Related papers: Sparse sampling recovery by greedy algorithms
We study a pair of budget- and performance-constrained weak-submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We consider the problem of approximating a function in general nonlinear subsets of $L^2$ when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…
Greedy algorithms for feature selection are widely used for recovering sparse high-dimensional vectors in linear models. In classical procedures, the main emphasis was put on the sample complexity, with little or no consideration of the…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be…
Dense kernel matrices resulting from pairwise evaluations of a kernel function arise naturally in machine learning and statistics. Previous work in constructing sparse approximate inverse Cholesky factors of such matrices by minimizing…
Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the…
In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
We investigate the problem of reconstructing sparse multivariate trigonometric polynomials from few randomly taken samples by Basis Pursuit and greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Thresholding. While recovery by…
The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…
Probabilistic Graphical Models (PGMs) are generative models of complex systems. They rely on conditional independence assumptions between variables to learn sparse representations which can be visualized in a form of a graph. Such models…
Let $0 < \theta \leqslant 1$. A sequence of positive integers $(b_n)_{n=1}^\infty$ is called a weak greedy approximation of $\theta$ if $\sum_{n=1}^{\infty}1/b_n = \theta$. We introduce the weak greedy approximation algorithm (WGAA), which,…
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…