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Graph sparsification is a well-established technique for accelerating graph-based learning algorithms, which uses edge sampling to approximate dense graphs with sparse ones. Because the sparsification error is random and unknown, users must…

Machine Learning · Computer Science 2025-03-12 Siyao Wang , Miles E. Lopes

Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…

Applications · Statistics 2012-06-20 Sooraj K. Ambat , Saikat Chatterjee , K. V. S. Hari

Several learning applications require solving high-dimensional regression problems where the relevant features belong to a small number of (overlapping) groups. For very large datasets and under standard sparsity constraints, hard…

Machine Learning · Statistics 2016-05-30 Prateek Jain , Nikhil Rao , Inderjit Dhillon

For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among…

Information Theory · Computer Science 2013-10-29 Dennis Sundman , Saikat Chatterjee , Mikael Skoglund

It is a survey on recent results in constructive sparse approximation. Three directions are discussed here: (1) Lebesgue-type inequalities for greedy algorithms with respect to a special class of dictionaries, (2) constructive sparse…

Numerical Analysis · Mathematics 2015-11-06 Vladimir Temlyakov

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…

Data Structures and Algorithms · Computer Science 2009-06-26 Mohamed-Ali Belabbas , Patrick J. Wolfe

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

Numerical Analysis · Mathematics 2017-12-04 Anindya Bhaduri , Lori Graham-Brady

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

Machine Learning · Computer Science 2020-08-26 Chiwoo Park , David J. Borth , Nicholas S. Wilson , Chad N. Hunter

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…

Statistics Theory · Mathematics 2014-02-25 Divyanshu Vats , Richard G. Baraniuk

Traffic flow modeling relies heavily on fundamental diagrams. However, deterministic fundamental diagrams, such as single or multi-regime models, cannot capture the uncertainty pattern that underlies traffic flow. To address this…

Applications · Statistics 2024-11-25 Yuan-Zheng Lei , Yaobang Gong , Xianfeng Terry Yang

Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient…

Machine Learning · Statistics 2016-07-13 Rajiv Khanna , Joydeep Ghosh , Russell Poldrack , Oluwasanmi Koyejo

Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used…

Image and Video Processing · Electrical Eng. & Systems 2018-12-31 Elad Plaut , Raja Giryes

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements…

Machine Learning · Statistics 2012-06-05 V. N. Temlyakov

Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…

Machine Learning · Statistics 2016-03-23 Sohail Bahmani , Petros T. Boufounos , Bhiksha Raj

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Machine Learning · Statistics 2011-06-28 Suvrit Sra , Dongmin Kim

Motivated by the question of optimal functional approximation via compressed sensing, we propose generalizations of the Iterative Hard Thresholding and the Compressive Sampling Matching Pursuit algorithms able to promote sparse in levels…

Information Theory · Computer Science 2021-11-01 Ben Adcock , Simone Brugiapaglia , Matthew King-Roskamp

For certain dynamical systems it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system close to a non-hyperbolic…

Dynamical Systems · Mathematics 2020-09-22 Bernard Haasdonk , Boumediene Hamzi , Gabriele Santin , Dominik Wittwar

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…

Machine Learning · Computer Science 2011-11-24 Francis Bach , Rodolphe Jenatton , Julien Mairal , Guillaume Obozinski

The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…

Methodology · Statistics 2025-02-04 Yidong Zhou , Hans-Georg Müller

Sparse signal recovery deals with finding the sparsest solution of an under-determined linear system $\vx = \mQ\vs$. In this paper, we propose a novel greedy approach to addressing the challenges from such a problem. Such an approach is…

Information Theory · Computer Science 2026-04-09 Gang Li , Qiuwei Li , Shuang Li , Wu Angela Li