{"id":8928,"date":"2025-12-08T07:02:51","date_gmt":"2025-12-08T07:02:51","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/12\/08\/2512-05611\/"},"modified":"2025-12-08T07:02:51","modified_gmt":"2025-12-08T07:02:51","slug":"2512-05611","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/12\/08\/2512-05611\/","title":{"rendered":"Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches"},"content":{"rendered":"

Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches
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arXiv:2512.05611v1 Announce Type: new
\nAbstract: We study the calibration of Gaussian process (GP) predictive distributions in the interpolation setting from a design-marginal perspective. Conditioning on the data and averaging over a design measure mu, we formalize mu-coverage for central intervals and mu-probabilistic calibration through randomized probability integral transforms. We introduce two methods. cps-gp adapts conformal predictive systems to GP interpolation using standardized leave-one-out residuals, yielding stepwise predictive distributions with finite-sample marginal calibration. bcr-gp retains the GP posterior mean and replaces the Gaussian residual by a generalized normal model fitted to cross-validated standardized residuals. A Bayesian selection rule-based either on a posterior upper quantile of the variance for conservative prediction or on a cross-posterior Kolmogorov-Smirnov criterion for probabilistic calibration-controls dispersion and tail behavior while producing smooth predictive distributions suitable for sequential design. Numerical experiments on benchmark functions compare cps-gp, bcr-gp, Jackknife+ for GPs, and the full conformal Gaussian process, using calibration metrics (coverage, Kolmogorov-Smirnov, integral absolute error) and accuracy or sharpness through the scaled continuous ranked probability score.<\/div>\n

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\n Aur’elien Pion, Emmanuel Vazquez
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Design-marginal calibration of Gaussian process predictive distributions: Bayesian and conformal approaches arXiv:2512.05611v1 Announce Type: new Abstract: We study the calibration of Gaussian process (GP) predictive distributions in the interpolation setting from a design-marginal perspective. Conditioning on the data and averaging over a design measure mu, we formalize mu-coverage for central intervals and mu-probabilistic calibration through […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,183,112],"tags":[1227,2290,716],"class_list":["post-8928","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-me","category-stat-ml","tag-calibration","tag-gp","tag-predictive"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8928"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=8928"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8928\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=8928"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=8928"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=8928"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}