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Sparse recovery under matrix uncertainty
Mathieu Rosenbaum, Alexandre B. Tsybakov
We consider the model {eqnarray*}y=Xθ^*+ξ, Z=X+Ξ,{eqnarray*} where the random vector and the random matrix are observed, the matrix $…
Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity
Arnak Dalalyan, Alexandre Tsybakov
We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via…
Hierarchical selection of variables in sparse high-dimensional regression
Peter J. Bickel, Ya'acov Ritov, Alexander B. Tsybakov
We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sp…
Simultaneous analysis of Lasso and Dantzig selector
Peter J. Bickel, Ya'acov Ritov, Alexandre B. Tsybakov
We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the gener…