English
Related papers

Related papers: Support union recovery in high-dimensional multiva…

200 papers

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…

Information Theory · Computer Science 2010-03-02 Pablo Sprechmann , Ignacio Ramirez , Guillermo Sapiro , Yonina C. Eldar

This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…

Numerical Analysis · Mathematics 2017-09-12 Clarice Poon , Gabriel Peyré

In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is…

Information Theory · Computer Science 2021-07-27 Saurabh Khanna , Chandra R. Murthy

We focus on the high-dimensional linear regression problem, where the algorithmic goal is to efficiently infer an unknown feature vector $\beta^*\in\mathbb{R}^p$ from its linear measurements, using a small number $n$ of samples. Unlike most…

Statistics Theory · Mathematics 2023-09-19 David Gamarnik , Eren C. Kızıldağ , Ilias Zadik

We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…

Statistics Theory · Mathematics 2019-09-24 David Gamarnik , Ilias Zadik

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…

Information Theory · Computer Science 2014-07-28 Samet Oymak , Amin Jalali , Maryam Fazel , Yonina C. Eldar , Babak Hassibi

This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…

Information Theory · Computer Science 2021-02-23 Martin Genzel , Gitta Kutyniok , Maximilian März

We study the problem of community recovery and detection in multi-layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two-block model, we…

Statistics Theory · Mathematics 2023-11-15 Jing Lei , Anru R. Zhang , Zihan Zhu

We characterize the effectiveness of a classical algorithm for recovering the Markov graph of a general discrete pairwise graphical model from i.i.d. samples. The algorithm is (appropriately regularized) maximum conditional log-likelihood,…

Machine Learning · Computer Science 2019-06-20 Shanshan Wu , Sujay Sanghavi , Alexandros G. Dimakis

We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…

Econometrics · Economics 2024-11-18 Matteo Mogliani , Anna Simoni

A structured variable selection problem is considered in which the covariates, divided into predefined groups, activate according to sparse patterns with few nonzero entries per group. Capitalizing on the concept of atomic norm, a composite…

Machine Learning · Computer Science 2023-11-03 David Gregoratti , Xavier Mestre , Carlos Buelga

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…

Machine Learning · Statistics 2026-01-29 Meixia Lin , Meijiao Shi , Yunhai Xiao , Qian Zhang

This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…

Methodology · Statistics 2011-03-28 Kengo Kato

Many statistical $M$-estimators are based on convex optimization problems formed by the combination of a data-dependent loss function with a norm-based regularizer. We analyze the convergence rates of projected gradient and composite…

Machine Learning · Statistics 2012-07-26 Alekh Agarwal , Sahand N. Negahban , Martin J. Wainwright

High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…

Statistics Theory · Mathematics 2013-03-13 Sahand N. Negahban , Pradeep Ravikumar , Martin J. Wainwright , Bin Yu

In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…

Information Theory · Computer Science 2011-09-13 Charles Dossal , Marie-Line Chabanol , Gabriel Peyré , Jalal Fadili

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

Machine Learning · Statistics 2020-09-04 Quentin Bertrand , Mathurin Massias , Alexandre Gramfort , Joseph Salmon

This paper considers the recovery of group sparse signals over a multi-agent network, where the measurements are subject to sparse errors. We first investigate the robust group LASSO model and its centralized algorithm based on the…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-01-12 Manxi Wang , Yongcheng Li , Xiaohan Wei , Qing Ling

In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…

Statistics Theory · Mathematics 2017-02-21 Martin Genzel

Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML)…

Machine Learning · Statistics 2013-10-10 E. Chunikhina , R. Raich , T. Nguyen