Related papers: Sparse linear regression from perturbed data
Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…
A recent line of research termed unlabeled sensing and shuffled linear regression has been exploring under great generality the recovery of signals from subsampled and permuted measurements; a challenging problem in diverse fields of data…
Sparse Ising problems can be found in application areas such as logistics, condensed matter physics and training of deep Boltzmann networks, but can be very difficult to tackle with high efficiency and accuracy. This report presents new…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…
We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, \rho =b$, where $A$ is an $N\times K$ measurement matrix. We assume…
We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
Neural networks are becoming increasingly popular in applications, but our mathematical understanding of their potential and limitations is still limited. In this paper, we further this understanding by developing statistical guarantees for…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision and pattern recognition. Sparse representation also has a good reputation in both theoretical research and…
This paper provides a novel approach for finding sparse state-space realizations of linear systems (e.g., controllers). Sparse controllers are commonly used in distributed control, where a controller is synthesized with some sparsity…
In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…
The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…