{"id":"https://openalex.org/W2963536736","doi":"https://doi.org/10.1609/aaai.v33i01.33014488","title":"Bias-Variance Trade-Off in Hierarchical Probabilistic Models Using Higher-Order Feature Interactions","display_name":"Bias-Variance Trade-Off in Hierarchical Probabilistic Models Using Higher-Order Feature Interactions","publication_year":2019,"publication_date":"2019-07-17","ids":{"openalex":"https://openalex.org/W2963536736","doi":"https://doi.org/10.1609/aaai.v33i01.33014488","mag":"2963536736"},"language":"en","primary_location":{"id":"doi:10.1609/aaai.v33i01.33014488","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v33i01.33014488","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4362/4240","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4362/4240","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032717607","display_name":"Simon Luo","orcid":"https://orcid.org/0000-0002-7660-2230"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Simon Luo","raw_affiliation_strings":["The University of Sydney"],"affiliations":[{"raw_affiliation_string":"The University of Sydney","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066053285","display_name":"Mahito Sugiyama","orcid":"https://orcid.org/0000-0001-5907-9831"},"institutions":[{"id":"https://openalex.org/I184597095","display_name":"National Institute of Informatics","ror":"https://ror.org/04ksd4g47","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I184597095","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mahito Sugiyama","raw_affiliation_strings":["National Institute of Informatics"],"affiliations":[{"raw_affiliation_string":"National Institute of Informatics","institution_ids":["https://openalex.org/I184597095"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032717607"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":null,"apc_paid":null,"fwci":1.6287,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8241206,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"33","issue":"01","first_page":"4488","last_page":"4495"},"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":0.993399977684021,"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":0.993399977684021,"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":0.9908999800682068,"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":0.9886999726295471,"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/variance","display_name":"Variance (accounting)","score":0.6978275179862976},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5777324438095093},{"id":"https://openalex.org/keywords/variance-based-sensitivity-analysis","display_name":"Variance-based sensitivity analysis","score":0.5613695383071899},{"id":"https://openalex.org/keywords/gibbs-sampling","display_name":"Gibbs sampling","score":0.5115805268287659},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5114959478378296},{"id":"https://openalex.org/keywords/variance-decomposition-of-forecast-errors","display_name":"Variance decomposition of forecast errors","score":0.508155345916748},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4919271469116211},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48218265175819397},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.45344218611717224},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.4391363263130188},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3832298517227173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35849058628082275},{"id":"https://openalex.org/keywords/one-way-analysis-of-variance","display_name":"One-way analysis of variance","score":0.3555963635444641},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.32228201627731323},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2902827262878418},{"id":"https://openalex.org/keywords/analysis-of-variance","display_name":"Analysis of variance","score":0.2299502193927765},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.21384850144386292}],"concepts":[{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.6978275179862976},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5777324438095093},{"id":"https://openalex.org/C108311543","wikidata":"https://www.wikidata.org/wiki/Q7915756","display_name":"Variance-based sensitivity analysis","level":4,"score":0.5613695383071899},{"id":"https://openalex.org/C158424031","wikidata":"https://www.wikidata.org/wiki/Q1191905","display_name":"Gibbs sampling","level":3,"score":0.5115805268287659},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5114959478378296},{"id":"https://openalex.org/C89715816","wikidata":"https://www.wikidata.org/wiki/Q7915763","display_name":"Variance decomposition of forecast errors","level":2,"score":0.508155345916748},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4919271469116211},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48218265175819397},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.45344218611717224},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4391363263130188},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3832298517227173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35849058628082275},{"id":"https://openalex.org/C152587130","wikidata":"https://www.wikidata.org/wiki/Q7092351","display_name":"One-way analysis of variance","level":3,"score":0.3555963635444641},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32228201627731323},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2902827262878418},{"id":"https://openalex.org/C99476002","wikidata":"https://www.wikidata.org/wiki/Q42297","display_name":"Analysis of variance","level":2,"score":0.2299502193927765},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.21384850144386292},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1609/aaai.v33i01.33014488","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v33i01.33014488","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4362/4240","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1609/aaai.v33i01.33014488","is_oa":true,"landing_page_url":"https://doi.org/10.1609/aaai.v33i01.33014488","pdf_url":"https://ojs.aaai.org/index.php/AAAI/article/download/4362/4240","source":{"id":"https://openalex.org/S4210191458","display_name":"Proceedings of the AAAI Conference on Artificial Intelligence","issn_l":"2159-5399","issn":["2159-5399","2374-3468"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320058","host_organization_name":"Association for the Advancement of Artificial Intelligence","host_organization_lineage":["https://openalex.org/P4310320058"],"host_organization_lineage_names":["Association for the Advancement of Artificial Intelligence"],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the AAAI Conference on Artificial Intelligence","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963536736.pdf","grobid_xml":"https://content.openalex.org/works/W2963536736.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W44815768","https://openalex.org/W189596042","https://openalex.org/W1480376833","https://openalex.org/W1512984504","https://openalex.org/W1641020902","https://openalex.org/W1997063559","https://openalex.org/W2020999234","https://openalex.org/W2064630666","https://openalex.org/W2071709160","https://openalex.org/W2093397547","https://openalex.org/W2097230740","https://openalex.org/W2116064496","https://openalex.org/W2116825644","https://openalex.org/W2120503473","https://openalex.org/W2122565151","https://openalex.org/W2131939418","https://openalex.org/W2168919237","https://openalex.org/W2294861638","https://openalex.org/W2950181613","https://openalex.org/W3098805594","https://openalex.org/W4247612853","https://openalex.org/W4255825300","https://openalex.org/W6607775107","https://openalex.org/W6636779153","https://openalex.org/W6660690085","https://openalex.org/W6673656472","https://openalex.org/W6684951692","https://openalex.org/W6697285969","https://openalex.org/W6734288423","https://openalex.org/W6785554505"],"related_works":["https://openalex.org/W2560234381","https://openalex.org/W3004061946","https://openalex.org/W3083098637","https://openalex.org/W203276098","https://openalex.org/W2606174408","https://openalex.org/W2380339771","https://openalex.org/W1580490668","https://openalex.org/W2898283737","https://openalex.org/W2081927997","https://openalex.org/W2586412761"],"abstract_inverted_index":{"Hierarchical":[0],"probabilistic":[1],"models":[2],"are":[3],"able":[4],"to":[5,12,41,98],"use":[6],"a":[7,14,17,42,48,83,95,120,124],"large":[8],"number":[9,29],"of":[10,30,36,77,85,127],"parameters":[11,31],"create":[13],"model":[15,38],"with":[16,123],"high":[18],"representation":[19],"power.":[20],"However,":[21],"it":[22,46],"is":[23,47],"well":[24,62],"known":[25],"that":[26,112],"increasing":[27],"the":[28,34,37,51,74,78,100],"also":[32],"increases":[33],"complexity":[35],"which":[39],"leads":[40],"bias-variance":[43,52,96],"trade-off.":[44],"Although":[45],"classical":[49],"problem,":[50],"trade-off":[53],"between":[54],"hiddenlayers":[55],"and":[56,88,105,116,129],"higher-order":[57,79,106,117],"interactions":[58,118,132],"have":[59,110,119],"not":[60],"been":[61],"studied.":[63],"In":[64],"our":[65],"study,":[66],"we":[67],"propose":[68],"an":[69],"efficient":[70],"inference":[71],"algorithm":[72],"for":[73,136],"log-linear":[75],"formulation":[76],"Boltzmann":[80],"machine":[81],"using":[82,113,130],"combination":[84],"Gibbs":[86],"sampling":[87],"annealed":[89],"importance":[90],"sampling.":[91],"We":[92],"then":[93],"perform":[94],"decomposition":[97],"study":[99],"differences":[101],"in":[102],"hidden":[103,114],"layers":[104,115],"interactions.":[107],"Our":[108],"results":[109],"shown":[111],"comparable":[121],"error":[122],"similar":[125],"order":[126],"magnitude":[128],"higherorder":[131],"produce":[133],"less":[134],"variance":[135],"smaller":[137],"sample":[138],"size.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}