Related papers: Theoretical Analysis of Sparse Optimization with R…

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…

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types of nonconvex sparsity-inducing terms, bringing strong applicability to a…

An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of $\ell_1$…

Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD,…

Finding the sparse solution of an underdetermined system of linear equations has many applications, especially, it is used in Compressed Sensing (CS), Sparse Component Analysis (SCA), and sparse decomposition of signals on overcomplete…

Learning sparse models from data is an important task in all those frameworks where relevant information should be identified within a large dataset. This can be achieved by formulating and solving suitable sparsity promoting optimization…

The main contribution of the paper is a new approach to subspace clustering that is significantly more computationally efficient and scalable than existing state-of-the-art methods. The central idea is to modify the regression technique in…

We consider the problem of learning a sparse graph under the Laplacian constrained Gaussian graphical models. This problem can be formulated as a penalized maximum likelihood estimation of the Laplacian constrained precision matrix. Like in…

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…

Loss of plasticity, trainability loss, and primacy bias have been identified as issues arising when training deep neural networks on sequences of tasks -- all referring to the increased difficulty in training on new tasks. We propose to use…

In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into…

In compressed sensing sparse solutions are usually obtained by solving an $\ell^1$-minimization problem. Furthermore, the sparsity of the signal does need not be directly given. In fact, it is sufficient to have a signal that is sparse…

We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…

In this paper, we consider the $L_1/L_2 $ minimization for sparse recovery and study its relationship with the $L_1$-$ \alpha L_2 $ model. Based on this relationship, we propose three numerical algorithms to minimize this ratio model, two…

Concept shift is a prevailing problem in natural tasks like medical image segmentation where samples usually come from different subpopulations with variant correlations between features and labels. One common type of concept shift in…

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse…

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of…

This paper presents a regularization technique incorporating a non-convex and non-smooth term, $\ell_{1}^{2}-\eta\ell_{2}^{2}$, with parameters $0<\eta\leq 1$ designed to address ill-posed linear problems that yield sparse solutions. We…

Sparsity is one of the key concepts that allows the recovery of signals that are subsampled at a rate significantly lower than required by the Nyquist-Shannon sampling theorem. Our proposed framework uses arbitrary multiscale transforms,…

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement…