Related papers: Structured Sparsity via Alternating Direction Meth…
Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or…
An important problem in the analysis of high-dimensional omics data is to identify subsets of molecular variables that are associated with a phenotype of interest. This requires addressing the challenges of high dimensionality, strong…
We study a norm for structured sparsity which leads to sparse linear predictors whose supports are unions of prede ned overlapping groups of variables. We call the obtained formulation latent group Lasso, since it is based on applying the…
We present an alternating direction method of multipliers (ADMM) for a generic overlapping group lasso problem, where the groups can be overlapping in an arbitrary way. Meanwhile, we prove the lower bounds and upper bounds for both the…
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an $\ell_2$ data-fidelity term and a…
The deployment of large language models (LLMs) is often constrained by their substantial computational and memory demands. While structured pruning presents a viable approach by eliminating entire network components, existing methods suffer…
This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
We consider the general nonlinear optimization problem where the objective function has an additional term defined by the $ \ell_0 $-quasi-norm in order to promote sparsity of a solution. This problem is highly difficult due to its…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Typical dimension reduction techniques for nonoverlapping sparse optimization involve screening or sieving strategies based on a dual certificate derived from the first-order optimality condition, approximating the gradients or exploiting…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
The primary goal of this paper is to provide an efficient solution algorithm based on the augmented Lagrangian framework for optimization problems with a stochastic objective function and deterministic constraints. Our main contribution is…
Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the $\ell_{1,\infty}$-norm constrained multi-task learning problem, which promotes a shared feature representation while…
We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…
In this paper, we propose a novel sparse learning based feature selection method that directly optimizes a large margin linear classification model sparsity with l_(2,p)-norm (0 < p < 1)subject to data-fitting constraints, rather than using…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…