{"id":"https://openalex.org/W3087720257","doi":"https://doi.org/10.32614/rj-2022-003","title":"RKHSMetaMod: An R Package to Estimate the Hoeffding Decomposition of a Complex Model by Solving RKHS Ridge Group Sparse Optimization Problem","display_name":"RKHSMetaMod: An R Package to Estimate the Hoeffding Decomposition of a Complex Model by Solving RKHS Ridge Group Sparse Optimization Problem","publication_year":2022,"publication_date":"2022-06-21","ids":{"openalex":"https://openalex.org/W3087720257","doi":"https://doi.org/10.32614/rj-2022-003","mag":"3087720257"},"language":"en","primary_location":{"id":"doi:10.32614/rj-2022-003","is_oa":true,"landing_page_url":"https://doi.org/10.32614/rj-2022-003","pdf_url":"https://journal.r-project.org/articles/RJ-2022-003/RJ-2022-003.pdf","source":{"id":"https://openalex.org/S2489169438","display_name":"The R Journal","issn_l":"2073-4859","issn":["2073-4859"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The R Journal","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journal.r-project.org/articles/RJ-2022-003/RJ-2022-003.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026211892","display_name":"Halaleh Kamari","orcid":null},"institutions":[{"id":"https://openalex.org/I4387153769","display_name":"Laboratoire de Math\u00e9matiques et Mod\u00e9lisation d'\u00c9vry","ror":"https://ror.org/03jca6281","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097372","https://openalex.org/I4387153769","https://openalex.org/I88467170"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Halaleh Kamari","raw_affiliation_strings":["UMR 8071 Laboratoire de Math\u00e9matiques et Mod\u00e9lisation d'\u00c9vry (LaMME)"],"affiliations":[{"raw_affiliation_string":"UMR 8071 Laboratoire de Math\u00e9matiques et Mod\u00e9lisation d'\u00c9vry (LaMME)","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4387153769"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034156811","display_name":"Sylvie Huet","orcid":"https://orcid.org/0000-0003-2973-7738"},"institutions":[{"id":"https://openalex.org/I4210159481","display_name":"Math\u00e9matiques et Informatique Appliqu\u00e9es du G\u00e9nome \u00e0 l'Environnement","ror":"https://ror.org/05qdnns64","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210099460","https://openalex.org/I4210159481"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sylvie Huet","raw_affiliation_strings":["UR 1404 Math\u00e9matiques et Informatique Appliqu\u00e9es du G\u00e9nome \u00e0\nl'Environnement (MaIAGE)"],"affiliations":[{"raw_affiliation_string":"UR 1404 Math\u00e9matiques et Informatique Appliqu\u00e9es du G\u00e9nome \u00e0\nl'Environnement (MaIAGE)","institution_ids":["https://openalex.org/I4210159481"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011210786","display_name":"Marie\u2010Luce Taupin","orcid":"https://orcid.org/0009-0001-9400-9844"},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4387153769","display_name":"Laboratoire de Math\u00e9matiques et Mod\u00e9lisation d'\u00c9vry","ror":"https://ror.org/03jca6281","country_code":null,"type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210097372","https://openalex.org/I4387153769","https://openalex.org/I88467170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marie-Luce Taupin","raw_affiliation_strings":["UMR 8071 Laboratoire de Math\u00e9matiques et Mod\u00e9lisation d'\u00c9vry (LaMME)"],"affiliations":[{"raw_affiliation_string":"UMR 8071 Laboratoire de Math\u00e9matiques et Mod\u00e9lisation d'\u00c9vry (LaMME)","institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4387153769"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026211892"],"corresponding_institution_ids":["https://openalex.org/I4210155549","https://openalex.org/I4387153769"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00295243,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"1","first_page":"101","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5603503584861755},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.4978609085083008},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4630826413631439},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45381683111190796},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4389486610889435},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4326225519180298},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4312068521976471},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.3883926272392273},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33766859769821167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22689032554626465},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14672929048538208}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5603503584861755},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.4978609085083008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4630826413631439},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45381683111190796},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4389486610889435},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4326225519180298},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4312068521976471},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3883926272392273},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33766859769821167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22689032554626465},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14672929048538208}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.32614/rj-2022-003","is_oa":true,"landing_page_url":"https://doi.org/10.32614/rj-2022-003","pdf_url":"https://journal.r-project.org/articles/RJ-2022-003/RJ-2022-003.pdf","source":{"id":"https://openalex.org/S2489169438","display_name":"The R Journal","issn_l":"2073-4859","issn":["2073-4859"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The R Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.13695","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.13695","pdf_url":"https://arxiv.org/pdf/1905.13695","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"},{"id":"mag:3087720257","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1905.13695.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-04430130v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04430130","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://journal.r-project.org/","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1905.13695","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1905.13695","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.32614/rj-2022-003","is_oa":true,"landing_page_url":"https://doi.org/10.32614/rj-2022-003","pdf_url":"https://journal.r-project.org/articles/RJ-2022-003/RJ-2022-003.pdf","source":{"id":"https://openalex.org/S2489169438","display_name":"The R Journal","issn_l":"2073-4859","issn":["2073-4859"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The R Journal","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3087720257.pdf","grobid_xml":"https://content.openalex.org/works/W3087720257.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W65928136","https://openalex.org/W91227773","https://openalex.org/W585085135","https://openalex.org/W593611996","https://openalex.org/W1460189015","https://openalex.org/W1523985187","https://openalex.org/W1535712589","https://openalex.org/W1565176583","https://openalex.org/W1596126913","https://openalex.org/W1695563742","https://openalex.org/W1797402740","https://openalex.org/W1840389249","https://openalex.org/W1854939505","https://openalex.org/W1973333099","https://openalex.org/W1986280275","https://openalex.org/W1996475268","https://openalex.org/W2002355073","https://openalex.org/W2008623081","https://openalex.org/W2010737928","https://openalex.org/W2024419927","https://openalex.org/W2026645785","https://openalex.org/W2029767409","https://openalex.org/W2045355467","https://openalex.org/W2049774453","https://openalex.org/W2056958800","https://openalex.org/W2080726496","https://openalex.org/W2089520569","https://openalex.org/W2093994886","https://openalex.org/W2097441841","https://openalex.org/W2098043077","https://openalex.org/W2102760656","https://openalex.org/W2106398669","https://openalex.org/W2106600817","https://openalex.org/W2107412135","https://openalex.org/W2111857777","https://openalex.org/W2113117406","https://openalex.org/W2120539875","https://openalex.org/W2137087688","https://openalex.org/W2138019504","https://openalex.org/W2145102541","https://openalex.org/W2148388532","https://openalex.org/W2153542182","https://openalex.org/W2164278908","https://openalex.org/W2321957512","https://openalex.org/W2342500502","https://openalex.org/W2593996946","https://openalex.org/W2963446226","https://openalex.org/W2963839891","https://openalex.org/W2964237950","https://openalex.org/W2970559110","https://openalex.org/W2995161752","https://openalex.org/W3122455945","https://openalex.org/W4206742934","https://openalex.org/W4292363360","https://openalex.org/W4391285994","https://openalex.org/W4399546877","https://openalex.org/W6674698904","https://openalex.org/W6805403146","https://openalex.org/W6987374284"],"related_works":["https://openalex.org/W2947017472","https://openalex.org/W2509171749","https://openalex.org/W2116680122","https://openalex.org/W2167999092","https://openalex.org/W2757512748","https://openalex.org/W173194853","https://openalex.org/W3171264960","https://openalex.org/W3043245007","https://openalex.org/W3005703306","https://openalex.org/W2419326183","https://openalex.org/W2124509762","https://openalex.org/W2405306243","https://openalex.org/W2962755279","https://openalex.org/W3206075628","https://openalex.org/W2001351287","https://openalex.org/W3177113147","https://openalex.org/W2061929219","https://openalex.org/W2197043100","https://openalex.org/W2752674399","https://openalex.org/W2077002103"],"abstract_inverted_index":{"In":[0,134],"this":[1,161],"paper,":[2],"we":[3],"propose":[4,187],"an":[5,119],"R":[6,123,182],"package,":[7],"called":[8,86],"[RKHSMetaMod](https://CRAN.R-project.org/package=RKHSMetaMod),":[9],"that":[10,49,112,151],"implements":[11],"a":[12,16,19,44,53,68,149,188],"procedure":[13],"for":[14,148],"estimating":[15],"meta-model":[17,23,63],"of":[18,28,56,61,67,76,157,160],"complex":[20,30],"model.":[21],"The":[22,59,115],"approximates":[24],"the":[25,29,62,65,74,77,81,97,100,109,122,128,139,144,158,166,181],"Hoeffding":[26,101],"decomposition":[27],"model":[31],"and":[32,80,95,103,107,132,142,172],"allows":[33,91],"us":[34],"to":[35,43,93,105,127,136,186],"perform":[36],"sensitivity":[37],"analysis":[38],"on":[39],"it.":[40],"It":[41],"belongs":[42],"reproducing":[45],"kernel":[46],"Hilbert":[47,57,78],"space":[48],"is":[50,64,152],"constructed":[51],"as":[52],"direct":[54],"sum":[55,75],"spaces.":[58],"estimator":[60],"solution":[66],"penalized":[69],"empirical":[70,82],"least-squares":[71],"minimization":[72],"with":[73],"norm":[79],"$L^2$-norm.":[83],"This":[84],"procedure,":[85],"RKHS":[87],"ridge":[88],"group":[89],"sparse,":[90],"both":[92],"select":[94,106],"estimate":[96,108],"terms":[98],"in":[99,154,180,184],"decomposition,":[102],"therefore,":[104],"Sobol":[110],"indices":[111],"are":[113,163,177],"non-zero.":[114],"[RKHSMetaMod](https://CRAN.R-project.org/package=RKHSMetaMod)":[116],"package":[117,162],"provides":[118],"interface":[120],"from":[121],"statistical":[124],"computing":[125],"environment":[126,183],"C++":[129,168],"libraries":[130,169],"Eigen":[131],"GSL.":[133],"order":[135,185],"speed":[137],"up":[138],"execution":[140],"time":[141],"optimize":[143],"storage":[145],"memory,":[146],"except":[147],"function":[150],"written":[153,164],"R,":[155],"all":[156],"functions":[159,176],"using":[165],"efficient":[167],"through":[170],"[RcppEigen](https://CRAN.R-project.org/package=RcppEigen)":[171],"[RcppGSL](https://CRAN.R-project.org/package=RcppGSL)":[173],"packages.":[174],"These":[175],"then":[178],"interfaced":[179],"user-friendly":[189],"package.":[190]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
