{"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-weighted-kendall-and-high-order-kernels","title":"The Weighted Kendall and High-order Kernels for Permutations","arxiv_id":"1802.08526","date":"2018-02-23","proceeding":"ICML 2018 7","authors":["Yunlong Jiao","Jean-Philippe Vert"],"abstract":"We propose new positive definite kernels for permutations. First we introduce\na weighted version of the Kendall kernel, which allows to weight unequally the\ncontributions of different item pairs in the permutations depending on their\nranks. Like the Kendall kernel, we show that the weighted version is invariant\nto relabeling of items and can be computed efficiently in $O(n \\ln(n))$\noperations, where $n$ is the number of items in the permutation. Second, we\npropose a supervised approach to learn the weights by jointly optimizing them\nwith the function estimated by a kernel machine. Third, while the Kendall\nkernel considers pairwise comparison between items, we extend it by considering\nhigher-order comparisons among tuples of items and show that the supervised\napproach of learning the weights can be systematically generalized to\nhigher-order permutation kernels.","url_abs":"http://arxiv.org/abs/1802.08526v2","url_pdf":"http://arxiv.org/pdf/1802.08526v2.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-weighted-kendall-and-high-order-kernels","repo_url":"https://github.com/YunlongJiao/kernrank","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"the-weighted-kendall-and-high-order-kernels","repo_url":"https://github.com/YunlongJiao/weightedkendall","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1802.08526","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}