{"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-set-functions-that-are-sparse-in-non","title":"Learning Set Functions that are Sparse in Non-Orthogonal Fourier Bases","arxiv_id":"2010.00439","date":"2020-10-01","proceeding":null,"authors":["Chris Wendler","Andisheh Amrollahi","Bastian Seifert","Andreas Krause","Markus Püschel"],"abstract":"Many applications of machine learning on discrete domains, such as learning preference functions in recommender systems or auctions, can be reduced to estimating a set function that is sparse in the Fourier domain. In this work, we present a new family of algorithms for learning Fourier-sparse set functions. They require at most $nk - k \\log_2 k + k$ queries (set function evaluations), under mild conditions on the Fourier coefficients, where $n$ is the size of the ground set and $k$ the number of non-zero Fourier coefficients. In contrast to other work that focused on the orthogonal Walsh-Hadamard transform, our novel algorithms operate with recently introduced non-orthogonal Fourier transforms that offer different notions of Fourier-sparsity. These naturally arise when modeling, e.g., sets of items forming substitutes and complements. We demonstrate effectiveness on several real-world applications.","url_abs":"https://arxiv.org/abs/2010.00439v3","url_pdf":"https://arxiv.org/pdf/2010.00439v3.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-set-functions-that-are-sparse-in-non","repo_url":"https://github.com/chrislybaer/aaai-ssft","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"learning-set-functions-that-are-sparse-in-non","repo_url":"https://github.com/marketdesignresearch/FA-based-ICAs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"AGPL-3.0"}},{"paper_slug":"learning-set-functions-that-are-sparse-in-non","repo_url":"https://github.com/marketdesignresearch/FA_based_ICAs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"recommendation-systems","task_name":"Recommendation Systems"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}