Related papers: Screening Rules for Lasso with Non-Convex Sparse R…

In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be written as the difference of two convex…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

Screening rules were recently introduced as a technique for explicitly identifying active structures such as sparsity, in optimization problem arising in machine learning. This has led to new methods of acceleration based on a substantial…

In this paper, nonconvex and nonsmooth models for compressed sensing (CS) and low rank matrix completion (MC) is studied. The problem is formulated as a nonconvex regularized leat square optimization problems, in which the l0-norm and the…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

We propose a convex formulation of the fused lasso signal approximation problem consisting of non-convex penalty functions. The fused lasso signal model aims to estimate a sparse piecewise constant signal from a noisy observation.…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…

This work addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction which employs the $\ell_1$-norm as the loss function for the residual error and…

This paper considers the problem of signal denoising using a sparse tight-frame analysis prior. The L1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the…

The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…

A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…

Iteratively reweighted least square (IRLS) is a popular approach to solve sparsity-enforcing regression problems in machine learning. State of the art approaches are more efficient but typically rely on specific coordinate pruning schemes.…

Sparse classifiers such as the support vector machines (SVM) are efficient in test-phases because the classifier is characterized only by a subset of the samples called support vectors (SVs), and the rest of the samples (non SVs) have no…

Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…

Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…

In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection…

The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its…