Related papers: On the optimality of Orthogonal Greedy Algorithm f…
We study here sparse recovery problems in the presence of additive noise. We analyze a thresholding version of the CoSaMP algorithm, named Thresholding Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
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 investigate online maximum cardinality matching, a central problem in ad allocation. In this problem, users are revealed sequentially, and each new user can be paired with any previously unmatched campaign that it is compatible with.…
Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…
The great success of modern machine learning models on large datasets is contingent on extensive computational resources with high financial and environmental costs. One way to address this is by extracting subsets that generalize on par…
A greedy algorithm is proposed for sparse-sensor selection in reduced-order sensing that contains correlated noise in measurement. The sensor selection is carried out by maximizing the determinant of the Fisher information matrix in a…
In this paper, we consider the problem of compressed sensing where the goal is to recover almost all the sparse vectors using a small number of fixed linear measurements. For this problem, we propose a novel partial hard-thresholding…
Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the…
We explore the problems of classification of composite object (images, speech signals) with low number of models per class. We study the question of improving recognition performance for medium-sized database (thousands of classes). The key…
We analyze the convergence rate of the multiplicative gradient (MG) method for PET-type problems with $m$ component functions and an $n$-dimensional optimization variable. We show that the MG method has an $O(\ln(n)/t)$ convergence rate, in…
Orthogonal matching pursuit (OMP) is a widely used compressive sensing (CS) algorithm for recovering sparse signals in noisy linear regression models. The performance of OMP depends on its stopping criteria (SC). SC for OMP discussed in…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
Tropp's analysis of Orthogonal Matching Pursuit (OMP) using the Exact Recovery Condition (ERC) is extended to a first exact recovery analysis of Orthogonal Least Squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly…
In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the traditional mutual coherence and the restricted isometry constant. By exploring this relationship, we…
This study investigated typical performance of approximation algorithms known as belief propagation, greedy algorithm, and linear-programming relaxation for maximum coverage problems on sparse biregular random graphs. After using the cavity…
Orthogonal matching pursuit~(OMP) is a commonly used greedy algorithm for recovering sparse signals from compressed measurements. In this paper, we introduce a variant of the OMP algorithm to reduce the complexity of reconstructing a class…