The weighted Kendall and high-order kernels for permutations
We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version...
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| Format: | Conference item |
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PMLR
2018
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| _version_ | 1826285926647595008 |
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| author | Jiao, Y Vert, J |
| author_facet | Jiao, Y Vert, J |
| author_sort | Jiao, Y |
| collection | OXFORD |
| description | We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to relabeling of items and can be computed efficiently in O(n ln(n)) operations, where n is the number of items in the permutation. Second, we propose a supervised approach to learn the weights by jointly optimizing them with the function estimated by a kernel machine. Third, while the Kendall kernel considers pairwise comparison between items, we extend it by considering higher-order comparisons among tuples of items and show that the supervised approach of learning the weights can be systematically generalized to higher-order permutation kernels. |
| first_indexed | 2024-03-07T01:36:09Z |
| format | Conference item |
| id | oxford-uuid:953f68ad-c9ee-4384-8b4e-839d747c577f |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:36:09Z |
| publishDate | 2018 |
| publisher | PMLR |
| record_format | dspace |
| spelling | oxford-uuid:953f68ad-c9ee-4384-8b4e-839d747c577f2022-03-26T23:44:59ZThe weighted Kendall and high-order kernels for permutationsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:953f68ad-c9ee-4384-8b4e-839d747c577fSymplectic Elements at OxfordPMLR2018Jiao, YVert, JWe propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks. Like the Kendall kernel, we show that the weighted version is invariant to relabeling of items and can be computed efficiently in O(n ln(n)) operations, where n is the number of items in the permutation. Second, we propose a supervised approach to learn the weights by jointly optimizing them with the function estimated by a kernel machine. Third, while the Kendall kernel considers pairwise comparison between items, we extend it by considering higher-order comparisons among tuples of items and show that the supervised approach of learning the weights can be systematically generalized to higher-order permutation kernels. |
| spellingShingle | Jiao, Y Vert, J The weighted Kendall and high-order kernels for permutations |
| title | The weighted Kendall and high-order kernels for permutations |
| title_full | The weighted Kendall and high-order kernels for permutations |
| title_fullStr | The weighted Kendall and high-order kernels for permutations |
| title_full_unstemmed | The weighted Kendall and high-order kernels for permutations |
| title_short | The weighted Kendall and high-order kernels for permutations |
| title_sort | weighted kendall and high order kernels for permutations |
| work_keys_str_mv | AT jiaoy theweightedkendallandhighorderkernelsforpermutations AT vertj theweightedkendallandhighorderkernelsforpermutations AT jiaoy weightedkendallandhighorderkernelsforpermutations AT vertj weightedkendallandhighorderkernelsforpermutations |