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- Publications
- Influence

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

- V. Koltchinskii, Alexandre B. 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

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

High-dimensional covariance matrix estimation with missing observations

- Karim Lounici
- Mathematics
- 12 January 2012

In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in… Expand

Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators

- Karim Lounici
- Mathematics
- 29 January 2008

We derive the l! convergence rate simultaneously for Lasso and Dantzig estimators in a high-dimensional linear regression model under a mutual coherence assumption on the Gram matrix of the design… Expand

Concentration inequalities and moment bounds for sample covariance operators

- V. Koltchinskii, Karim Lounici
- Mathematics
- 10 May 2014

Let $X,X_1,\dots, X_n,\dots$ be i.i.d. centered Gaussian random variables in a separable Banach space $E$ with covariance operator $\Sigma:$ $$ \Sigma:E^{\ast}\mapsto E,\ \ \Sigma u = {\mathbb… Expand

Taking Advantage of Sparsity in Multi-Task Learning

- Karim Lounici, M. Pontil, A. Tsybakov, S. Geer
- Computer Science, Mathematics
- COLT
- 9 March 2009

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008],… Expand

Asymptotics and Concentration Bounds for Bilinear Forms of Spectral Projectors of Sample Covariance

- V. Koltchinskii, Karim Lounici
- Mathematics
- 20 August 2014

Let $X,X_1,\dots, X_n$ be i.i.d. Gaussian random variables with zero mean and covariance operator $\Sigma={\mathbb E}(X\otimes X)$ taking values in a separable Hilbert space ${\mathbb H}.$ Let $$… Expand

Normal approximation and concentration of spectral projectors of sample covariance

- V. Koltchinskii, Karim Lounici
- Mathematics
- 28 April 2015

Let $X,X_1,\dots, X_n$ be i.i.d. Gaussian random variables in a separable Hilbert space ${\mathbb H}$ with zero mean and covariance operator $\Sigma={\mathbb E}(X\otimes X),$ and let $\hat… Expand

Robust matrix completion

- O. Klopp, Karim Lounici, A. Tsybakov
- Mathematics
- 28 December 2014

This paper considers the problem of estimation of a low-rank matrix when most of its entries are not observed and some of the observed entries are corrupted. The observations are noisy realizations… Expand