English
Related papers

Related papers: Provable Guarantees for Sparsity Recovery with Det…

200 papers

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…

Information Theory · Computer Science 2011-02-21 Yoshiyuki Kabashima , Tadashi Wadayama

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

Machine Learning · Statistics 2013-01-15 Yudong Chen , Constantine Caramanis , Shie Mannor

We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement…

Information Theory · Computer Science 2015-06-02 Vipul Gupta , Bhavya Kailkhura , Thakshila Wimalajeewa , Pramod K. Varshney

We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…

Machine Learning · Computer Science 2023-06-23 Yao Ji , Gesualdo Scutari , Ying Sun , Harsha Honnappa

Much work has been done recently to make neural networks more interpretable, and one obvious approach is to arrange for the network to use only a subset of the available features. In linear models, Lasso (or $\ell_1$-regularized) regression…

Machine Learning · Statistics 2021-06-17 Ismael Lemhadri , Feng Ruan , Louis Abraham , Robert Tibshirani

In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…

Methodology · Statistics 2021-11-08 Dimitris Bertsimas , Jean Pauphilet , Bart Van Parys

Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…

Machine Learning · Statistics 2017-07-14 Devansh Arpit , Yingbo Zhou , Hung Q. Ngo , Nils Napp , Venu Govindaraju

In this paper, we will investigate the efficacy of IMAT (Iterative Method of Adaptive Thresholding) in recovering the sparse signal (parameters) for linear models with missing data. Sparse recovery rises in compressed sensing and machine…

Machine Learning · Computer Science 2016-06-14 Ashkan Esmaeili , Farokh Marvasti

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…

Machine Learning · Computer Science 2012-02-28 Ali Jalali , Pradeep Ravikumar , Sujay Sanghavi

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

Information Theory · Computer Science 2012-05-09 Thomas Blumensath

Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying…

Computer Vision and Pattern Recognition · Computer Science 2014-04-22 Xiao Bian , Hamid Krim

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…

Machine Learning · Statistics 2015-03-31 Ravi Ganti , Rebecca M. Willett

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

Systems and Control · Electrical Eng. & Systems 2026-05-05 Yanxin Fu , Wenxiao Zhao

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…

Numerical Analysis · Mathematics 2007-05-23 Massimo Fornasier , Holger Rauhut

We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…

Information Theory · Computer Science 2011-12-08 Christoph Studer , Patrick Kuppinger , Graeme Pope , Helmut Bölcskei

Sparse recovery can recover sparse signals from a set of underdetermined linear measurements. Motivated by the need to monitor large-scale networks from a limited number of measurements, this paper addresses the problem of recovering sparse…

Information Theory · Computer Science 2015-03-20 Meng Wang , Weiyu Xu , Enrique Mallada , Ao Tang

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

Data Structures and Algorithms · Computer Science 2022-03-09 Jonathan A. Kelner , Jerry Li , Allen Liu , Aaron Sidford , Kevin Tian

Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…

Machine Learning · Statistics 2026-04-27 Aoran Zhang , Tianyao Wei , Maria J. Guerrero , César A. Uribe

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and…

Machine Learning · Statistics 2017-02-27 Simon S. Du , Sivaraman Balakrishnan , Aarti Singh

Penalized regression methods, most notably the lasso, are a popular approach to analyzing high-dimensional data. An attractive property of the lasso is that it naturally performs variable selection. An important area of concern, however, is…

Methodology · Statistics 2026-05-13 Ryan Miller , Patrick Breheny