Aggregation by exponential weighting, sharp oracle inequalities and sparsity (2008)
Dalalyan, Arnak, Tsybakov, Alexandre B.
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 exponential...
Simultaneous analysis of Lasso and Dantzig selector (2008)
Bickel, Peter J., Ritov, Ya'acov, Tsybakov, Alexandre B.
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 general nonparametric...
Aggregation for Gaussian regression (2007)
Bunea, Florentina, Tsybakov, Alexandre B., Wegkamp, Marten H.
This paper studies statistical aggregation procedures in the regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing...
Fast learning rates for plug-in classifiers (2007)
Audibert, Jean-Yves, Tsybakov, Alexandre B.
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, that is, rates faster than...
Regularization in statistics (2006)
Bickel, Peter J, Li, Bo, Tsybakov, Alexandre B., Geer, Sara A. Van De, Yu, Bin, Valdés, Teófilo, ...
This paper is a selective review of the regularization methods scattered in statistics literature. We introduce a general conceptual approach to regularization and fit most existing methods into it....
Fast learning rates for plug-in classifiers under the margin condition (2005)
Audibert, Jean-Yves, Tsybakov, Alexandre B.
It has been recently shown that, under the margin (or low noise) assumption, there exist classifiers attaining fast rates of convergence of the excess Bayes risk, i.e., the rates faster than...
Sharp optimality for density deconvolution with dominating bias (2004)
Butucea, Cristina, Tsybakov, Alexandre B.
We consider estimation of the common probability density $f$ of i.i.d. random variables $X_i$ that are observed with an additive i.i.d. noise. We assume that the unknown density $f$ belongs to a...