Related papers: Sparse recovery under matrix uncertainty
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
Much of the existing literature in sparse recovery is concerned with the following question: given a sparsity pattern and a corresponding regularizer, derive conditions on the dictionary under which exact recovery is possible. In this…
We consider a problem of estimating a sparse group of sparse normal mean vectors. The proposed approach is based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
This study explores the estimation of parameters in a matrix-valued linear regression model, where the $T$ responses $(Y_t)_{t=1}^T \in \mathbb{R}^{n \times p}$ and predictors $(X_t)_{t=1}^T \in \mathbb{R}^{m \times q}$ satisfy the…
Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed…
The theory of compressive sensing (CS) asserts that an unknown signal $\mathbf{x} \in \mathbb{C}^N$ can be accurately recovered from $m$ measurements with $m\ll N$ provided that $\mathbf{x}$ is sparse. Most of the recovery algorithms need…
In this paper, we propose a new framework to construct confidence sets for a $d$-dimensional unknown sparse parameter $\theta$ under the normal mean model $X\sim N(\theta,\sigma^2I)$. A key feature of the proposed confidence set is its…
This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely…