Thorough understanding of linear regression.


  • P. Alquier and M. Hebiri. “Transductive versions of the LASSO and the dantzig selec- tor". Journal of Statistical Planning and Inference, 142(9):2485–2500, 2012

  • P. Bellec, A. Dalalyan, E. Grappin and Q. Paris. “On the prediction loss of the lasso in the partially labeled setting". Submitted

  • A. Dalalyan, M. Hebiri, and J. Lederer. “On the Prediction Performance of the Lasso". Bernoulli, 23(1), pp. 552–581, 2017

  • T. Hastie, R. Tibshirani and M. J. Wainwright. Statistical Learning with Sparsity: the Lasso and Generalizations. Chapman and Hall/CRC Press, Series in Statistics and Applied Probability, 2015

  • S. van de Geer. Estimation and Testing under Sparsity: École d'Éte de Saint-Flour XLV, Spinger, 2016

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The lecture will take place at the Department of Statistics of the University of Washington

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