{"id":"https://openalex.org/W4416009033","doi":"https://doi.org/10.1007/s10994-025-06915-w","title":"Efficient quantification on large-scale networks","display_name":"Efficient quantification on large-scale networks","publication_year":2025,"publication_date":"2025-11-07","ids":{"openalex":"https://openalex.org/W4416009033","doi":"https://doi.org/10.1007/s10994-025-06915-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-025-06915-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-025-06915-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06915-w.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06915-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010923663","display_name":"Alessio Micheli","orcid":"https://orcid.org/0000-0001-5764-5238"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessio Micheli","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086354805","display_name":"Alejandro Moreo","orcid":"https://orcid.org/0000-0002-0377-1025"},"institutions":[{"id":"https://openalex.org/I122991210","display_name":"Istituto di Scienza e Tecnologie dell'Informazione \"Alessandro Faedo\"","ror":"https://ror.org/05kacka20","country_code":"IT","type":"facility","lineage":["https://openalex.org/I122991210","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alejandro Moreo","raw_affiliation_strings":["Istituto di Scienza e Tecnologie dell\u2019Informazione, Consiglio Nazionale delle Ricerche, Via Giuseppe Moruzzi 1, 56124, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto di Scienza e Tecnologie dell\u2019Informazione, Consiglio Nazionale delle Ricerche, Via Giuseppe Moruzzi 1, 56124, Pisa, Italy","institution_ids":["https://openalex.org/I122991210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027095496","display_name":"Marco Podda","orcid":"https://orcid.org/0000-0003-1497-9515"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Marco Podda","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063975186","display_name":"Fabrizio Sebastiani","orcid":"https://orcid.org/0000-0003-4221-6427"},"institutions":[{"id":"https://openalex.org/I122991210","display_name":"Istituto di Scienza e Tecnologie dell'Informazione \"Alessandro Faedo\"","ror":"https://ror.org/05kacka20","country_code":"IT","type":"facility","lineage":["https://openalex.org/I122991210","https://openalex.org/I4210155236"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabrizio Sebastiani","raw_affiliation_strings":["Istituto di Scienza e Tecnologie dell\u2019Informazione, Consiglio Nazionale delle Ricerche, Via Giuseppe Moruzzi 1, 56124, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Istituto di Scienza e Tecnologie dell\u2019Informazione, Consiglio Nazionale delle Ricerche, Via Giuseppe Moruzzi 1, 56124, Pisa, Italy","institution_ids":["https://openalex.org/I122991210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5119880419","display_name":"William Simoni","orcid":null},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"William Simoni","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068896301","display_name":"Domenico Tortorella","orcid":"https://orcid.org/0000-0003-3910-7713"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Domenico Tortorella","raw_affiliation_strings":["Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica, Universit\u00e0 di Pisa, Largo Bruno Pontecorvo, 3, 56127, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5010923663"],"corresponding_institution_ids":["https://openalex.org/I108290504"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.3431,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.91664699,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"114","issue":"12","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9750000238418579,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9750000238418579,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0024999999441206455,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.002099999925121665,"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/scalability","display_name":"Scalability","score":0.7019000053405762},{"id":"https://openalex.org/keywords/flexibility","display_name":"Flexibility (engineering)","score":0.6259999871253967},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5867999792098999},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4893999993801117},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4571000039577484},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.3898000121116638},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.34290000796318054}],"concepts":[{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.7019000053405762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6682000160217285},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.6259999871253967},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5867999792098999},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4893999993801117},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4571000039577484},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4494999945163727},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.40869998931884766},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3898000121116638},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.382099986076355},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3310999870300293},{"id":"https://openalex.org/C2779585090","wikidata":"https://www.wikidata.org/wiki/Q3457762","display_name":"Resilience (materials science)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2883000075817108},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.274399995803833},{"id":"https://openalex.org/C106937863","wikidata":"https://www.wikidata.org/wiki/Q7236518","display_name":"Power graph analysis","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C175154964","wikidata":"https://www.wikidata.org/wiki/Q380077","display_name":"Task analysis","level":3,"score":0.2655999958515167},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.26440000534057617},{"id":"https://openalex.org/C16311509","wikidata":"https://www.wikidata.org/wiki/Q4148050","display_name":"Dependency graph","level":3,"score":0.259799987077713}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10994-025-06915-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-025-06915-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06915-w.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1333401","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s10994-025-06915-w","pdf_url":null,"source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:dnet:iris________::96583122ae7c705996ea2bcc69702c35","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407055261","display_name":"ISTI Open Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MACHINE LEARNING, vol. 114 (issue 12)","raw_type":"Journal article"}],"best_oa_location":{"id":"doi:10.1007/s10994-025-06915-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-025-06915-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-025-06915-w.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G100767060","display_name":null,"funder_award_id":"T4-AN-07","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G1145458839","display_name":null,"funder_award_id":"PRIN 2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2922057910","display_name":null,"funder_award_id":"000001","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G4508289328","display_name":null,"funder_award_id":"PE00000013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5557213161","display_name":null,"funder_award_id":"00000","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G6788846316","display_name":null,"funder_award_id":"I53C22001300001","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G6870533126","display_name":null,"funder_award_id":"2014-2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7022670847","display_name":null,"funder_award_id":"POS 2014-2020","funder_id":"https://openalex.org/F4320321781","funder_display_name":"Ministero della Salute"},{"id":"https://openalex.org/G7670308920","display_name":"GENETIC AND GENOMIC STUDY OF CELL COMPETITION IN DROSOPHILA","funder_award_id":"200130","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8409961469","display_name":null,"funder_award_id":"Spoke 1","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8893660128","display_name":null,"funder_award_id":"PE0000001","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321781","display_name":"Ministero della Salute","ror":"https://ror.org/00789fa95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416009033.pdf","grobid_xml":"https://content.openalex.org/works/W4416009033.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1497163089","https://openalex.org/W1967622058","https://openalex.org/W1972047492","https://openalex.org/W2041345655","https://openalex.org/W2084933300","https://openalex.org/W2116341502","https://openalex.org/W2125204570","https://openalex.org/W2139906443","https://openalex.org/W2141253686","https://openalex.org/W2153513200","https://openalex.org/W2158243283","https://openalex.org/W2162630660","https://openalex.org/W2171865010","https://openalex.org/W2182824870","https://openalex.org/W2232384272","https://openalex.org/W2548695521","https://openalex.org/W2757560572","https://openalex.org/W2789973986","https://openalex.org/W2907492528","https://openalex.org/W2966214395","https://openalex.org/W2974133468","https://openalex.org/W2997785591","https://openalex.org/W2997992893","https://openalex.org/W2998496395","https://openalex.org/W3133423348","https://openalex.org/W3160872503","https://openalex.org/W3213800059","https://openalex.org/W3214007446","https://openalex.org/W4211120392","https://openalex.org/W4292938137","https://openalex.org/W4312410287","https://openalex.org/W4320060387","https://openalex.org/W4360998196","https://openalex.org/W4366778531","https://openalex.org/W4382405183","https://openalex.org/W4392925809","https://openalex.org/W4393618259","https://openalex.org/W4400147561","https://openalex.org/W4406844427","https://openalex.org/W4410132809"],"related_works":[],"abstract_inverted_index":{"Network":[0],"quantification":[1,156],"(NQ)":[2],"is":[3,26],"the":[4,8,38,43,67,91,96,118,135,153,162,166],"problem":[5],"of":[6,10,18,62,69,95,121,165,178],"estimating":[7],"proportions":[9],"nodes":[11,39],"belonging":[12],"to":[13,57,66,73,78,117,158,180],"each":[14],"class":[15,44],"in":[16,55,130],"subsets":[17],"unlabelled":[19],"graph":[20,187],"nodes.":[21],"When":[22],"prior":[23],"probability":[24],"shift":[25],"at":[27],"play,":[28],"this":[29,169],"task":[30],"cannot":[31],"be":[32],"effectively":[33],"addressed":[34],"by":[35,101],"first":[36],"classifying":[37],"and":[40,71,93,149],"then":[41],"counting":[42],"predictions.":[45],"In":[46,76,126],"addition,":[47],"unlike":[48],"non-relational":[49],"quantification,":[50],"NQ":[51],"demands":[52],"enhanced":[53],"flexibility":[54,92],"order":[56,77],"capture":[58],"a":[59,86,113,122,175],"broad":[60],"range":[61],"connectivity":[63],"patterns,":[64],"resilience":[65],"challenge":[68],"heterophily,":[70],"scalability":[72],"large":[74],"networks.":[75],"meet":[79],"these":[80],"stringent":[81],"requirements,":[82],"we":[83,132,144],"introduce":[84],"XNQ,":[85],"novel":[87],"method":[88],"that":[89,111,146],"synergizes":[90],"efficiency":[94],"unsupervised":[97],"node":[98,124],"embeddings":[99],"computed":[100],"randomized":[102],"recursive":[103],"Graph":[104],"Neural":[105],"Networks,":[106],"with":[107],"an":[108,127],"Expectation-Maximization":[109],"algorithm":[110],"provides":[112,174],"robust":[114],"quantification-aware":[115],"adjustment":[116],"output":[119],"probabilities":[120],"calibrated":[123],"classifier.":[125],"extensive":[128],"evaluation,":[129],"which":[131],"also":[133,173],"validate":[134],"design":[136],"choices":[137],"underpinning":[138],"XNQ":[139,147,172],"through":[140],"comprehensive":[141],"ablation":[142],"experiments,":[143],"find":[145],"consistently":[148],"significantly":[150],"improves":[151],"on":[152,186],"best":[154],"network":[155],"methods":[157,184],"date,":[159],"thereby":[160],"setting":[161],"new":[163],"state":[164],"art":[167],"for":[168],"challenging":[170],"task.":[171],"training":[176],"speed-up":[177],"up":[179],"10x\u2013100x":[181],"over":[182],"other":[183],"based":[185],"learning.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-11-07T00:00:00"}