{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/sampling-requirements-and-accelerated-schemes","title":"Sampling Requirements and Accelerated Schemes for Sparse Linear Regression with Orthogonal Least-Squares","arxiv_id":"1608.02549","date":"2016-08-08","proceeding":null,"authors":["Abolfazl Hashemi","Haris Vikalo"],"abstract":"We study the problem of inferring a sparse vector from random linear\ncombinations of its components. We propose the Accelerated Orthogonal\nLeast-Squares (AOLS) algorithm that improves performance of the well-known\nOrthogonal Least-Squares (OLS) algorithm while requiring significantly lower\ncomputational costs. While OLS greedily selects columns of the coefficient\nmatrix that correspond to non-zero components of the sparse vector, AOLS\nemploys a novel computationally efficient procedure that speeds up the search\nby anticipating future selections via choosing $L$ columns in each step, where\n$L$ is an adjustable hyper-parameter. We analyze the performance of AOLS and\nestablish lower bounds on the probability of exact recovery for both noiseless\nand noisy random linear measurements. In the noiseless scenario, it is shown\nthat when the coefficients are samples from a Gaussian distribution, AOLS with\nhigh probability recovers a $k$-sparse $m$-dimensional sparse vector using\n${\\cal O}(k\\log \\frac{m}{k+L-1})$ measurements. Similar result is established\nfor the bounded-noise scenario where an additional condition on the smallest\nnonzero element of the unknown vector is required. The asymptotic sampling\ncomplexity of AOLS is lower than the asymptotic sampling complexity of the\nexisting sparse reconstruction algorithms. In simulations, AOLS is compared to\nstate-of-the-art sparse recovery techniques and shown to provide better\nperformance in terms of accuracy, running time, or both. Finally, we consider\nan application of AOLS to clustering high-dimensional data lying on the union\nof low-dimensional subspaces and demonstrate its superiority over existing\nmethods.","url_abs":"http://arxiv.org/abs/1608.02549v2","url_pdf":"http://arxiv.org/pdf/1608.02549v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"sampling-requirements-and-accelerated-schemes","repo_url":"https://github.com/realabolfazl/AOLS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}