{"id":"https://openalex.org/W4225149062","doi":"https://doi.org/10.48550/arxiv.2204.13290","title":"On the Normalizing Constant of the Continuous Categorical Distribution","display_name":"On the Normalizing Constant of the Continuous Categorical Distribution","publication_year":2022,"publication_date":"2022-04-28","ids":{"openalex":"https://openalex.org/W4225149062","doi":"https://doi.org/10.48550/arxiv.2204.13290"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2204.13290","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.13290","pdf_url":"https://arxiv.org/pdf/2204.13290","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2204.13290","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065923620","display_name":"Elliott Gordon-Rodr\u00edguez","orcid":"https://orcid.org/0000-0002-2720-1756"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gordon-Rodriguez, Elliott","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020477291","display_name":"Gabriel Loaiza-Ganem","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Loaiza-Ganem, Gabriel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018500293","display_name":"Andres Potapczynski","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Potapczynski, Andres","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030697996","display_name":"John P. Cunningham","orcid":"https://orcid.org/0000-0001-9125-3027"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cunningham, John P.","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065923620"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9846000075340271,"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"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9846000075340271,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9599000215530396,"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":0.95660001039505,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.8680726289749146},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.7631131410598755},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7189300060272217},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.6774654388427734},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.6433511972427368},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5266002416610718},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5255005359649658},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4998798370361328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43920889496803284},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.4321005940437317},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4246438145637512},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36870378255844116},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24799740314483643},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1747913956642151},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14027318358421326},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11531758308410645},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06320768594741821}],"concepts":[{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.8680726289749146},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.7631131410598755},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7189300060272217},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.6774654388427734},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.6433511972427368},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5266002416610718},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5255005359649658},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4998798370361328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43920889496803284},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.4321005940437317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4246438145637512},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36870378255844116},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24799740314483643},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1747913956642151},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14027318358421326},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11531758308410645},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06320768594741821},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2204.13290","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.13290","pdf_url":"https://arxiv.org/pdf/2204.13290","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2204.13290","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2204.13290","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2204.13290","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.13290","pdf_url":"https://arxiv.org/pdf/2204.13290","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2368019753","https://openalex.org/W2333930193","https://openalex.org/W2737356002","https://openalex.org/W2246241526","https://openalex.org/W4301122218","https://openalex.org/W2374150061","https://openalex.org/W2081340182","https://openalex.org/W2369703001","https://openalex.org/W2372323577","https://openalex.org/W3166198130"],"abstract_inverted_index":{"Probability":[0],"distributions":[1,23],"supported":[2],"on":[3],"the":[4,27,42,70,82,86,106],"simplex":[5],"enjoy":[6],"a":[7,18,47],"wide":[8],"range":[9],"of":[10,21,41,63,69,85,105],"applications":[11,104],"across":[12],"statistics":[13],"and":[14,89,93],"machine":[15],"learning.":[16],"Recently,":[17],"novel":[19],"family":[20,31],"such":[22],"has":[24],"been":[25],"discovered:":[26],"continuous":[28,107],"categorical.":[29],"This":[30],"enjoys":[32],"remarkable":[33],"mathematical":[34,65],"simplicity;":[35],"its":[36],"density":[37],"function":[38],"resembles":[39],"that":[40,50,96],"Dirichlet":[43],"distribution,":[44],"but":[45],"with":[46],"normalizing":[48,71,87],"constant":[49,72,88],"can":[51],"be":[52],"written":[53],"in":[54,98],"closed":[55],"form":[56],"using":[57],"elementary":[58],"functions":[59],"only.":[60],"In":[61,77],"spite":[62],"this":[64,78],"simplicity,":[66],"our":[67],"understanding":[68],"remains":[73],"far":[74],"from":[75],"complete.":[76],"work,":[79],"we":[80,90],"characterize":[81],"numerical":[83],"behavior":[84],"present":[91],"theoretical":[92],"methodological":[94],"advances":[95],"can,":[97],"turn,":[99],"help":[100],"to":[101],"enable":[102],"broader":[103],"categorical":[108],"distribution.":[109],"Our":[110],"code":[111],"is":[112],"available":[113],"at":[114],"https://github.com/cunningham-lab/cb_and_cc/.":[115]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
