{"id":2746,"date":"2025-03-31T07:05:58","date_gmt":"2025-03-31T07:05:58","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/31\/2503-21980\/"},"modified":"2025-03-31T07:05:58","modified_gmt":"2025-03-31T07:05:58","slug":"2503-21980","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/31\/2503-21980\/","title":{"rendered":"Rolled Gaussian process models for curves on manifolds"},"content":{"rendered":"<p>    Rolled Gaussian process models for curves on manifolds<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2503.21980v1 Announce Type: cross<br \/>\nAbstract: Given a planar curve, imagine rolling a sphere along that curve without slipping or twisting, and by this means tracing out a curve on the sphere. It is well known that such a rolling operation induces a local isometry between the sphere and the plane so that the two curves uniquely determine each other, and moreover, the operation extends to a general class of manifolds in any dimension. We use rolling to construct an analogue of a Gaussian process on a manifold starting from a Euclidean Gaussian process. The resulting model is generative, and is amenable to statistical inference given data as curves on a manifold. We illustrate with examples on the unit sphere, symmetric positive-definite matrices, and with a robotics application involving 3D orientations.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Simon Preston, Karthik Bharath, Pablo Lopez-Custodio, Alfred Kume<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2503.21980\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rolled Gaussian process models for curves on manifolds arXiv:2503.21980v1 Announce Type: cross Abstract: Given a planar curve, imagine rolling a sphere along that curve without slipping or twisting, and by this means tracing out a curve on the sphere. It is well known that such a rolling operation induces a local isometry between the sphere [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,190,183,112,191],"tags":[2203,338,114],"class_list":["post-2746","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-math-st","category-stat-me","category-stat-ml","category-stat-th","tag-curves","tag-gaussian","tag-process"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2746"}],"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=2746"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2746\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}