{"id":10368,"date":"2026-02-10T07:02:23","date_gmt":"2026-02-10T07:02:23","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/02\/10\/2602-07632\/"},"modified":"2026-02-10T07:02:23","modified_gmt":"2026-02-10T07:02:23","slug":"2602-07632","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/02\/10\/2602-07632\/","title":{"rendered":"Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization"},"content":{"rendered":"<p>    Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2602.07632v1 Announce Type: new<br \/>\nAbstract: In this work, we investigate the large-scale mean-field variational inference (MFVI) problem from a mini-batch primal-dual perspective. By reformulating MFVI as a constrained finite-sum problem, we develop a novel primal-dual algorithm based on an augmented Lagrangian formulation, termed primal-dual variational inference (PD-VI). PD-VI jointly updates global and local variational parameters in the evidence lower bound in a scalable manner. To further account for heterogeneous loss geometry across different variational parameter blocks, we introduce a block-preconditioned extension, P$^2$D-VI, which adapts the primal-dual updates to the geometry of each parameter block and improves both numerical robustness and practical efficiency. We establish convergence guarantees for both PD-VI and P$^2$D-VI under properly chosen constant step size, without relying on conjugacy assumptions or explicit bounded-variance conditions. In particular, we prove $O(1\/T)$ convergence to a stationary point in general settings and linear convergence under strong convexity. Numerical experiments on synthetic data and a real large-scale spatial transcriptomics dataset demonstrate that our methods consistently outperform existing stochastic variational inference approaches in terms of convergence speed and solution quality.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Jinhua Lyu, Tianmin Yu, Ying Ma, Naichen Shi<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2602.07632\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization arXiv:2602.07632v1 Announce Type: new Abstract: In this work, we investigate the large-scale mean-field variational inference (MFVI) problem from a mini-batch primal-dual perspective. By reformulating MFVI as a constrained finite-sum problem, we develop a novel primal-dual algorithm based on an augmented Lagrangian formulation, termed primal-dual variational inference (PD-VI). [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[1151,4751,936],"class_list":["post-10368","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-dual","tag-primal","tag-variational"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10368"}],"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=10368"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10368\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}