Related papers: Basis pursuit by inconsistent alternating projecti…
In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues.…
Efficient algorithms for the sparse solution of under-determined linear systems $Ax = b$ are known for matrices $A$ satisfying suitable assumptions like the restricted isometry property (RIP). Without such assumptions little is known and…
The $\ell_{1\text{-}2}$ regularization method has a strong sparsity promoting capability in approaching sparse solutions of linear inverse problems and gained successful applications in various mathematics and applied science fields. This…
During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
The augmentation scheme provides a nontraditional approach to nonlinear integer programming by iteratively refining incumbent solutions along objective-improving directions from the Graver basis. Its main computational bottleneck, however,…
In this paper, we study the solution uniqueness of an individual feasible vector of a class of convex optimization problems involving convex piecewise affine functions and subject to general polyhedral constraints. This class of problems…
Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…
An important benefit of multi-objective search is that it maintains a diverse population of candidates, which helps in deceptive problems in particular. Not all diversity is useful, however: candidates that optimize only one objective while…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
Inspired by alternating direction method of multipliers and the idea of operator splitting, we propose a efficient algorithm for solving large-scale quadratically constrained basis pursuit. Experimental results show that the proposed…
Is it possible to find the sparsest vector (direction) in a generic subspace $\mathcal{S} \subseteq \mathbb{R}^p$ with $\mathrm{dim}(\mathcal{S})= n < p$? This problem can be considered a homogeneous variant of the sparse recovery problem,…
In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
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…
This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
The sparse linear reconstruction problem is a core problem in signal processing which aims to recover sparse solutions to linear systems. The original problem regularized by the total number of nonzero components (also known as $L_0$…