{"id":"https://openalex.org/W1964482013","doi":"https://doi.org/10.1109/itw.2012.6404734","title":"Sequential normalized maximum likelihood in log-loss prediction","display_name":"Sequential normalized maximum likelihood in log-loss prediction","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W1964482013","doi":"https://doi.org/10.1109/itw.2012.6404734","mag":"1964482013"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2012.6404734","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2012.6404734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Information Theory Workshop","raw_type":"proceedings-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/A5001603308","display_name":"Wojciech Kot\u0142owski","orcid":"https://orcid.org/0000-0002-5905-8069"},"institutions":[{"id":"https://openalex.org/I46597724","display_name":"Pozna\u0144 University of Technology","ror":"https://ror.org/00p7p3302","country_code":"PL","type":"education","lineage":["https://openalex.org/I46597724"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Wojciech Kotlowski","raw_affiliation_strings":["Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965, Poland#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Computing Science, Poznan University of Technology, Piotrowo 2, 60-965, Poland#TAB#","institution_ids":["https://openalex.org/I46597724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079050279","display_name":"Peter Gr\u00fcnwald","orcid":"https://orcid.org/0000-0001-9832-9936"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Peter Grunwald","raw_affiliation_strings":["Centrum Wiskunde & Informatica, Amsterdam, Netherlands","Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, Netherlands"],"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde & Informatica, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I1341640284"]},{"raw_affiliation_string":"Centrum Wiskunde & Informatica, Science Park 123, 1098 XG Amsterdam, Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001603308"],"corresponding_institution_ids":["https://openalex.org/I46597724"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.11012174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":null,"first_page":"547","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9983000159263611,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regret","display_name":"Regret","score":0.7656203508377075},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.7196775078773499},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.6792992353439331},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.634262204170227},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6153095364570618},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5879708528518677},{"id":"https://openalex.org/keywords/maximum-likelihood-sequence-estimation","display_name":"Maximum likelihood sequence estimation","score":0.5616299510002136},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5107100009918213},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5010392665863037},{"id":"https://openalex.org/keywords/bayes-theorem","display_name":"Bayes' theorem","score":0.4673232138156891},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4285636246204376},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42746487259864807},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4095459282398224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3733903765678406},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.32025861740112305},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.2884410619735718}],"concepts":[{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.7656203508377075},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7196775078773499},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.6792992353439331},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.634262204170227},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6153095364570618},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5879708528518677},{"id":"https://openalex.org/C191462741","wikidata":"https://www.wikidata.org/wiki/Q6795902","display_name":"Maximum likelihood sequence estimation","level":3,"score":0.5616299510002136},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5107100009918213},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5010392665863037},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.4673232138156891},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4285636246204376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42746487259864807},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4095459282398224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3733903765678406},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32025861740112305},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.2884410619735718},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw.2012.6404734","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2012.6404734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Information Theory Workshop","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1491039392","https://openalex.org/W1506313179","https://openalex.org/W1518095400","https://openalex.org/W1570963478","https://openalex.org/W1819033929","https://openalex.org/W2015540623","https://openalex.org/W2062900220","https://openalex.org/W2068782468","https://openalex.org/W2099111195","https://openalex.org/W2102098892","https://openalex.org/W2290825520","https://openalex.org/W2394555834","https://openalex.org/W2395176238","https://openalex.org/W2404984384","https://openalex.org/W3015736691","https://openalex.org/W3123545922","https://openalex.org/W6696468186","https://openalex.org/W6712313866"],"related_works":["https://openalex.org/W1499442185","https://openalex.org/W2366184732","https://openalex.org/W2379466508","https://openalex.org/W1985311370","https://openalex.org/W1573889165","https://openalex.org/W1516206434","https://openalex.org/W2392411825","https://openalex.org/W2375134271","https://openalex.org/W1559074081","https://openalex.org/W3023909498"],"abstract_inverted_index":{"The":[0,69],"paper":[1],"considers":[2],"sequential":[3,82],"prediction":[4],"of":[5,15,36,59,66],"individual":[6],"sequences":[7],"with":[8,144],"log":[9],"loss":[10],"using":[11],"an":[12,31,112],"exponential":[13,93],"family":[14],"distributions.":[16],"We":[17,40,88,109,135],"first":[18],"show":[19,42,89],"that":[20,43,90,123],"the":[21,37,52,57,60,67,78,81,95,100,128,138,141],"commonly":[22],"used":[23],"maximum":[24,61,84,117],"likelihood":[25,85],"strategy":[26,70,143],"is":[27,75,97],"suboptimal":[28],"and":[29,103],"requires":[30],"additional":[32,133],"assumption":[33],"about":[34],"boundedness":[35],"data":[38],"sequence.":[39],"then":[41],"both":[44],"problems":[45],"can":[46],"be":[47,48],"addressed":[49],"by":[50,64,99],"adding":[51],"currently":[53],"predicted":[54],"outcome":[55],"to":[56,107,114,121,140],"calculation":[58],"likelihood,":[62,118],"followed":[63],"normalization":[65],"distribution.":[68],"obtained":[71],"in":[72,77],"this":[73],"way":[74],"known":[76],"literature":[79],"as":[80],"normalized":[83],"(SNML)":[86],"strategy.":[87],"for":[91],"general":[92],"families,":[94],"regret":[96,130],"bounded":[98],"familiar":[101],"(k/2)logn":[102],"thus":[104],"optimal":[105,129],"up":[106],"O(1).":[108],"also":[110],"introduce":[111],"approximation":[113],"SNML,":[115],"flattened":[116],"much":[119],"easier":[120],"compute":[122],"SNML":[124],"itself,":[125],"while":[126],"retaining":[127],"under":[131],"some":[132],"assumptions.":[134],"finally":[136],"discuss":[137],"relationship":[139],"Bayes":[142],"Jeffreys'":[145],"prior.":[146]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
