{"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/learning-a-compressed-sensing-measurement","title":"Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling","arxiv_id":"1806.10175","date":"2018-06-26","proceeding":null,"authors":["Shanshan Wu","Alexandros G. Dimakis","Sujay Sanghavi","Felix X. Yu","Daniel Holtmann-Rice","Dmitry Storcheus","Afshin Rostamizadeh","Sanjiv Kumar"],"abstract":"Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt to data, while still performing well with the widely used $\\ell_1$ decoder. The convex $\\ell_1$ decoder prevents gradient propagation as needed in standard gradient-based training. Our method is based on the insight that unrolling the convex decoder into $T$ projected subgradient steps can address this issue. Our method can be seen as a data-driven way to learn a compressed sensing measurement matrix. We compare the empirical performance of 10 algorithms over 6 sparse datasets (3 synthetic and 3 real). Our experiments show that there is indeed additional structure beyond sparsity in the real datasets; our method is able to discover it and exploit it to create excellent reconstructions with fewer measurements (by a factor of 1.1-3x) compared to the previous state-of-the-art methods. We illustrate an application of our method in learning label embeddings for extreme multi-label classification, and empirically show that our method is able to match or outperform the precision scores of SLEEC, which is one of the state-of-the-art embedding-based approaches.","url_abs":"https://arxiv.org/abs/1806.10175v4","url_pdf":"https://arxiv.org/pdf/1806.10175v4.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":"learning-a-compressed-sensing-measurement","repo_url":"https://github.com/wushanshan/L1AE","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"},{"task_slug":"extreme-multi-label-classification","task_name":"Extreme Multi-Label Classification"},{"task_slug":"multi-label-classification-2","task_name":"MUlTI-LABEL-ClASSIFICATION"},{"task_slug":"multi-label-classification","task_name":"Multi-Label Classification"},{"task_slug":"multi-label-learning","task_name":"Multi-Label Learning"},{"task_slug":"unrolling","task_name":"Rolling Shutter Correction"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}