Related papers: Beyond L1: Faster and Better Sparse Models with sk…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…

Sparse signal recovery has been dominated by the basis pursuit denoise (BPDN) problem formulation for over a decade. In this paper, we propose an algorithm that outperforms BPDN in finding sparse solutions to underdetermined linear systems…

Compared with digital methods, sparse recovery based on spiking neural networks has great advantages like high computational efficiency and low power-consumption. However, current spiking algorithms cannot guarantee more accurate estimates…

Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…

Sparse prediction with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection…

Generalized sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. Here we show that SpGEMM also yields efficient…

Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…

This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of…

We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the…

We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low…

Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the…

We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

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…