Related papers: Swapping Variables for High-Dimensional Sparse Reg…
Orthogonal matching pursuit (OMP) is a widely used algorithm for recovering sparse high dimensional vectors in linear regression models. The optimal performance of OMP requires \textit{a priori} knowledge of either the sparsity of…
As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing…
We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…
This paper proposes a simple yet highly accurate prediction-correction algorithm, SHARP, for unconstrained time-varying optimization problems. Its prediction is based on an extrapolation derived from the Lagrange interpolation of past…
This paper studies the joint support recovery of similar sparse vectors on the basis of a limited number of noisy linear measurements, i.e., in a multiple measurement vector (MMV) model. The additive noise signals on each measurement vector…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…
Highly coherent sensing matrices arise in discretization of continuum problems such as radar and medical imaging when the grid spacing is below the Rayleigh threshold as well as in using highly coherent, redundant dictionaries as…
Given the ever-increasing size of modern neural networks, the significance of sparse architectures has surged due to their accelerated inference speeds and minimal memory demands. When it comes to global pruning techniques, Iterative…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We…
The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner…
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…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…
Recovering the support of sparse vectors in underdetermined linear regression models, \textit{aka}, compressive sensing is important in many signal processing applications. High SNR consistency (HSC), i.e., the ability of a support recovery…
Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…
A reliable support detection is essential for a greedy algorithm to reconstruct a sparse signal accurately from compressed and noisy measurements. This paper proposes a novel support detection method for greedy algorithms, which is referred…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…