{"id":"https://openalex.org/W3150767555","doi":"https://doi.org/10.1162/evco_a_00294","title":"Shape-Constrained Symbolic Regression\u2014Improving Extrapolation with Prior Knowledge","display_name":"Shape-Constrained Symbolic Regression\u2014Improving Extrapolation with Prior Knowledge","publication_year":2021,"publication_date":"2021-04-15","ids":{"openalex":"https://openalex.org/W3150767555","doi":"https://doi.org/10.1162/evco_a_00294","mag":"3150767555","pmid":"https://pubmed.ncbi.nlm.nih.gov/34623432"},"language":"en","primary_location":{"id":"doi:10.1162/evco_a_00294","is_oa":true,"landing_page_url":"https://doi.org/10.1162/evco_a_00294","pdf_url":"https://direct.mit.edu/evco/article-pdf/30/1/75/1995582/evco_a_00294.pdf","source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://direct.mit.edu/evco/article-pdf/30/1/75/1995582/evco_a_00294.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019952173","display_name":"Gabriel Kronberger","orcid":"https://orcid.org/0000-0002-3012-3189"},"institutions":[{"id":"https://openalex.org/I4210136249","display_name":"University of Applied Sciences Upper Austria","ror":"https://ror.org/03jqp6d56","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210136249"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"G. Kronberger","raw_affiliation_strings":["Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria gabriel.kronberger@fh-ooe.at"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria gabriel.kronberger@fh-ooe.at","institution_ids":["https://openalex.org/I4210136249"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010769668","display_name":"Fabr\u00edcio Olivetti de Fran\u00e7a","orcid":"https://orcid.org/0000-0002-2741-8736"},"institutions":[{"id":"https://openalex.org/I71715416","display_name":"Universidade Federal do ABC","ror":"https://ror.org/028kg9j04","country_code":"BR","type":"education","lineage":["https://openalex.org/I71715416"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"F. O. de Franca","raw_affiliation_strings":["Center for Mathematics, Computation and Cognition (CMCC), Heuristics, Analysis and Learning Laboratory (HAL), Federal University of ABC, Santo Andre, Brazil folivetti@ufabc.edu.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Mathematics, Computation and Cognition (CMCC), Heuristics, Analysis and Learning Laboratory (HAL), Federal University of ABC, Santo Andre, Brazil folivetti@ufabc.edu.br","institution_ids":["https://openalex.org/I71715416"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071749418","display_name":"Bogdan Burlacu","orcid":"https://orcid.org/0000-0001-8785-2959"},"institutions":[{"id":"https://openalex.org/I4210136249","display_name":"University of Applied Sciences Upper Austria","ror":"https://ror.org/03jqp6d56","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210136249"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"B. Burlacu","raw_affiliation_strings":["Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria bogdan.burlacu@fh-hagenberg.at"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria bogdan.burlacu@fh-hagenberg.at","institution_ids":["https://openalex.org/I4210136249"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033231632","display_name":"Christian Haider","orcid":"https://orcid.org/0000-0002-3039-8844"},"institutions":[{"id":"https://openalex.org/I4210136249","display_name":"University of Applied Sciences Upper Austria","ror":"https://ror.org/03jqp6d56","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210136249"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"C. Haider","raw_affiliation_strings":["Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria christian.haider@fh-hagenberg.at"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria christian.haider@fh-hagenberg.at","institution_ids":["https://openalex.org/I4210136249"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004674296","display_name":"Michael Kommenda","orcid":"https://orcid.org/0000-0003-2049-723X"},"institutions":[{"id":"https://openalex.org/I4210136249","display_name":"University of Applied Sciences Upper Austria","ror":"https://ror.org/03jqp6d56","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210136249"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"M. Kommenda","raw_affiliation_strings":["Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria michael.kommenda@fh-hagenberg.at"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232 Hagenberg, Austria michael.kommenda@fh-hagenberg.at","institution_ids":["https://openalex.org/I4210136249"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004674296","https://openalex.org/A5010769668","https://openalex.org/A5019952173","https://openalex.org/A5033231632","https://openalex.org/A5071749418"],"corresponding_institution_ids":["https://openalex.org/I4210136249","https://openalex.org/I71715416"],"apc_list":null,"apc_paid":null,"fwci":5.3229,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.9621965,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"30","issue":"1","first_page":"75","last_page":"98"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11975","display_name":"Evolutionary Algorithms and Applications","score":1.0,"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/T11975","display_name":"Evolutionary Algorithms and Applications","score":1.0,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9932000041007996,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/symbolic-regression","display_name":"Symbolic regression","score":0.8767560720443726},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.6422953009605408},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5853734016418457},{"id":"https://openalex.org/keywords/genetic-programming","display_name":"Genetic programming","score":0.5535498261451721},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.5254375338554382},{"id":"https://openalex.org/keywords/polynomial-regression","display_name":"Polynomial regression","score":0.5181764364242554},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4638528823852539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46129143238067627},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4593193531036377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44806092977523804},{"id":"https://openalex.org/keywords/evolutionary-algorithm","display_name":"Evolutionary algorithm","score":0.4397844672203064},{"id":"https://openalex.org/keywords/test-set","display_name":"Test set","score":0.4259997606277466},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.41690629720687866},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4019005298614502},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34975025057792664},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3411399722099304},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16231855750083923}],"concepts":[{"id":"https://openalex.org/C2776400721","wikidata":"https://www.wikidata.org/wiki/Q18171762","display_name":"Symbolic regression","level":3,"score":0.8767560720443726},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.6422953009605408},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5853734016418457},{"id":"https://openalex.org/C110332635","wikidata":"https://www.wikidata.org/wiki/Q629498","display_name":"Genetic programming","level":2,"score":0.5535498261451721},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.5254375338554382},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.5181764364242554},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4638528823852539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46129143238067627},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4593193531036377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44806092977523804},{"id":"https://openalex.org/C159149176","wikidata":"https://www.wikidata.org/wiki/Q14489129","display_name":"Evolutionary algorithm","level":2,"score":0.4397844672203064},{"id":"https://openalex.org/C169903167","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Test set","level":2,"score":0.4259997606277466},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.41690629720687866},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4019005298614502},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34975025057792664},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3411399722099304},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16231855750083923},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D005075","descriptor_name":"Biological Evolution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1162/evco_a_00294","is_oa":true,"landing_page_url":"https://doi.org/10.1162/evco_a_00294","pdf_url":"https://direct.mit.edu/evco/article-pdf/30/1/75/1995582/evco_a_00294.pdf","source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},{"id":"pmid:34623432","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34623432","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":"Evolutionary computation","raw_type":null},{"id":"pmh:oai:arXiv.org:2103.15624","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.15624","pdf_url":"https://arxiv.org/pdf/2103.15624","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"doi:10.1162/evco_a_00294","is_oa":true,"landing_page_url":"https://doi.org/10.1162/evco_a_00294","pdf_url":"https://direct.mit.edu/evco/article-pdf/30/1/75/1995582/evco_a_00294.pdf","source":{"id":"https://openalex.org/S38677346","display_name":"Evolutionary Computation","issn_l":"1063-6560","issn":["1063-6560","1530-9304"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Evolutionary Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313144","display_name":"ITEA","ror":null},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":86,"referenced_works":["https://openalex.org/W117221855","https://openalex.org/W121066256","https://openalex.org/W158805453","https://openalex.org/W199024138","https://openalex.org/W243424403","https://openalex.org/W850812170","https://openalex.org/W1501347617","https://openalex.org/W1506283822","https://openalex.org/W1519072852","https://openalex.org/W1547227782","https://openalex.org/W1549749298","https://openalex.org/W1576818901","https://openalex.org/W1795093649","https://openalex.org/W1973385701","https://openalex.org/W1974805999","https://openalex.org/W1978467861","https://openalex.org/W1979378106","https://openalex.org/W2001466640","https://openalex.org/W2030947209","https://openalex.org/W2041091076","https://openalex.org/W2059396387","https://openalex.org/W2087512478","https://openalex.org/W2099272284","https://openalex.org/W2109042184","https://openalex.org/W2120235997","https://openalex.org/W2131480237","https://openalex.org/W2149362532","https://openalex.org/W2166140447","https://openalex.org/W2167706908","https://openalex.org/W2169840877","https://openalex.org/W2182361439","https://openalex.org/W2248060815","https://openalex.org/W2296218809","https://openalex.org/W2346300282","https://openalex.org/W2559655401","https://openalex.org/W2583555143","https://openalex.org/W2588072912","https://openalex.org/W2590737734","https://openalex.org/W2735219249","https://openalex.org/W2782083374","https://openalex.org/W2804860342","https://openalex.org/W2809630376","https://openalex.org/W2897535352","https://openalex.org/W2908541468","https://openalex.org/W2914260592","https://openalex.org/W2945976633","https://openalex.org/W2953148557","https://openalex.org/W2954009196","https://openalex.org/W2954765142","https://openalex.org/W2963019788","https://openalex.org/W2963407939","https://openalex.org/W2963860056","https://openalex.org/W2964239200","https://openalex.org/W2967169354","https://openalex.org/W2991933648","https://openalex.org/W2995937720","https://openalex.org/W3004042307","https://openalex.org/W3006755302","https://openalex.org/W3016214060","https://openalex.org/W3016401366","https://openalex.org/W3022177149","https://openalex.org/W3082465854","https://openalex.org/W3098038161","https://openalex.org/W3111210983","https://openalex.org/W3118689318","https://openalex.org/W4246840991","https://openalex.org/W4287996090","https://openalex.org/W4289765664","https://openalex.org/W4293842096","https://openalex.org/W4295295918","https://openalex.org/W4299658469","https://openalex.org/W4302567106","https://openalex.org/W6630229783","https://openalex.org/W6676279030","https://openalex.org/W6684752182","https://openalex.org/W6684891276","https://openalex.org/W6690771958","https://openalex.org/W6732851056","https://openalex.org/W6739219954","https://openalex.org/W6752296227","https://openalex.org/W6752744206","https://openalex.org/W6758062395","https://openalex.org/W6758700839","https://openalex.org/W6772046325","https://openalex.org/W6773942789","https://openalex.org/W6776058146"],"related_works":["https://openalex.org/W2968285896","https://openalex.org/W2381504162","https://openalex.org/W1567571923","https://openalex.org/W2472646430","https://openalex.org/W2610450612","https://openalex.org/W2549153708","https://openalex.org/W2897801744","https://openalex.org/W2147355282","https://openalex.org/W2394133867","https://openalex.org/W1662819506"],"abstract_inverted_index":{"We":[0,60],"investigate":[1],"the":[2,7,14,38,62,65,90,101,104,153,156,162,172,176,183,187],"addition":[3],"of":[4,16,37,64,81,130,165],"constraints":[5,149,168],"on":[6,127,171],"function":[8,39],"image":[9],"and":[10,29,54,67,69,93,119,133,175],"its":[11],"derivatives":[12],"for":[13,34,74,117,155,186],"incorporation":[15],"prior":[17],"knowledge":[18],"in":[19,89],"symbolic":[20,27,76,158],"regression.":[21],"The":[22,43,123],"approach":[23],"is":[24,45,151,169],"called":[25],"shape-constrained":[26,75],"regression":[28,136,159,181],"allows":[30],"us":[31],"to":[32,46,51,114,142,147],"enforce,":[33],"example,":[35],"monotonicity":[36],"over":[40],"selected":[41],"inputs.":[42],"aim":[44],"find":[47],"models":[48,118,144,166],"which":[49,55,85,145,150],"conform":[50,146],"expected":[52],"behavior":[53],"have":[56],"improved":[57],"extrapolation":[58],"capabilities.":[59],"demonstrate":[61],"feasibility":[63],"idea":[66],"propose":[68],"compare":[70],"two":[71],"evolutionary":[72,97],"algorithms":[73,109,124,139],"regression:":[77],"(i)":[78],"an":[79],"extension":[80],"tree-based":[82],"genetic":[83],"programming":[84],"discards":[86],"infeasible":[87,105],"solutions":[88],"selection":[91],"step,":[92],"(ii)":[94],"a":[95,128],"two-population":[96],"algorithm":[98],"that":[99],"separates":[100],"feasible":[102],"from":[103],"solutions.":[106],"In":[107],"both":[108],"we":[110],"use":[111],"interval":[112],"arithmetic":[113],"approximate":[115],"bounds":[116],"their":[120],"partial":[121],"derivatives.":[122],"are":[125,140],"tested":[126],"set":[129,174,189],"19":[131],"synthetic":[132],"four":[134],"real-world":[135],"problems.":[137],"Both":[138],"able":[141],"identify":[143],"shape":[148],"not":[152],"case":[154],"unmodified":[157],"algorithms.":[160],"However,":[161],"predictive":[163],"accuracy":[164],"with":[167],"worse":[170],"training":[173],"test":[177,188],"set.":[178],"Shape-constrained":[179],"polynomial":[180],"produces":[182],"best":[184],"results":[185],"but":[190],"also":[191],"significantly":[192],"larger":[193],"models.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}