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Nuclear norm penalization and optimal rates for noisy low rank matrix completion
Vladimir Koltchinskii, Alexandre B. Tsybakov, Karim Lounici
This paper deals with the trace regression model where entries or linear combinations of entries of an unknown matrix corrupted by noise are observed. We…
Oracle Inequalities and Optimal Inference under Group Sparsity
Karim Lounici, Massimiliano Pontil, Alexandre B. Tsybakov +1
We consider the problem of estimating a sparse linear regression vector under a gaussian noise model, for the purpose of both prediction and model selection. We assume that p…
Exponential Screening and optimal rates of sparse estimation
Philippe Rigollet, Alexandre Tsybakov
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key…
Mirror averaging with sparsity priors
Arnak S. Dalalyan, Alexandre B. Tsybakov
We consider the problem of aggregating the elements of a possibly infinite dictionary for building a decision procedure that aims at minimizing a given criterion. Along with the di…