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Since an adaptive search of such hyperparameters is quite expensive from the computational point of view, we propose the use of a leave-one-out cross-validation (LOOCV) technique combined with univariate global optimization tools from the class of Lipschitz derivative-free methods. Conventional LOOCV methods often suffer from ill-conditioning, particularly in high-dimensional settings, leading to computational inefficiencies. To address these issues, we consider efficient global optimization strategies characterized by optimistic and pessimistic improvements. The resulting algorithm allows us to improve the performance of the standard approach in terms of both accuracy and efficiency. Numerical results deriving from the study of some test cases and an application to real-world data support our analysis.<\/jats:p>","DOI":"10.1007\/s00500-025-10624-w","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T04:11:42Z","timestamp":1747109502000},"page":"3733-3748","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Adaptive hyperparameter selection in kernel-based partition of unity methods by global optimization techniques"],"prefix":"10.1007","volume":"29","author":[{"given":"Roberto","family":"Cavoretto","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandra","family":"De Rossi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adeeba","family":"Haider","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaroslav D.","family":"Sergeyev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"10624_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-24494-1","volume-title":"Bayesian optimization and data science","author":"F Archetti","year":"2019","unstructured":"Archetti F, Candelieri A (2019) Bayesian optimization and data science. 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