{"id":"https://openalex.org/W4322707172","doi":"https://doi.org/10.1109/tit.2023.3250099","title":"Martingale Methods for Sequential Estimation of Convex Functionals and Divergences","display_name":"Martingale Methods for Sequential Estimation of Convex Functionals and Divergences","publication_year":2023,"publication_date":"2023-02-28","ids":{"openalex":"https://openalex.org/W4322707172","doi":"https://doi.org/10.1109/tit.2023.3250099"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2023.3250099","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3250099","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044922903","display_name":"Tudor Manole","orcid":"https://orcid.org/0000-0002-1550-0732"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tudor Manole","raw_affiliation_strings":["Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1550-0732","affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032389695","display_name":"Aaditya Ramdas","orcid":"https://orcid.org/0000-0003-0497-311X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaditya Ramdas","raw_affiliation_strings":["Department of Statistics and Data Science and the Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science and the Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":2.5429,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.90453727,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"69","issue":"7","first_page":"4641","last_page":"4658"},"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":0.9902999997138977,"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":0.9902999997138977,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9789000153541565,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8067548274993896},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4747332036495209},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.47248998284339905},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46423688530921936},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.45301204919815063},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.444273978471756},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.42676737904548645},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.4124051332473755},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37512820959091187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3591632843017578},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35287922620773315},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23556867241859436},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18084776401519775}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8067548274993896},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4747332036495209},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.47248998284339905},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46423688530921936},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.45301204919815063},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.444273978471756},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.42676737904548645},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4124051332473755},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37512820959091187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3591632843017578},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35287922620773315},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23556867241859436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18084776401519775},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2023.3250099","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2023.3250099","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1513720433","display_name":null,"funder_award_id":"DMS 1916320","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/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":111,"referenced_works":["https://openalex.org/W152055444","https://openalex.org/W650378347","https://openalex.org/W840677367","https://openalex.org/W1480398149","https://openalex.org/W1527849298","https://openalex.org/W1560724230","https://openalex.org/W1585160083","https://openalex.org/W1837324686","https://openalex.org/W1964836112","https://openalex.org/W1987820735","https://openalex.org/W1988645907","https://openalex.org/W1989187542","https://openalex.org/W2000992741","https://openalex.org/W2004216344","https://openalex.org/W2007316542","https://openalex.org/W2010353172","https://openalex.org/W2014801173","https://openalex.org/W2021801262","https://openalex.org/W2025533349","https://openalex.org/W2030532031","https://openalex.org/W2045381365","https://openalex.org/W2047023085","https://openalex.org/W2059475362","https://openalex.org/W2080186821","https://openalex.org/W2081780098","https://openalex.org/W2083454075","https://openalex.org/W2085839414","https://openalex.org/W2096696702","https://openalex.org/W2097854052","https://openalex.org/W2115669037","https://openalex.org/W2131940723","https://openalex.org/W2149268774","https://openalex.org/W2166944917","https://openalex.org/W2328111639","https://openalex.org/W2492708226","https://openalex.org/W2530707152","https://openalex.org/W2551879329","https://openalex.org/W2552366573","https://openalex.org/W2569091092","https://openalex.org/W2787248994","https://openalex.org/W2791953709","https://openalex.org/W2807841289","https://openalex.org/W2896880697","https://openalex.org/W2949220468","https://openalex.org/W2963134136","https://openalex.org/W2963389257","https://openalex.org/W2971073828","https://openalex.org/W2973816395","https://openalex.org/W2974112908","https://openalex.org/W2996880337","https://openalex.org/W3003196782","https://openalex.org/W3008527562","https://openalex.org/W3011123070","https://openalex.org/W3027822437","https://openalex.org/W3028378217","https://openalex.org/W3030671780","https://openalex.org/W3034485607","https://openalex.org/W3035624438","https://openalex.org/W3037514556","https://openalex.org/W3089631225","https://openalex.org/W3094719384","https://openalex.org/W3101432917","https://openalex.org/W3103787556","https://openalex.org/W3104981656","https://openalex.org/W3126216366","https://openalex.org/W3159649695","https://openalex.org/W3172015733","https://openalex.org/W3206919724","https://openalex.org/W3215133059","https://openalex.org/W3216378235","https://openalex.org/W4211192810","https://openalex.org/W4221147473","https://openalex.org/W4245577611","https://openalex.org/W4285526256","https://openalex.org/W4287067445","https://openalex.org/W4287113906","https://openalex.org/W4287671088","https://openalex.org/W4287811395","https://openalex.org/W4288412961","https://openalex.org/W4293580076","https://openalex.org/W4294993322","https://openalex.org/W4297729355","https://openalex.org/W4300905261","https://openalex.org/W4318718417","https://openalex.org/W4320086610","https://openalex.org/W6623482642","https://openalex.org/W6630462033","https://openalex.org/W6638829535","https://openalex.org/W6640210951","https://openalex.org/W6688325169","https://openalex.org/W6690827235","https://openalex.org/W6729450178","https://openalex.org/W6729788535","https://openalex.org/W6748535288","https://openalex.org/W6755368936","https://openalex.org/W6756497570","https://openalex.org/W6760835095","https://openalex.org/W6762602374","https://openalex.org/W6772214887","https://openalex.org/W6775939608","https://openalex.org/W6778954091","https://openalex.org/W6779380531","https://openalex.org/W6779912533","https://openalex.org/W6782217644","https://openalex.org/W6783157684","https://openalex.org/W6790812262","https://openalex.org/W6797797949","https://openalex.org/W6799045178","https://openalex.org/W6810245030","https://openalex.org/W6849673424","https://openalex.org/W6849807069"],"related_works":["https://openalex.org/W2952185452","https://openalex.org/W2230781071","https://openalex.org/W2292447985","https://openalex.org/W2035707149","https://openalex.org/W4300420636","https://openalex.org/W2104815277","https://openalex.org/W2952398272","https://openalex.org/W2076458153","https://openalex.org/W2963863608","https://openalex.org/W1865390738"],"abstract_inverted_index":{"We":[0,85],"present":[1],"a":[2,92],"unified":[3],"technique":[4],"for":[5,62],"sequential":[6,121],"estimation":[7],"of":[8,35,95,164],"convex":[9,45,83,156],"divergences":[10,46],"between":[11],"distributions,":[12],"including":[13],"integral":[14],"probability":[15],"metrics":[16],"like":[17,24,158],"the":[18,25,55,75,130,135,159],"kernel":[19],"maximum":[20],"mean":[21],"discrepancy,$\\varphi":[22],"$-divergences":[23],"Kullback-Leibler":[26],"divergence,":[27],"and":[28,71,82,167],"optimal":[29],"transport":[30],"costs,":[31],"such":[32,63],"as":[33],"powers":[34],"Wasserstein":[36],"distances.":[37],"This":[38],"is":[39],"achieved":[40],"by":[41],"observing":[42],"that":[43,90,104],"empirical":[44,165],"are":[47,150],"(partially":[48],"ordered)":[49],"reverse":[50],"submartingales":[51],"with":[52,59],"respect":[53],"to":[54,68,74,153],"exchangeable":[56],"filtration,":[57],"coupled":[58],"maximal":[60],"inequalities":[61,99],"processes.":[64],"These":[65,148],"techniques":[66],"appear":[67],"be":[69,106],"complementary":[70],"powerful":[72],"additions":[73],"existing":[76,96],"literature":[77],"on":[78,138],"both":[79],"confidence":[80,102,113],"sequences":[81,103],"divergences.":[84],"construct":[86],"an":[87,125],"offline-to-sequential":[88],"device":[89],"converts":[91],"wide":[93],"array":[94],"offline":[97],"concentration":[98],"into":[100],"time-uniform":[101],"can":[105],"continuously":[107],"monitored,":[108],"providing":[109],"valid":[110],"tests":[111],"or":[112,143],"intervals":[114],"at":[115],"arbitrary":[116],"stopping":[117],"times.":[118],"The":[119],"resulting":[120],"bounds":[122],"pay":[123],"only":[124],"iterated":[126],"logarithmic":[127],"price":[128],"over":[129],"corresponding":[131],"fixed-time":[132],"bounds,":[133],"retaining":[134],"same":[136],"dependence":[137],"problem":[139],"parameters":[140],"(like":[141],"dimension":[142],"alphabet":[144],"size":[145],"if":[146],"applicable).":[147],"results":[149],"also":[151],"applicable":[152],"more":[154],"general":[155],"functionals,":[157],"negative":[160],"differential":[161],"entropy,":[162],"suprema":[163],"processes,":[166],"V-Statistics.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":6}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}