{"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/efficient-computation-of-higher-order","title":"Efficient computation of higher order cumulant tensors","arxiv_id":"1701.05420","date":"2017-01-19","proceeding":null,"authors":["Krzysztof Domino","Piotr Gawron","Łukasz Pawela"],"abstract":"In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented using tensor operations. The algorithm provided in the paper takes advantage of super-symmetry of cumulant and moment tensors. We show that the proposed algorithm considerably reduces the computational complexity and the computational memory requirement of cumulant calculation as compared with existing algorithms. For the sizes of interest, the reduction is of the order of $d!$ compared to the naive algorithm.","url_abs":"http://arxiv.org/abs/1701.05420v4","url_pdf":"http://arxiv.org/pdf/1701.05420v4.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"efficient-computation-of-higher-order","repo_url":"https://github.com/UnofficialJuliaMirrorSnapshots/Cumulants.jl-01e79fc4-f247-5fa3-af0e-2bd1d4cc767f","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"efficient-computation-of-higher-order","repo_url":"https://github.com/ZKSI/Cumulants.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"efficient-computation-of-higher-order","repo_url":"https://github.com/iitis/Cumulants.jl","is_official":0,"mentioned_in_paper":0,"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}