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For compressive sensing of dynamic sparse signals, we develop an iterative pursuit algorithm. A dynamic sparse signal process is characterized by varying sparsity patterns over time/space. For such signals, the developed algorithm is able…

Statistics Theory · Mathematics 2012-10-15 Dave Zachariah , Saikat Chatterjee , Magnus Jansson

This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…

Numerical Analysis · Mathematics 2025-02-18 Licheng Dai , Xiliang Lu , Juntao You

We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss…

Statistics Theory · Mathematics 2014-05-05 Dan Yang , Zongming Ma , Andreas Buja

In this paper, we consider an LQR design problem for distributed control systems. For large-scale distributed systems, finding a solution might be computationally demanding due to communications among agents. To this aim, we deal with LQR…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-09-02 Myung Cho

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Numerical Analysis · Mathematics 2019-07-08 Ashish Kumar Nandi , Jajati Keshari Sahoo , Debasisha Mishra

Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…

Data Structures and Algorithms · Computer Science 2019-08-07 Brian Brubach , Karthik Abinav Sankararaman , Aravind Srinivasan , Pan Xu

Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…

Machine Learning · Statistics 2010-09-21 Arash Ali Amini , Massoud Babaie-Zadeh , Christian Jutten

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

Signal Processing · Electrical Eng. & Systems 2024-04-18 Geethu Joseph

We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…

Information Theory · Computer Science 2014-08-12 Mahmoud Abo Khamis , Anna C. Gilbert , Hung Q. Ngo , Atri Rudra

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…

Information Theory · Computer Science 2024-03-20 Jian-Feng Cai , Yu Long , Ruixue Wen , Jiaxi Ying

The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem -- the need to find a…

Functional Analysis · Mathematics 2014-01-06 Raja Giryes , Sangnam Nam , Michael Elad , Rémi Gribonval , Mike E. Davies

Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…

Mathematical Software · Computer Science 2026-05-25 Xiaoye Sherry Li , Yang Liu

We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…

Optimization and Control · Mathematics 2018-12-04 Tomoya Murata , Taiji Suzuki

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…

Information Theory · Computer Science 2016-05-04 Tomoyuki Obuchi , Yoshiyuki Kabashima

We consider the maximum likelihood estimation of sparse inverse covariance matrices. We demonstrate that current heuristic approaches primarily encourage robustness, instead of the desired sparsity. We give a novel approach that solves the…

Machine Learning · Statistics 2021-11-08 Dimitris Bertsimas , Jourdain Lamperski , Jean Pauphilet

In our recent work \cite{StojnicCSetam09,StojnicUpper10} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved results related to performance of a…

Information Theory · Computer Science 2013-04-02 Mihailo Stojnic

Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…

Optimization and Control · Mathematics 2007-06-13 Alexandre d'Aspremont , Onureena Banerjee , Laurent El Ghaoui

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…

Machine Learning · Computer Science 2023-09-28 Xiyang Hu , Cynthia Rudin , Margo Seltzer

Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The…

Machine Learning · Computer Science 2016-05-04 Ulugbek S. Kamilov , Hassan Mansour

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2015-04-29 Chen Chen , Junzhou Huang , Lei He , Hongsheng Li