{"id":"https://openalex.org/W7133537458","doi":"https://doi.org/10.48550/arxiv.2603.02673","title":"Exact Functional ANOVA Decomposition for Categorical Inputs Models","display_name":"Exact Functional ANOVA Decomposition for Categorical Inputs Models","publication_year":2026,"publication_date":"2026-03-03","ids":{"openalex":"https://openalex.org/W7133537458","doi":"https://doi.org/10.48550/arxiv.2603.02673"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05531600v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05531600","pdf_url":"https://hal.science/hal-05531600/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"Preprints, Working Papers, ..."},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-05531600/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119918356","display_name":"Baptiste Ferrere","orcid":null},"institutions":[{"id":"https://openalex.org/I41918367","display_name":"Sinclair Community College","ror":"https://ror.org/00pczg388","country_code":"US","type":"education","lineage":["https://openalex.org/I41918367"]},{"id":"https://openalex.org/I4210096366","display_name":"Sinclair Pharma","ror":"https://ror.org/00ab7gt92","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210096366"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Ferrere, Baptiste","raw_affiliation_strings":["IMT, SINCLAIR AI Lab"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMT, SINCLAIR AI Lab","institution_ids":["https://openalex.org/I4210096366","https://openalex.org/I41918367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044190443","display_name":"Nicol\u00e1s Bousquet","orcid":"https://orcid.org/0000-0003-0170-0503"},"institutions":[{"id":"https://openalex.org/I41918367","display_name":"Sinclair Community College","ror":"https://ror.org/00pczg388","country_code":"US","type":"education","lineage":["https://openalex.org/I41918367"]},{"id":"https://openalex.org/I4210096366","display_name":"Sinclair Pharma","ror":"https://ror.org/00ab7gt92","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210096366"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Bousquet, Nicolas","raw_affiliation_strings":["SINCLAIR AI Lab"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SINCLAIR AI Lab","institution_ids":["https://openalex.org/I4210096366","https://openalex.org/I41918367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121506800","display_name":"Fabrice Gamboa","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gamboa, Fabrice","raw_affiliation_strings":["IMT, ANITI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMT, ANITI","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Loubes, Jean-Michel","orcid":null},"institutions":[{"id":"https://openalex.org/I1280339224","display_name":"United States Nuclear Regulatory Commission","ror":"https://ror.org/03nhmbj89","country_code":"US","type":"government","lineage":["https://openalex.org/I1280339224"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Loubes, Jean-Michel","raw_affiliation_strings":["IMT, REGALIA, ANITI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMT, REGALIA, ANITI","institution_ids":["https://openalex.org/I1280339224"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024069297","display_name":"Joseph Mur\u00e9","orcid":"https://orcid.org/0000-0003-4147-1143"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mur\u00e9, Joseph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5119918356"],"corresponding_institution_ids":["https://openalex.org/I41918367","https://openalex.org/I4210096366"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.8937000036239624,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.8937000036239624,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.017400000244379044,"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/T10845","display_name":"Advanced Causal Inference Techniques","score":0.01209999993443489,"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/categorical-variable","display_name":"Categorical variable","score":0.8718000054359436},{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.82669997215271},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6489999890327454},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5916000008583069},{"id":"https://openalex.org/keywords/functional-data-analysis","display_name":"Functional data analysis","score":0.3799999952316284},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.37299999594688416},{"id":"https://openalex.org/keywords/additive-model","display_name":"Additive model","score":0.33250001072883606}],"concepts":[{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.8718000054359436},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.82669997215271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6902999877929688},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6489999890327454},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5916000008583069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39160001277923584},{"id":"https://openalex.org/C51820054","wikidata":"https://www.wikidata.org/wiki/Q5508814","display_name":"Functional data analysis","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.37299999594688416},{"id":"https://openalex.org/C203223496","wikidata":"https://www.wikidata.org/wiki/Q4681344","display_name":"Additive model","level":2,"score":0.33250001072883606},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.3287000060081482},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C99476002","wikidata":"https://www.wikidata.org/wiki/Q42297","display_name":"Analysis of variance","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2971999943256378},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2892000079154968},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.27799999713897705},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2687999904155731}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05531600v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05531600","pdf_url":"https://hal.science/hal-05531600/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.2603.02673","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.02673","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":"pmh:oai:HAL:hal-05531600v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05531600","pdf_url":"https://hal.science/hal-05531600/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2026","raw_type":"Preprints, Working Papers, ..."},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7133537458.pdf","grobid_xml":"https://content.openalex.org/works/W7133537458.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Functional":[0],"ANOVA":[1,119],"offers":[2],"a":[3,10,34,81,125],"principled":[4],"framework":[5,123],"for":[6,47,65,131],"interpretability":[7],"by":[8],"decomposing":[9],"model's":[11],"prediction":[12],"into":[13],"main":[14],"effects":[15],"and":[16,31,100,118],"higher-order":[17],"interactions.":[18],"For":[19],"independent":[20,98],"features,":[21],"this":[22,63],"decomposition":[23,83],"is":[24,89],"well-defined,":[25],"strongly":[26],"linked":[27],"with":[28,72,108],"SHAP":[29,117,129],"values,":[30],"serves":[32],"as":[33],"cornerstone":[35],"of":[36,42,75,128],"additive":[37],"explainability.":[38],"However,":[39],"the":[40,73,96,113,132],"lack":[41],"an":[43],"explicit":[44],"closed-form":[45,82],"expression":[46],"general":[48,133],"dependent":[49],"distributions":[50,107],"has":[51],"forced":[52],"practitioners":[53],"to":[54,102],"rely":[55],"on":[56],"costly":[57],"sampling-based":[58],"approximations.":[59],"We":[60],"completely":[61],"resolve":[62],"limitation":[64],"categorical":[66,134],"inputs.":[67],"By":[68],"bridging":[69],"functional":[70],"analysis":[71],"extension":[74],"discrete":[76],"Fourier":[77],"analysis,":[78],"we":[79],"derive":[80],"without":[84],"any":[85],"assumption.":[86],"Our":[87],"formulation":[88],"computationally":[90],"very":[91],"efficient.":[92],"It":[93],"seamlessly":[94],"recovers":[95],"classical":[97],"case":[99],"extends":[101],"arbitrary":[103],"dependence":[104],"structures,":[105],"including":[106],"non-rectangular":[109],"support.":[110],"Furthermore,":[111],"leveraging":[112],"intrinsic":[114],"link":[115],"between":[116],"under":[120],"independence,":[121],"our":[122],"yields":[124],"natural":[126],"generalization":[127],"values":[130],"setting.":[135]},"counts_by_year":[],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2026-03-05T00:00:00"}