{"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/as-you-like-it-localization-via-paired","title":"As you like it: Localization via paired comparisons","arxiv_id":"1802.10489","date":"2018-02-19","proceeding":null,"authors":["Andrew K. Massimino","Mark A. Davenport"],"abstract":"Suppose that we wish to estimate a vector $\\mathbf{x}$ from a set of binary paired comparisons of the form \"$\\mathbf{x}$ is closer to $\\mathbf{p}$ than to $\\mathbf{q}$\" for various choices of vectors $\\mathbf{p}$ and $\\mathbf{q}$. The problem of estimating $\\mathbf{x}$ from this type of observation arises in a variety of contexts, including nonmetric multidimensional scaling, \"unfolding,\" and ranking problems, often because it provides a powerful and flexible model of preference. We describe theoretical bounds for how well we can expect to estimate $\\mathbf{x}$ under a randomized model for $\\mathbf{p}$ and $\\mathbf{q}$. We also present results for the case where the comparisons are noisy and subject to some degree of error. Additionally, we show that under a randomized model for $\\mathbf{p}$ and $\\mathbf{q}$, a suitable number of binary paired comparisons yield a stable embedding of the space of target vectors. Finally, we also show that we can achieve significant gains by adaptively changing the distribution for choosing $\\mathbf{p}$ and $\\mathbf{q}$.","url_abs":"https://arxiv.org/abs/1802.10489v2","url_pdf":"https://arxiv.org/pdf/1802.10489v2.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":"as-you-like-it-localization-via-paired","repo_url":"https://github.com/siplab-gt/pairsearch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}