{"id":9918,"date":"2026-01-22T07:02:37","date_gmt":"2026-01-22T07:02:37","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/01\/22\/2601-14515\/"},"modified":"2026-01-22T07:02:37","modified_gmt":"2026-01-22T07:02:37","slug":"2601-14515","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/01\/22\/2601-14515\/","title":{"rendered":"Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions"},"content":{"rendered":"

Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions
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arXiv:2601.14515v1 Announce Type: new
\nAbstract: Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete) graph constructed from the full dataset. In finite dimensions the asymptotics in the large (unlabeled) data limit are well understood with convergence from the graph setting to a continuum Sobolev semi-norm weighted by the Lebesgue density of the data-generating measure. The lack of the Lebesgue measure on infinite-dimensional spaces requires rethinking the analysis if the data aren’t finite-dimensional. In this paper we make a first step in this direction by analyzing the setting when the data are generated by a Gaussian measure on a Hilbert space and proving pointwise convergence of the graph Dirichlet energy.<\/div>\n

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\n Zhengang Zhong, Yury Korolev, Matthew Thorpe
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Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions arXiv:2601.14515v1 Announce Type: new Abstract: Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete) graph […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,450,451,112],"tags":[84,515,4649],"class_list":["post-9918","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-cs-na","category-math-na","category-stat-ml","tag-data","tag-large","tag-measure"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9918"}],"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=9918"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9918\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}