Related papers: Sparse Polynomial Chaos Expansions via Compressed …
Remarkable properties of Compressed sensing (CS) has led researchers to utilize it in various other fields where a solution to an underdetermined system of linear equations is needed. One such application is in the area of array signal…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods.…
For a large class of orthogonal basis functions, there has been a recent identification of expansion methods for computing accurate, stable approximations of a quantity of interest. This paper presents, within the context of uncertainty…
We propose a new iterative greedy algorithm for reconstructions of sparse signals with or without noisy perturbations in compressed sensing. The proposed algorithm, called \emph{subspace thresholding pursuit} (STP) in this paper, is a…
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly…
The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained…
In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest. In this work we present a survey of recent progress in this emerging topic. Our main focus is on the…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments. We consider a relaxation of the full optimization formulation of…
The recovery of approximately sparse or compressible coefficients in a Polynomial Chaos Expansion is a common goal in modern parametric uncertainty quantification (UQ). However, relatively little effort in UQ has been directed toward…
In this work, we propose a novel sampling method for Design of Experiments. This method allows to sample such input values of the parameters of a computational model for which the constructed surrogate model will have the least possible…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…
We study sparsity in the max-plus algebraic setting. We seek both exact and approximate solutions of the max-plus linear equation with minimum cardinality of support. In the former case, the sparsest solution problem is shown to be…
In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…
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…