Related papers: Variable Selection in High Dimensions with Random …
Applying the theory of compressive sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement for sparse recovery is analyzed when both…
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
In high-dimensional sparse regression, would increasing the signal-to-noise ratio while fixing the sparsity level always lead to better model selection? For high-dimensional sparse regression problems, surprisingly, in this paper we answer…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
Sparse estimation methods capable of tolerating outliers have been broadly investigated in the last decade. We contribute to this research considering high-dimensional regression problems contaminated by multiple mean-shift outliers which…
We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…
Sparsity is a basic property of real vectors that is exploited in a wide variety of applications. In this work, we describe property testing algorithms for sparsity that observe a low-dimensional projection of the input. We consider two…
Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones.…
We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a…
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance.…
Large-scale sparse multi-objective optimization problems (LSMOPs) are prevalent in real-world applications, where optimal solutions typically contain only a few nonzero variables, such as in adversarial attacks, critical node detection, and…
A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation…
Sparse representation of astronomical images is discussed. It is shown that a significant gain in sparsity is achieved when particular mixed dictionaries are used for approximating these types of images with greedy selection strategies.…
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…
We address the exact recovery of the support of a k-sparse vector with Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a noiseless setting. We consider the scenario where OMP/OLS have selected good atoms during the…
We study the problem of inferring a sparse vector from random linear combinations of its components. We propose the Accelerated Orthogonal Least-Squares (AOLS) algorithm that improves performance of the well-known Orthogonal Least-Squares…
We shall show that if the restricted isometry constant (RIC) $\delta_{s+1}(A)$ of the measurement matrix $A$ satisfies $$ \delta_{s+1}(A) < \frac{1}{\sqrt{s + 1}}, $$ then the greedy algorithm Orthogonal Matching Pursuit(OMP) will succeed.…
This paper proposes two novel schemes of wideband compressive spectrum sensing (CSS) via block orthogonal matching pursuit (BOMP) algorithm, for achieving high sensing accuracy in real time. These schemes aim to reliably recover the…