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We review recent results for high-dimensional sparse linear regression in thepractical case of unknown variance. Different sparsity settings are covered,including coordinate-sparsity, group-sparsity and variation-sparsity. Theemphasis is put on non-asymptotic analyses and feasible procedures. Inaddition, a small numerical study compares the practical performance of threeschemes for tuning the Lasso estimator and some references are collected forsome more general models, including multivariate regression and nonparametricregression.

High-dimensional regression with unknown variance