{"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/algorithm-for-an-arbitrary-order-cumulant","title":"Algorithm for an arbitrary-order cumulant tensor calculation in a sliding window of data streams","arxiv_id":"1701.06446","date":"2017-01-20","proceeding":null,"authors":["Krzysztof Domino","Piotr Gawron"],"abstract":"High order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary order in a sliding window for data streams. We showed that this algorithms enables speedups of cumulants updates compared to current algorithms. This algorithm can be used for processing on-line high-frequency multivariate data and can find applications in, e.g., on-line signal filtering and classification of data streams. To present an application of this algorithm, we propose an estimator of non-Gaussianity of a data stream based on the norms of high-order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a~data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ the block structure to store and calculate only one hyper-pyramid part of such tensors.","url_abs":"http://arxiv.org/abs/1701.06446v3","url_pdf":"http://arxiv.org/pdf/1701.06446v3.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":"algorithm-for-an-arbitrary-order-cumulant","repo_url":"https://github.com/UnofficialJuliaMirror/CumulantsUpdates.jl-d4707d7b-0fe1-5399-a86f-c75188857573","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"algorithm-for-an-arbitrary-order-cumulant","repo_url":"https://github.com/ZKSI/CumulantsUpdates.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}