{"id":1797,"date":"2025-02-12T07:02:36","date_gmt":"2025-02-12T07:02:36","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/02\/12\/2502-07265\/"},"modified":"2025-02-12T07:02:36","modified_gmt":"2025-02-12T07:02:36","slug":"2502-07265","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/02\/12\/2502-07265\/","title":{"rendered":"Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds"},"content":{"rendered":"

Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds
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arXiv:2502.07265v1 Announce Type: new
\nAbstract: We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the Riemannian Heat-kernel (RHK) oracle. We establish high-accuracy sampling guarantees for the Riemannian Proximal Sampler, showing that generating samples with $varepsilon$-accuracy requires $O(log(1\/varepsilon))$ iterations in Kullback-Leibler divergence assuming access to exact oracles and $O(log^2(1\/varepsilon))$ iterations in the total variation metric assuming access to sufficiently accurate inexact oracles. Furthermore, we present practical implementations of these oracles by leveraging heat-kernel truncation and Varadhan’s asymptotics. In the latter case, we interpret the Riemannian Proximal Sampler as a discretization of the entropy-regularized Riemannian Proximal Point Method on the associated Wasserstein space. We provide preliminary numerical results that illustrate the effectiveness of the proposed methodology.<\/div>\n

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\n Yunrui Guan, Krishnakumar Balasubramanian, Shiqian Ma
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Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds arXiv:2502.07265v1 Announce Type: new Abstract: We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the Riemannian Heat-kernel (RHK) oracle. We establish high-accuracy […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,190,112,191],"tags":[586,1718,1719],"class_list":["post-1797","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-proximal","tag-riemannian","tag-sampler"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1797"}],"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=1797"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1797\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1797"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=1797"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=1797"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}