{"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/the-xyz-algorithm-for-fast-interaction-search","title":"The xyz algorithm for fast interaction search in high-dimensional data","arxiv_id":"1610.05108","date":"2016-10-17","proceeding":null,"authors":["Gian-Andrea Thanei","Nicolai Meinshausen","Rajen D. Shah"],"abstract":"When performing regression on a dataset with $p$ variables, it is often of\ninterest to go beyond using main linear effects and include interactions as\nproducts between individual variables. For small-scale problems, these\ninteractions can be computed explicitly but this leads to a computational\ncomplexity of at least $\\mathcal{O}(p^2)$ if done naively. This cost can be\nprohibitive if $p$ is very large. We introduce a new randomised algorithm that\nis able to discover interactions with high probability and under mild\nconditions has a runtime that is subquadratic in $p$. We show that strong\ninteractions can be discovered in almost linear time, whilst finding weaker\ninteractions requires $\\mathcal{O}(p^\\alpha)$ operations for $1 < \\alpha < 2$\ndepending on their strength. The underlying idea is to transform interaction\nsearch into a closestpair problem which can be solved efficiently in\nsubquadratic time. The algorithm is called $\\mathit{xyz}$ and is implemented in\nthe language R. We demonstrate its efficiency for application to genome-wide\nassociation studies, where more than $10^{11}$ interactions can be screened in\nunder $280$ seconds with a single-core $1.2$ GHz CPU.","url_abs":"http://arxiv.org/abs/1610.05108v4","url_pdf":"http://arxiv.org/pdf/1610.05108v4.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":"the-xyz-algorithm-for-fast-interaction-search","repo_url":"https://github.com/gathanei/xyz","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":null,"task_name":"CPU"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}