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Introduction to Nonparametric Estimation

- A. Tsybakov
- Computer Science, Mathematics
- Springer series in statistics
- 22 October 2008

TLDR

SIMULTANEOUS ANALYSIS OF LASSO AND DANTZIG SELECTOR

- P. Bickel, Y. Ritov, A. Tsybakov
- Mathematics
- 7 January 2008

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk… Expand

Smooth Discrimination Analysis

- E. Mammen, A. Tsybakov
- Mathematics
- 1 December 1999

Discriminant analysis for two data sets in IRd with probability densities f and g can be based on the estimation of the set G = {x : f(x) I g(x)}. We consider applications where it is appropriate to… Expand

Nuclear norm penalization and optimal rates for noisy low rank matrix completion

- V. Koltchinskii, A. Tsybakov, Karim Lounici
- Mathematics
- 29 November 2010

This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new… Expand

Fast learning rates for plug-in classifiers

- Jean-Yves Audibert, A. Tsybakov
- Mathematics
- 1 April 2007

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 n -1/2 .… Expand

Minimax theory of image reconstruction

- A. Korostelev, A. Tsybakov
- Mathematics
- 1993

Image processing is an increasingly important area of research and there exists a large variety of image reconstruction methods proposed by different authors. This book is concerned with a technique… Expand

Exponential Screening and optimal rates of sparse estimation

- P. Rigollet, A. Tsybakov
- Mathematics
- 12 March 2010

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 assumptions for… Expand

Optimal Rates of Aggregation

- A. Tsybakov
- Mathematics, Computer Science
- COLT
- 2003

TLDR

Oracle Inequalities and Optimal Inference under Group Sparsity

- Karim Lounici, M. Pontil, A. Tsybakov, S. Geer
- Mathematics
- 11 July 2010

We consider the problem of estimating a sparse linear regression vector s* under a gaussian noise model, for the purpose of both prediction and model selection. We assume that prior knowledge is… Expand

Sparsity oracle inequalities for the Lasso

- F. Bunea, A. Tsybakov, M. Wegkamp
- Mathematics
- 23 May 2007

This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity… Expand

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