{"660238":{"#nid":"660238","#data":{"type":"event","title":"ARC Colloquium: Yuansi Chen (Duke University)","body":[{"value":"\u003Cp align =\u0022center\u0022\u003E\u003Cstrong\u003EAlgorithms \u0026amp; Randomness Center (ARC)\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003EYuansi Chen (Duke University)\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003ESeptember 12, 2022\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align = \u0022center\u0022\u003E\u003Cstrong\u003EKlaus 1116 - 11:00 am\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ETitle:\u003C\/strong\u003E Localization\u0026nbsp;schemes: A framework for proving mixing bounds for Markov chains\u003Cstrong\u003E \u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAbstract:\u0026nbsp;\u0026nbsp;\u003C\/strong\u003EOur work is motivated by two recent and seemingly-unrelated techniques for proving mixing bounds for Markov chains:\u003C\/p\u003E\r\n\r\n\u003Cp\u003E(i) the concept of spectral independence, introduced by Anari, Liu and Oveis Gharan, and its numerous extensions, which have given rise to\u0026nbsp;several breakthroughs in the analysis of mixing times of discrete Markov chains and\u003Cbr \/\u003E\r\n(ii) the stochastic\u0026nbsp;localization\u0026nbsp;technique which has proven useful in establishing mixing and expansion bounds for both log-concave measures and\u0026nbsp;for measures on the discrete hypercube.\u003Cbr \/\u003E\r\n\u0026nbsp;\u003Cbr \/\u003E\r\nIn this work, we present a framework which connects ideas from both techniques and allows us to unify proofs in the mixing time of MCMC\u0026nbsp;algorithms on high dimensional distributions. In its center is the concept of a\u0026nbsp;localization\u0026nbsp;scheme which, to every probability measure , assigns a\u0026nbsp;martingale of probability measures which localize in space as time evolves. This viewpoint provides tools for deriving mixing bounds for the\u0026nbsp;dynamics through the analysis of the corresponding\u0026nbsp;localization\u0026nbsp;process.\u0026nbsp; Generalizations of concepts of spectral independence naturally arise\u0026nbsp;from our definitions. In particular we show via our framework that it is possible to recover the main theorems in the spectral independence\u0026nbsp;frameworks via simple martingale arguments, while completely bypassing the theory of high-dimensional expanders.\u0026nbsp; As applications, we discuss\u0026nbsp;how to use it to obtain the first O(nlogn) bound for mixing time of the hardcore-model (of arbitrary degree) in the tree-uniqueness regime, under\u0026nbsp;Glauber dynamics and to prove a KL-divergence decay bound for log-concave sampling via the Restricted Gaussian Oracle, which achieves\u0026nbsp;optimal mixing under any exp(n)-warm start.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E---------------------------------------------------------------\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Ca href=\u0022http:\/\/www2.stat.duke.edu\/~yc443\/\u0022\u003ESpeaker\u0026#39;s Webpage\u003C\/a\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cem\u003EVideos of recent talks are available at: \u003C\/em\u003E\u003Ca href=\u0022https:\/\/smartech.gatech.edu\/handle\/1853\/46836\u0022\u003E\u003Cem\u003Ehttps:\/\/smartech.gatech.edu\/handle\/1853\/46836\u003C\/em\u003E\u003C\/a\u003E\u003Cem\u003E and \u003Ca href=\u0022http:\/\/arc.gatech.edu\/node\/121\u0022\u003Ehttp:\/\/arc.gatech.edu\/node\/121\u003C\/a\u003E \u003C\/em\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Ca href=\u0022https:\/\/mailman.cc.gatech.edu\/mailman\/listinfo\/arc-colloq\u0022\u003E\u003Cem\u003EClick here to subscribe to the seminar email list: arc-colloq@Klauscc.gatech.edu\u003C\/em\u003E\u003C\/a\u003E\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Localization schemes: A framework for proving mixing bounds for Markov chains - Klaus 1116 at 11am"}],"uid":"35702","created_gmt":"2022-08-17 13:45:34","changed_gmt":"2022-08-29 15:30:47","author":"mb121","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2022-09-12T12:00:00-04:00","event_time_end":"2022-09-12T13:00:00-04:00","event_time_end_last":"2022-09-12T13:00:00-04:00","gmt_time_start":"2022-09-12 16:00:00","gmt_time_end":"2022-09-12 17:00:00","gmt_time_end_last":"2022-09-12 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"70263","name":"ARC"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"177814","name":"Postdoc"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}