{"id":"https://openalex.org/W3164467453","doi":"https://doi.org/10.1109/tpami.2021.3084598","title":"Shell Theory: A Statistical Model of Reality","display_name":"Shell Theory: A Statistical Model of Reality","publication_year":2021,"publication_date":"2021-05-28","ids":{"openalex":"https://openalex.org/W3164467453","doi":"https://doi.org/10.1109/tpami.2021.3084598","mag":"3164467453","pmid":"https://pubmed.ncbi.nlm.nih.gov/34048335"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2021.3084598","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3084598","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5068556469","display_name":"Wen-Yan Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I79891267","display_name":"Singapore Management University","ror":"https://ror.org/050qmg959","country_code":"SG","type":"education","lineage":["https://openalex.org/I79891267"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Wen-Yan Lin","raw_affiliation_strings":["Singapore Management University, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Singapore Management University, Singapore, Singapore","institution_ids":["https://openalex.org/I79891267"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100620147","display_name":"Siying Liu","orcid":"https://orcid.org/0000-0003-0104-2045"},"institutions":[{"id":"https://openalex.org/I3005327000","display_name":"Institute for Infocomm Research","ror":"https://ror.org/053rfa017","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3005327000","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Siying Liu","raw_affiliation_strings":["Institute for Infocomm Research (I2R), Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Institute for Infocomm Research (I2R), Singapore, Singapore","institution_ids":["https://openalex.org/I3005327000"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076359457","display_name":"Changhao Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I152815399","display_name":"Singapore University of Technology and Design","ror":"https://ror.org/05j6fvn87","country_code":"SG","type":"education","lineage":["https://openalex.org/I152815399"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Changhao Ren","raw_affiliation_strings":["Singapore University of Technology and Design, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Singapore University of Technology and Design, Singapore, Singapore","institution_ids":["https://openalex.org/I152815399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057453537","display_name":"Ngai\u2010Man Cheung","orcid":"https://orcid.org/0000-0003-0135-3791"},"institutions":[{"id":"https://openalex.org/I152815399","display_name":"Singapore University of Technology and Design","ror":"https://ror.org/05j6fvn87","country_code":"SG","type":"education","lineage":["https://openalex.org/I152815399"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Ngai-Man Cheung","raw_affiliation_strings":["Singapore University of Technology and Design, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Singapore University of Technology and Design, Singapore, Singapore","institution_ids":["https://openalex.org/I152815399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101819061","display_name":"Hongdong Li","orcid":"https://orcid.org/0000-0003-4125-1554"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Hongdong Li","raw_affiliation_strings":["Australian National University, Canberra, ACT, Australia"],"affiliations":[{"raw_affiliation_string":"Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033986386","display_name":"Yasuyuki Matsushita","orcid":"https://orcid.org/0000-0002-1935-4752"},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasuyuki Matsushita","raw_affiliation_strings":["Osaka University, Osaka, Japan"],"affiliations":[{"raw_affiliation_string":"Osaka University, Osaka, Japan","institution_ids":["https://openalex.org/I98285908"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5068556469"],"corresponding_institution_ids":["https://openalex.org/I79891267"],"apc_list":null,"apc_paid":null,"fwci":0.9797,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80364524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"44","issue":"10","first_page":"6438","last_page":"6453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9973999857902527,"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/T10320","display_name":"Neural Networks and Applications","score":0.9973999857902527,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9936000108718872,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9922000169754028,"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/computer-science","display_name":"Computer science","score":0.6830596923828125},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6803387403488159},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.637201189994812},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6227362751960754},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.5941109657287598},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.5834034085273743},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.5553193688392639},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5058912634849548},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.49511995911598206},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4745244085788727},{"id":"https://openalex.org/keywords/statistical-theory","display_name":"Statistical theory","score":0.44852134585380554},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.42864441871643066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21692267060279846}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6830596923828125},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6803387403488159},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.637201189994812},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6227362751960754},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.5941109657287598},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.5834034085273743},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.5553193688392639},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5058912634849548},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.49511995911598206},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4745244085788727},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.44852134585380554},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.42864441871643066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21692267060279846},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2021.3084598","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2021.3084598","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:34048335","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34048335","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":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:ink.library.smu.edu.sg:sis_research-7225","is_oa":false,"landing_page_url":"https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=7225&context=sis_research","pdf_url":null,"source":{"id":"https://openalex.org/S4377196871","display_name":"Institutional Knowledge (InK) - Institutional Knowledge at Singapore Management University (Singapore Management University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79891267","host_organization_name":"Singapore Management University","host_organization_lineage":["https://openalex.org/I79891267"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1109/TPAMI.2021.3084598","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W277886906","https://openalex.org/W1618905105","https://openalex.org/W1658960529","https://openalex.org/W1686810756","https://openalex.org/W1817561967","https://openalex.org/W1932198206","https://openalex.org/W1976394157","https://openalex.org/W1985690171","https://openalex.org/W2008056655","https://openalex.org/W2039507552","https://openalex.org/W2044554797","https://openalex.org/W2096733369","https://openalex.org/W2104052971","https://openalex.org/W2106044718","https://openalex.org/W2112301665","https://openalex.org/W2118585731","https://openalex.org/W2123256336","https://openalex.org/W2126487288","https://openalex.org/W2127017215","https://openalex.org/W2134665698","https://openalex.org/W2136745795","https://openalex.org/W2143159002","https://openalex.org/W2161336914","https://openalex.org/W2165533158","https://openalex.org/W2194775991","https://openalex.org/W2398119937","https://openalex.org/W2511261638","https://openalex.org/W2520832186","https://openalex.org/W2566079294","https://openalex.org/W2725606191","https://openalex.org/W2750384547","https://openalex.org/W2784010521","https://openalex.org/W2788388592","https://openalex.org/W2799796340","https://openalex.org/W2867167548","https://openalex.org/W2913429812","https://openalex.org/W2950928354","https://openalex.org/W2963330963","https://openalex.org/W2963775347","https://openalex.org/W2964218010","https://openalex.org/W3036644531","https://openalex.org/W3087124270","https://openalex.org/W3099661174","https://openalex.org/W3105432754","https://openalex.org/W3153872861","https://openalex.org/W3168316785","https://openalex.org/W4231510805","https://openalex.org/W4231610351","https://openalex.org/W4247388775","https://openalex.org/W4248681815","https://openalex.org/W4310348270","https://openalex.org/W4320013936","https://openalex.org/W6636501900","https://openalex.org/W6637373629","https://openalex.org/W6677656871","https://openalex.org/W6677919164","https://openalex.org/W6679792166","https://openalex.org/W6712574313","https://openalex.org/W6726866228","https://openalex.org/W6734641875","https://openalex.org/W6736583452","https://openalex.org/W6743688258","https://openalex.org/W6748102297","https://openalex.org/W6751866786","https://openalex.org/W6752760542","https://openalex.org/W7016021835"],"related_works":["https://openalex.org/W4365211920","https://openalex.org/W3014948380","https://openalex.org/W4380551139","https://openalex.org/W2280377497","https://openalex.org/W3174044702","https://openalex.org/W4238433571","https://openalex.org/W2967848559","https://openalex.org/W4283803360","https://openalex.org/W4317695495","https://openalex.org/W4387506531"],"abstract_inverted_index":{"The":[0,78,142],"foundational":[1],"assumption":[2],"of":[3,99,125],"machine":[4,73,149],"learning":[5,74,150],"is":[6,12,32,144],"that":[7,84,119,137],"the":[8,35,82,129,161],"data":[9],"under":[10],"consideration":[11],"separable":[13],"into":[14],"classes;":[15],"while":[16],"intuitively":[17],"reasonable,":[18],"separability":[19,154],"constraints":[20,155],"have":[21],"proven":[22],"remarkably":[23],"difficult":[24],"to":[25,55,94],"formulate":[26],"mathematically.":[27],"We":[28],"believe":[29],"this":[30,64,91,115],"problem":[31],"rooted":[33],"in":[34,75,114,120,128,152],"mismatch":[36],"between":[37],"existing":[38],"statistical":[39,52,70,110,148],"techniques":[40,53],"and":[41],"commonly":[42],"encountered":[43],"data;":[44],"object":[45,85],"representations":[46],"are":[47,131,157],"typically":[48],"high":[49,57,76,101],"dimensional":[50],"but":[51],"tend":[54],"treat":[56],"dimensions":[58],"a":[59,68,88,100,107,135,147],"degenerate":[60],"case.":[61],"To":[62],"address":[63],"problem,":[65],"we":[66,117],"develop":[67],"dedicated":[69],"framework":[71,79,151],"for":[72],"dimensions.":[77],"derives":[80],"from":[81,160],"observation":[83],"relations":[86],"form":[87],"natural":[89],"hierarchy;":[90],"leads":[92],"us":[93],"model":[95],"objects":[96],"as":[97],"instances":[98,124],"dimensional,":[102],"hierarchal":[103],"generative":[104,122,163],"processes.":[105],"Using":[106],"distance":[108],"based":[109],"technique,":[111],"also":[112],"developed":[113],"paper,":[116],"show":[118],"such":[121],"processes,":[123],"each":[126],"process":[127],"hierarchy,":[130],"almost-always":[132],"encapsulated":[133],"by":[134],"distinctive-shell":[136],"excludes":[138],"almost-all":[139],"other":[140],"instances.":[141],"result":[143],"shell":[145],"theory,":[146],"which":[153],"(distinctive-shells)":[156],"formally":[158],"derived":[159],"assumed":[162],"process.":[164]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}