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We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

Numerical Analysis · Computer Science 2009-01-08 Wei Dai , Olgica Milenkovic

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…

Signal Processing · Electrical Eng. & Systems 2019-09-04 Dror Simon , Jeremias Sulam , Yaniv Romano , Yue M. Lu , Michael Elad

Audio events are quite often overlapping in nature, and more prone to noise than visual signals. There has been increasing evidence for the superior performance of representations learned using sparse dictionaries for applications like…

Machine Learning · Computer Science 2017-12-05 Vaisakh Shaj , Puranjoy Bhattacharya

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…

Machine Learning · Computer Science 2020-10-22 Guannan Liang , Qianqian Tong , Jiahao Ding , Miao Pan , Jinbo Bi

A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…

Machine Learning · Statistics 2012-10-03 Rodolphe Jenatton , Rémi Gribonval , Francis Bach

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the…

Machine Learning · Statistics 2021-02-09 Robert Pinsler , Jonathan Gordon , Eric Nalisnick , José Miguel Hernández-Lobato

Deep reinforcement learning in partially observable environments is a difficult task in itself, and can be further complicated by a sparse reward signal. Most tasks involving navigation in three-dimensional environments provide the agent…

Machine Learning · Computer Science 2023-10-17 Matvey Gerasyov , Ilya Makarov

Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…

Machine Learning · Computer Science 2025-09-15 Boya Ma , Abram Magner , Maxwell McNeil , Petko Bogdanov

Sparse autoencoders (SAEs) provide a powerful mechanism for decomposing the dense representations produced by Large Language Models (LLMs) into interpretable latent features. We posit that SAEs constitute a natural foundation for Learned…

Machine Learning · Computer Science 2026-03-17 Thibault Formal , Maxime Louis , Hervé Dejean , Stéphane Clinchant

In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this…

Machine Learning · Statistics 2015-03-11 Matthias Seibert , Martin Kleinsteuber , Rémi Gribonval , Rodolphe Jenatton , Francis Bach

Data augmentation methods usually apply the same augmentation (or a mix of them) to all the training samples. For example, to perturb data with noise, the noise is sampled from a Normal distribution with a fixed standard deviation, for all…

Robotic assembly presents a long-standing challenge due to its requirement for precise, contact-rich manipulation. While simulation-based learning has enabled the development of robust assembly policies, their performance often degrades…

Robotics · Computer Science 2026-02-27 Yijie Guo , Iretiayo Akinola , Lars Johannsmeier , Hugo Hadfield , Abhishek Gupta , Yashraj Narang

We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting…

Machine Learning · Computer Science 2020-06-11 Prashant Shekhar , Abani Patra

Federated learning (FL) has emerged as a prominent method for collaboratively training machine learning models using local data from edge devices, all while keeping data decentralized. However, accounting for the quality of data contributed…

Machine Learning · Computer Science 2024-09-05 Haoyuan Li , Mathias Funk , Nezihe Merve Gürel , Aaqib Saeed

We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter…

Signal Processing · Electrical Eng. & Systems 2018-10-18 Y. Yu , H. Zhao , R. C. de Lamare

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

Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…

Statistics Theory · Mathematics 2015-03-31 Yudong Chen , Constantine Caramanis

Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…

Methodology · Statistics 2021-03-25 Ankit Kumar , Sharmodeep Bhattacharyya , Kristofer Bouchard

Autonomous systems can be used to search for sparse signals in a large space; e.g., aerial robots can be deployed to localize threats, detect gas leaks, or respond to distress calls. Intuitively, search algorithms may increase efficiency by…

Machine Learning · Statistics 2016-12-05 Yifei Ma , Roman Garnett , Jeff Schneider

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