{"id":"https://openalex.org/W2766700121","doi":"https://doi.org/10.1145/3188745.3188774","title":"Convergence rate of Riemannian Hamiltonian Monte Carlo and faster polytope volume computation","display_name":"Convergence rate of Riemannian Hamiltonian Monte Carlo and faster polytope volume computation","publication_year":2018,"publication_date":"2018-06-20","ids":{"openalex":"https://openalex.org/W2766700121","doi":"https://doi.org/10.1145/3188745.3188774","mag":"2766700121"},"language":"en","primary_location":{"id":"doi:10.1145/3188745.3188774","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3188745.3188774","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188774","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188774","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024980585","display_name":"Yin Tat Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yin Tat Lee","raw_affiliation_strings":["University of Washington, USA / Microsoft Research, USA","University of Washington, USA / Microsoft Research, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington, USA / Microsoft Research, USA","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I201448701"]},{"raw_affiliation_string":"University of Washington, USA / Microsoft Research, USA#TAB#","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101983359","display_name":"Santosh Vempala","orcid":"https://orcid.org/0000-0002-3779-433X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I2800444561","display_name":"Atlanta Technical College","ror":"https://ror.org/01s3vfp47","country_code":"US","type":"education","lineage":["https://openalex.org/I2800444561"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Santosh S. Vempala","raw_affiliation_strings":["Georgia Tech, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Tech, USA","institution_ids":["https://openalex.org/I130701444","https://openalex.org/I2800444561"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5443,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6367552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1115","last_page":"1121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7013723850250244},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6583267450332642},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.6477803587913513},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6454896926879883},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.550634503364563},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49862194061279297},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45427024364471436},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4331842064857483},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.42960768938064575},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4248260259628296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37589889764785767},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3307763934135437},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.25234249234199524},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.1115863025188446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1105450987815857},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07881206274032593}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7013723850250244},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6583267450332642},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6477803587913513},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6454896926879883},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.550634503364563},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49862194061279297},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45427024364471436},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4331842064857483},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.42960768938064575},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4248260259628296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37589889764785767},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3307763934135437},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25234249234199524},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.1115863025188446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1105450987815857},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07881206274032593},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3188745.3188774","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3188745.3188774","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188774","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1710.06261","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.06261","pdf_url":"https://arxiv.org/pdf/1710.06261","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2766700121","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.06261.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1710.06261","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.06261","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1145/3188745.3188774","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3188745.3188774","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3188745.3188774","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1906418360","display_name":"TRIPODS: Algorithms for Data Science: Complexity, Scalability, and Robustness.","funder_award_id":"1740551","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2798763028","display_name":"CAREER: The Interplay between Combinatorial Optimization and Algorithmic Convex Geometry","funder_award_id":"1749609","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3006642656","display_name":"AF:Small: Fundamental High-Dimensional Algorithms","funder_award_id":"1717349","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3184741441","display_name":"AF: Medium: Collaborative Research: The Power of Randomness for Approximate Counting","funder_award_id":"1563838","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2766700121.pdf","grobid_xml":"https://content.openalex.org/works/W2766700121.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1545319692","https://openalex.org/W1559116151","https://openalex.org/W1567512734","https://openalex.org/W1809030594","https://openalex.org/W1980621453","https://openalex.org/W1996999318","https://openalex.org/W2025334959","https://openalex.org/W2041990574","https://openalex.org/W2049731483","https://openalex.org/W2063342497","https://openalex.org/W2069691149","https://openalex.org/W2084990336","https://openalex.org/W2085800367","https://openalex.org/W2123493177","https://openalex.org/W2145089782","https://openalex.org/W2147487384","https://openalex.org/W2159000620","https://openalex.org/W2168908795","https://openalex.org/W2423159321","https://openalex.org/W2478027467","https://openalex.org/W2562438252","https://openalex.org/W2572702041","https://openalex.org/W2746461338","https://openalex.org/W3023788998"],"related_works":["https://openalex.org/W2963559717","https://openalex.org/W2912255742","https://openalex.org/W1968165373","https://openalex.org/W2739292280","https://openalex.org/W2949618791","https://openalex.org/W2756747830","https://openalex.org/W3087302502","https://openalex.org/W2092133847","https://openalex.org/W2613650536","https://openalex.org/W2338000073","https://openalex.org/W1504546788","https://openalex.org/W2754446433","https://openalex.org/W3126106683","https://openalex.org/W3182737390","https://openalex.org/W2033560593","https://openalex.org/W2345444914","https://openalex.org/W2929317504","https://openalex.org/W2963596125","https://openalex.org/W2044203216","https://openalex.org/W2030336883"],"abstract_inverted_index":{"We":[0,44],"give":[1],"the":[2,7,27,47,50,54,59,72,79,85,94,97,112],"first":[3],"rigorous":[4],"proof":[5,107],"of":[6,9,29,35,39,61,88,96,102,108,111],"convergence":[8,30],"Riemannian":[10,42],"Hamiltonian":[11],"Monte":[12],"Carlo,":[13],"a":[14,65,106],"general":[15],"(and":[16],"practical)":[17],"method":[18,48],"for":[19,115],"sampling":[20,64],"Gibbs":[21,116],"distributions.":[22],"Our":[23],"analysis":[24,104],"shows":[25],"that":[26],"rate":[28],"is":[31,91,105],"bounded":[32],"in":[33],"terms":[34],"natural":[36],"smoothness":[37],"parameters":[38],"an":[40,109],"associated":[41],"manifold.":[43],"then":[45],"apply":[46],"with":[49],"manifold":[51,80],"defined":[52],"by":[53,74],"log":[55],"barrier":[56],"function":[57],"to":[58,78],"problems":[60],"(1)":[62],"uniformly":[63],"polytope":[66],"and":[67],"(2)":[68],"computing":[69],"its":[70],"volume,":[71],"latter":[73],"extending":[75],"Gaussian":[76],"cooling":[77],"setting.":[81],"In":[82],"both":[83],"cases,":[84],"total":[86],"number":[87],"steps":[89],"needed":[90],"O*(mn2/3),":[92],"improving":[93],"state":[95],"art.":[98],"A":[99],"key":[100],"ingredient":[101],"our":[103],"analog":[110],"KLS":[113],"conjecture":[114],"distributions":[117],"over":[118],"manifolds.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}