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Nuclear norm penalization and optimal rates for noisy low rank matrix completion
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 newExpand
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Oracle Inequalities and Optimal Inference under Group Sparsity
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 isExpand
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High-dimensional covariance matrix estimation with missing observations
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 inExpand
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Sup-norm convergence rate and sign concentration property of Lasso and Dantzig estimators
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 designExpand
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Concentration inequalities and moment bounds for sample covariance operators
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 $\Sigma:$ $$ \Sigma:E^{\ast}\mapsto E,\ \ \Sigma u = {\mathbbExpand
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Taking Advantage of Sparsity in Multi-Task Learning
We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008],Expand
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Asymptotics and Concentration Bounds for Bilinear Forms of Spectral Projectors of Sample Covariance
Let $X,X_1,\dots, X_n$ be i.i.d. Gaussian random variables with zero mean and covariance operator $\Sigma={\mathbb E}(X\otimes X)$ taking values in a separable Hilbert space ${\mathbb H}.$ Let $$Expand
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Normal approximation and concentration of spectral projectors of sample covariance
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 $\hatExpand
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Robust matrix completion
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 realizationsExpand
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