{"id":7234,"date":"2025-09-30T07:02:26","date_gmt":"2025-09-30T07:02:26","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/09\/30\/2509-22766\/"},"modified":"2025-09-30T07:02:26","modified_gmt":"2025-09-30T07:02:26","slug":"2509-22766","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/09\/30\/2509-22766\/","title":{"rendered":"A theoretical guarantee for SyncRank"},"content":{"rendered":"<p>    A theoretical guarantee for SyncRank<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2509.22766v1 Announce Type: new<br \/>\nAbstract: We present a theoretical and empirical analysis of the SyncRank algorithm for recovering a global ranking from noisy pairwise comparisons. By adopting a complex-valued data model where the true ranking is encoded in the phases of a unit-modulus vector, we establish a sharp non-asymptotic recovery guarantee for the associated semidefinite programming (SDP) relaxation. Our main theorem characterizes a critical noise threshold &#8211; scaling as sigma = O(sqrt(n \/ log n)) &#8211; below which SyncRank achieves exact ranking recovery with high probability. Extensive experiments under this model confirm the theoretical predictions and demonstrate the algorithm&#8217;s robustness across varying problem sizes and noise regimes.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Yang Rao<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2509.22766\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A theoretical guarantee for SyncRank arXiv:2509.22766v1 Announce Type: new Abstract: We present a theoretical and empirical analysis of the SyncRank algorithm for recovering a global ranking from noisy pairwise comparisons. By adopting a complex-valued data model where the true ranking is encoded in the phases of a unit-modulus vector, we establish a sharp non-asymptotic recovery [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,187,113,112],"tags":[3921,3920,1628],"class_list":["post-7234","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-ai","category-cs-lg","category-stat-ml","tag-guarantee","tag-syncrank","tag-theoretical"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7234"}],"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=7234"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7234\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}