{"id":"https://openalex.org/W4400522942","doi":"https://doi.org/10.3390/e26070593","title":"NodeFlow: Towards End-to-End Flexible Probabilistic Regression on Tabular Data","display_name":"NodeFlow: Towards End-to-End Flexible Probabilistic Regression on Tabular Data","publication_year":2024,"publication_date":"2024-07-11","ids":{"openalex":"https://openalex.org/W4400522942","doi":"https://doi.org/10.3390/e26070593","pmid":"https://pubmed.ncbi.nlm.nih.gov/39056955"},"language":"en","primary_location":{"id":"doi:10.3390/e26070593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26070593","pdf_url":"https://www.mdpi.com/1099-4300/26/7/593/pdf?version=1720744650","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":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/26/7/593/pdf?version=1720744650","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021928064","display_name":"Patryk Wielopolski","orcid":"https://orcid.org/0000-0003-2579-8293"},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Patryk Wielopolski","raw_affiliation_strings":["Department of Artificial Intelligence, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"],"raw_orcid":"https://orcid.org/0000-0003-2579-8293","affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345","https://openalex.org/I686019"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098937078","display_name":"Oleksii Furman","orcid":null},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Oleksii Furman","raw_affiliation_strings":["Department of Artificial Intelligence, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345","https://openalex.org/I686019"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083652196","display_name":"Maciej Zi\u0119ba","orcid":"https://orcid.org/0000-0003-4217-7712"},"institutions":[{"id":"https://openalex.org/I11923345","display_name":"Wroc\u0142aw University of Science and Technology","ror":"https://ror.org/008fyn775","country_code":"PL","type":"education","lineage":["https://openalex.org/I11923345"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Maciej Zi\u0119ba","raw_affiliation_strings":["Department of Artificial Intelligence, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland","Tooploox Ltd., 53-601 Wroc\u0142aw, Poland"],"raw_orcid":"https://orcid.org/0000-0003-4217-7712","affiliations":[{"raw_affiliation_string":"Department of Artificial Intelligence, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I11923345","https://openalex.org/I686019"]},{"raw_affiliation_string":"Tooploox Ltd., 53-601 Wroc\u0142aw, Poland","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5021928064"],"corresponding_institution_ids":["https://openalex.org/I11923345","https://openalex.org/I686019"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6294,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73051835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"26","issue":"7","first_page":"593","last_page":"593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9991999864578247,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9991999864578247,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9987999796867371,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9979000091552734,"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":0.732121467590332},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.7308464646339417},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6074107885360718},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5982269048690796},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5432227253913879},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.49666720628738403},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4840647280216217},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.47271841764450073},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.464241623878479},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.45952731370925903},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.42494139075279236},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41584235429763794},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.34769803285598755},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.1215091347694397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.10062748193740845},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.093679279088974},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0787527859210968}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.732121467590332},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.7308464646339417},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6074107885360718},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5982269048690796},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5432227253913879},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.49666720628738403},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4840647280216217},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.47271841764450073},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.464241623878479},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.45952731370925903},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.42494139075279236},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41584235429763794},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.34769803285598755},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.1215091347694397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.10062748193740845},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.093679279088974},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0787527859210968},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26070593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26070593","pdf_url":"https://www.mdpi.com/1099-4300/26/7/593/pdf?version=1720744650","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:39056955","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39056955","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:pubmedcentral.nih.gov:11276552","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11276552","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11276552/pdf/entropy-26-00593.pdf","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":"pmh:oai:doaj.org/article:3d7724cabe1f45f3ba2039c5e0c13468","is_oa":true,"landing_page_url":"https://doaj.org/article/3d7724cabe1f45f3ba2039c5e0c13468","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 26, Iss 7, p 593 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26070593","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26070593","pdf_url":"https://www.mdpi.com/1099-4300/26/7/593/pdf?version=1720744650","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":[{"score":0.7599999904632568,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2146993335","display_name":null,"funder_award_id":"2021/43/B/ST6/02853","funder_id":"https://openalex.org/F4320326815","funder_display_name":"Infrastruktura PL-Grid"},{"id":"https://openalex.org/G4461236049","display_name":null,"funder_award_id":"2021/43/B/ST6/02853","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G5262859983","display_name":null,"funder_award_id":"PLG/2023/016636","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G6121994560","display_name":null,"funder_award_id":"PLG/2023/016636","funder_id":"https://openalex.org/F4320326815","funder_display_name":"Infrastruktura PL-Grid"}],"funders":[{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"},{"id":"https://openalex.org/F4320326815","display_name":"Infrastruktura PL-Grid","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4400522942.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W114730584","https://openalex.org/W582134693","https://openalex.org/W1719489212","https://openalex.org/W2295598076","https://openalex.org/W2556522401","https://openalex.org/W2560321925","https://openalex.org/W2768348081","https://openalex.org/W2798476254","https://openalex.org/W2889326414","https://openalex.org/W2895434480","https://openalex.org/W2972470287","https://openalex.org/W2979812796","https://openalex.org/W2986615800","https://openalex.org/W3171856801","https://openalex.org/W3174082502","https://openalex.org/W3202428668","https://openalex.org/W3209660231","https://openalex.org/W4387171495","https://openalex.org/W6730169791","https://openalex.org/W6790674540","https://openalex.org/W6857251634","https://openalex.org/W7006806681"],"related_works":["https://openalex.org/W1828158523","https://openalex.org/W2049578243","https://openalex.org/W2000145235","https://openalex.org/W2122079181","https://openalex.org/W1985848810","https://openalex.org/W2889939530","https://openalex.org/W2399195672","https://openalex.org/W3121881699","https://openalex.org/W2748838164","https://openalex.org/W2066015000"],"abstract_inverted_index":{"We":[0],"introduce":[1],"NodeFlow,":[2,42],"a":[3,52,65,157],"flexible":[4],"framework":[5],"for":[6,30,103,160,169],"probabilistic":[7,32,123,177],"regression":[8,124,132,178],"on":[9,109,179],"tabular":[10,49,180],"data":[11,50],"that":[12],"combines":[13],"Neural":[14],"Oblivious":[15],"Decision":[16],"Ensembles":[17],"(NODEs)":[18],"and":[19,84,96,105,126,152,162,171],"Conditional":[20],"Continuous":[21],"Normalizing":[22],"Flows":[23],"(CNFs).":[24],"It":[25],"offers":[26],"improved":[27],"modeling":[28],"capabilities":[29],"arbitrary":[31],"distributions,":[33],"addressing":[34],"the":[35,43,56,60,78,82,141,174],"limitations":[36],"of":[37,71,81,94,118,144,176],"traditional":[38],"parametric":[39],"approaches.":[40],"In":[41,146],"NODE":[44],"captures":[45],"complex":[46],"relationships":[47],"in":[48,121,130,173],"through":[51],"tree-like":[53],"structure,":[54],"while":[55],"conditional":[57],"CNF":[58],"utilizes":[59],"NODE's":[61],"output":[62],"space":[63],"as":[64],"conditioning":[66],"factor.":[67],"The":[68],"training":[69,150],"process":[70,151],"NodeFlow":[72,99],"employs":[73],"standard":[74],"gradient-based":[75],"learning,":[76],"facilitating":[77],"end-to-end":[79,149],"optimization":[80],"NODEs":[83],"CNF-based":[85],"density":[86],"estimation.":[87],"This":[88],"approach":[89],"ensures":[90],"outstanding":[91],"performance,":[92],"ease":[93],"implementation,":[95],"scalability,":[97],"making":[98],"an":[100],"appealing":[101],"choice":[102],"practitioners":[104,161],"researchers.":[106,163],"Comprehensive":[107],"assessments":[108],"benchmark":[110],"datasets":[111],"underscore":[112],"NodeFlow's":[113,148],"efficacy,":[114],"revealing":[115],"its":[116,127],"achievement":[117],"state-of-the-art":[119],"outcomes":[120],"multivariate":[122],"setup":[125],"strong":[128,153],"performance":[129,154],"univariate":[131],"tasks.":[133],"Furthermore,":[134],"ablation":[135],"studies":[136],"are":[137],"conducted":[138],"to":[139],"justify":[140],"design":[142],"choices":[143],"NodeFlow.":[145],"conclusion,":[147],"make":[155],"it":[156,165],"compelling":[158],"solution":[159],"Additionally,":[164],"opens":[166],"new":[167],"avenues":[168],"research":[170],"application":[172],"field":[175],"data.":[181]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}