{"id":"https://openalex.org/W3203433447","doi":"https://doi.org/10.3390/e24030328","title":"Probability Distribution on Full Rooted Trees","display_name":"Probability Distribution on Full Rooted Trees","publication_year":2022,"publication_date":"2022-02-24","ids":{"openalex":"https://openalex.org/W3203433447","doi":"https://doi.org/10.3390/e24030328","mag":"3203433447","pmid":"https://pubmed.ncbi.nlm.nih.gov/35327839"},"language":"en","primary_location":{"id":"doi:10.3390/e24030328","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030328","pdf_url":"https://www.mdpi.com/1099-4300/24/3/328/pdf?version=1648104580","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/3/328/pdf?version=1648104580","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082105955","display_name":"Yuta Nakahara","orcid":"https://orcid.org/0000-0002-0553-7910"},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuta Nakahara","raw_affiliation_strings":["Center for Data Science, Waseda University, Shinjuku-ku 169-8050, Tokyo, Japan","Waseda University"],"raw_orcid":"https://orcid.org/0000-0002-0553-7910","affiliations":[{"raw_affiliation_string":"Center for Data Science, Waseda University, Shinjuku-ku 169-8050, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Waseda University","institution_ids":["https://openalex.org/I150744194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032142245","display_name":"Shota Saito","orcid":"https://orcid.org/0000-0003-2256-4598"},"institutions":[{"id":"https://openalex.org/I165735259","display_name":"Gunma University","ror":"https://ror.org/046fm7598","country_code":"JP","type":"education","lineage":["https://openalex.org/I165735259"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shota Saito","raw_affiliation_strings":["Faculty of Informatics, Gunma University, Maebashi-shi 371-8510, Gunma, Japan","Gunma univ"],"raw_orcid":"https://orcid.org/0000-0003-2256-4598","affiliations":[{"raw_affiliation_string":"Faculty of Informatics, Gunma University, Maebashi-shi 371-8510, Gunma, Japan","institution_ids":["https://openalex.org/I165735259"]},{"raw_affiliation_string":"Gunma univ","institution_ids":["https://openalex.org/I165735259"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001719328","display_name":"Akira Kamatsuka","orcid":"https://orcid.org/0000-0001-5129-2638"},"institutions":[{"id":"https://openalex.org/I197425175","display_name":"Shonan Institute of Technology","ror":"https://ror.org/01bawqf59","country_code":"JP","type":"education","lineage":["https://openalex.org/I197425175"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akira Kamatsuka","raw_affiliation_strings":["Department of Information Science, Shonan Institute of Technology, Fujisawa-shi 251-8511, Kanagawa, Japan","Shonan Institute Of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Science, Shonan Institute of Technology, Fujisawa-shi 251-8511, Kanagawa, Japan","institution_ids":["https://openalex.org/I197425175"]},{"raw_affiliation_string":"Shonan Institute Of Technology","institution_ids":["https://openalex.org/I197425175"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110471799","display_name":"Toshiyasu Matsushima","orcid":null},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Toshiyasu Matsushima","raw_affiliation_strings":["Department of Applied Mathematics, Waseda University, Shinjuku-ku 169-8555, Tokyo, Japan","Waseda University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Waseda University, Shinjuku-ku 169-8555, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Waseda University","institution_ids":["https://openalex.org/I150744194"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00555675,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"3","first_page":"328","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9937999844551086,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9937999844551086,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9922999739646912,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9919999837875366,"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/overfitting","display_name":"Overfitting","score":0.8896082639694214},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.568943977355957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4974386990070343},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4894334375858307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4712638854980469},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.47095757722854614},{"id":"https://openalex.org/keywords/conjugate-prior","display_name":"Conjugate prior","score":0.4362521171569824},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.43362146615982056},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43050503730773926},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41737261414527893},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3968312442302704},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3349301218986511},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.3311140537261963},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17593470215797424},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.13185861706733704}],"concepts":[{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.8896082639694214},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.568943977355957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4974386990070343},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4894334375858307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4712638854980469},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.47095757722854614},{"id":"https://openalex.org/C26004113","wikidata":"https://www.wikidata.org/wiki/Q3711784","display_name":"Conjugate prior","level":4,"score":0.4362521171569824},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.43362146615982056},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43050503730773926},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41737261414527893},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3968312442302704},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3349301218986511},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3311140537261963},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17593470215797424},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.13185861706733704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e24030328","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030328","pdf_url":"https://www.mdpi.com/1099-4300/24/3/328/pdf?version=1648104580","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:35327839","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35327839","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:arXiv.org:2109.12825","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.12825","pdf_url":"https://arxiv.org/pdf/2109.12825","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:3203433447","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2109.12825v1","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":"pmh:oai:doaj.org/article:b5630a423ef24a38ad92da0c18b3ba64","is_oa":true,"landing_page_url":"https://doaj.org/article/b5630a423ef24a38ad92da0c18b3ba64","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 3, p 328 (2022)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:8947532","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8947532","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"doi:10.48550/arxiv.2109.12825","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2109.12825","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":"article-journal"}],"best_oa_location":{"id":"doi:10.3390/e24030328","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030328","pdf_url":"https://www.mdpi.com/1099-4300/24/3/328/pdf?version=1648104580","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4099999964237213}],"awards":[{"id":"https://openalex.org/G159413792","display_name":null,"funder_award_id":"JP17K06446, JP19K04914, and JP19K14989","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G2763343738","display_name":"Fundamental research on finite length analysis in information theory and optimization theory for practical, reliable, and highly efficient communications","funder_award_id":"17K06446","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6478739734","display_name":"A Study on Fundamental Limits of Lossy Compression Based on Distortion Ball Aiming for Practical Code Construction","funder_award_id":"19K14989","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6679162988","display_name":"Research on Data Analysis Platform for Business Value Creation and Time-Varying Collaborative Filtering","funder_award_id":"19K04914","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3203433447.pdf","grobid_xml":"https://content.openalex.org/works/W3203433447.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1558603822","https://openalex.org/W1663973292","https://openalex.org/W1988520084","https://openalex.org/W2146395539","https://openalex.org/W2156060128","https://openalex.org/W2163294786","https://openalex.org/W2165843147","https://openalex.org/W2295598076","https://openalex.org/W2478708596","https://openalex.org/W2911964244","https://openalex.org/W3045608583","https://openalex.org/W3102476541","https://openalex.org/W3168449777","https://openalex.org/W3175260198","https://openalex.org/W3193232953","https://openalex.org/W3197818463","https://openalex.org/W6633367976"],"related_works":["https://openalex.org/W3098934517","https://openalex.org/W2804961760","https://openalex.org/W2951091761","https://openalex.org/W2952528962","https://openalex.org/W2952720174","https://openalex.org/W2741898531","https://openalex.org/W338678865","https://openalex.org/W2949350662","https://openalex.org/W133532789","https://openalex.org/W1541126854","https://openalex.org/W1717259479","https://openalex.org/W3189168106","https://openalex.org/W2472863411","https://openalex.org/W2950558250","https://openalex.org/W11327913","https://openalex.org/W2065131135","https://openalex.org/W2563938752","https://openalex.org/W1572688531","https://openalex.org/W2972938171","https://openalex.org/W2520551056"],"abstract_inverted_index":{"The":[0],"recursive":[1,140],"and":[2,23,147,173],"hierarchical":[3],"structure":[4],"of":[5,28,97,123,136],"full":[6,32,63,124],"rooted":[7,33,64,125],"trees":[8],"is":[9,35,47,55,130],"applicable":[10,162],"to":[11,44,51,56,85,163,178],"statistical":[12],"models":[13,107],"in":[14,156],"various":[15],"fields,":[16],"such":[17,142,151],"as":[18,40,143],"data":[19],"compression,":[20],"image":[21],"processing,":[22],"machine":[24],"learning.":[25],"In":[26,112],"most":[27],"these":[29],"cases,":[30],"the":[31,62,68,89,95,98,106,134,144,180],"tree":[34],"not":[36],"a":[37,58,81,86,91,117,121],"random":[38],"variable;":[39],"such,":[41],"model":[42,70],"selection":[43,71,96],"avoid":[45],"overfitting":[46],"problematic.":[48],"One":[49],"method":[50],"solve":[52],"this":[53,113],"problem":[54],"assume":[57],"prior":[59,83],"distribution":[60,119,138],"on":[61,73,120],"trees.":[65,126],"This":[66],"enables":[67],"optimal":[69],"based":[72],"Bayes":[74],"decision":[75],"theory.":[76],"For":[77],"example,":[78],"by":[79,109],"assigning":[80],"low":[82],"probability":[84,118],"complex":[87,99],"model,":[88],"maximum":[90],"posteriori":[92],"estimator":[93],"prevents":[94],"one.":[100],"Furthermore,":[101],"we":[102,115,167],"can":[103],"average":[104],"all":[105],"weighted":[108],"their":[110,169],"posteriors.":[111],"paper,":[114],"propose":[116],"set":[122],"Its":[127],"parametric":[128],"representation":[129],"suitable":[131],"for":[132],"calculating":[133],"properties":[135],"our":[137],"using":[139],"functions,":[141],"mode,":[145],"expectation,":[146,181],"posterior":[148,182],"distribution.":[149],"Although":[150],"distributions":[152],"have":[153],"been":[154],"proposed":[155],"previous":[157],"studies,":[158],"they":[159],"are":[160],"only":[161],"specific":[164],"applications.":[165],"Therefore,":[166],"extract":[168],"mathematically":[170],"essential":[171],"components":[172],"derive":[174],"new":[175],"generalized":[176],"methods":[177],"calculate":[179],"distribution,":[183],"etc.":[184]},"counts_by_year":[],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}