{"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/provably-accurate-double-sparse-coding","title":"Provably Accurate Double-Sparse Coding","arxiv_id":"1711.03638","date":"2017-11-09","proceeding":null,"authors":["Thanh V. Nguyen","Raymond K. W. Wong","Chinmay Hegde"],"abstract":"Sparse coding is a crucial subroutine in algorithms for various signal\nprocessing, deep learning, and other machine learning applications. The central\ngoal is to learn an overcomplete dictionary that can sparsely represent a given\ninput dataset. However, a key challenge is that storage, transmission, and\nprocessing of the learned dictionary can be untenably high if the data\ndimension is high. In this paper, we consider the double-sparsity model\nintroduced by Rubinstein et al. (2010b) where the dictionary itself is the\nproduct of a fixed, known basis and a data-adaptive sparse component. First, we\nintroduce a simple algorithm for double-sparse coding that can be amenable to\nefficient implementation via neural architectures. Second, we theoretically\nanalyze its performance and demonstrate asymptotic sample complexity and\nrunning time benefits over existing (provable) approaches for sparse coding. To\nour knowledge, our work introduces the first computationally efficient\nalgorithm for double-sparse coding that enjoys rigorous statistical guarantees.\nFinally, we support our analysis via several numerical experiments on simulated\ndata, confirming that our method can indeed be useful in problem sizes\nencountered in practical applications.","url_abs":"http://arxiv.org/abs/1711.03638v2","url_pdf":"http://arxiv.org/pdf/1711.03638v2.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":"provably-accurate-double-sparse-coding","repo_url":"https://github.com/thanh-isu/double-sparse-coding","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}