Related papers: Trace Lasso: a trace norm regularization for corre…
In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell_1$ norm…
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
Regression with the lasso penalty is a popular tool for performing dimension reduction when the number of covariates is large. In many applications of the lasso, like in genomics, covariates are subject to measurement error. We study the…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
We introduce a novel method for sparse regression and variable selection, which is inspired by modern ideas in multiple testing. Imagine we have observations from the linear model y = X beta + z, then we suggest estimating the regression…
We consider the classical sensor scheduling problem for linear systems where only one sensor is activated at each time. We show that the sensor scheduling problem has a close relation to the sensor design problem and the solution of a…
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm.…
In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\ell_0$ pseudo norm…
In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter…
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…
The elastic net penalty is frequently employed in high-dimensional statistics for parameter regression and variable selection. It is particularly beneficial compared to lasso when the number of predictors greatly surpasses the number of…
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…
Alignments provide sophisticated diagnostics that pinpoint deviations in a trace with respect to a process model and their severity. However, approaches based on trace alignments use crisp process models as reference and recent…
Many recent developments in the high-dimensional statistical time series literature have centered around time-dependent applications that can be adapted to regularized least squares. Of particular interest is the lasso, which both serves to…
Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the…
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…