{"id":"https://openalex.org/W7221124121","doi":"https://doi.org/10.48550/arxiv.2610.10642","title":"From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier","display_name":"From Log-Odds to Shapley Values: An Explanatory Geometry for the Weighted Naive Bayes Classifier","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7221124121","doi":"https://doi.org/10.48550/arxiv.2610.10642"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10642","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10642","pdf_url":"https://arxiv.org/pdf/2610.10642","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10642","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158012876","display_name":"Vincent Lemaire","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19370010","display_name":"Orange (France)","ror":"https://ror.org/035j0tq82","country_code":"FR","type":"company","lineage":["https://openalex.org/I19370010"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lemaire, Vincent","raw_affiliation_strings":["Orange Research , France ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Orange Research , France ,","institution_ids":["https://openalex.org/I19370010"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087132141","display_name":"Fabrice Cl\u00e9rot","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19370010","display_name":"Orange (France)","ror":"https://ror.org/035j0tq82","country_code":"FR","type":"company","lineage":["https://openalex.org/I19370010"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cl\u00e9rot, Fabrice","raw_affiliation_strings":["Orange Research , France ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Orange Research , France ,","institution_ids":["https://openalex.org/I19370010"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I19370010"],"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":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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.0,"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/T13373","display_name":"Data Mining and Machine Learning Applications","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/shapley-value","display_name":"Shapley value","score":0.890999972820282},{"id":"https://openalex.org/keywords/log-odds","display_name":"log odds","score":0.8579999804496765},{"id":"https://openalex.org/keywords/manhattan-distance","display_name":"Manhattan distance","score":0.7319999933242798},{"id":"https://openalex.org/keywords/local-explanations","display_name":"local explanations","score":0.5830000042915344},{"id":"https://openalex.org/keywords/conditional-log-likelihood","display_name":"conditional log-likelihood","score":0.7429999709129333},{"id":"https://openalex.org/keywords/k-nearest-neighbors","display_name":"k-nearest neighbors","score":0.7179999947547913},{"id":"https://openalex.org/keywords/model-geometry","display_name":"model geometry","score":0.48399999737739563},{"id":"https://openalex.org/keywords/explainable-ai","display_name":"explainable AI","score":0.5580000281333923}],"concepts":[{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.682699978351593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.638700008392334},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5957000255584717},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.5539000034332275},{"id":"https://openalex.org/C52001869","wikidata":"https://www.wikidata.org/wiki/Q812530","display_name":"Naive Bayes classifier","level":3,"score":0.5476999878883362},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5440000295639038},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.47510001063346863},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4657999873161316},{"id":"https://openalex.org/C207201462","wikidata":"https://www.wikidata.org/wiki/Q182505","display_name":"Bayes' theorem","level":3,"score":0.398499995470047},{"id":"https://openalex.org/C136389625","wikidata":"https://www.wikidata.org/wiki/Q334384","display_name":"Supervised learning","level":3,"score":0.39739999175071716},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.38040000200271606},{"id":"https://openalex.org/C87465248","wikidata":"https://www.wikidata.org/wiki/Q1417790","display_name":"Minimum description length","level":2,"score":0.34709998965263367},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32749998569488525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3151000142097473},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.30559998750686646},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.302700012922287},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C185207860","wikidata":"https://www.wikidata.org/wiki/Q17004744","display_name":"Bayes classifier","level":4,"score":0.2590000033378601}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10642","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10642","pdf_url":"https://arxiv.org/pdf/2610.10642","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.10642","doi":"https://doi.org/10.48550/arxiv.2610.10642","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10642","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10642","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10642","pdf_url":"https://arxiv.org/pdf/2610.10642","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221124121.pdf","grobid_xml":"https://content.openalex.org/works/W7221124121.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2120199131","https://openalex.org/W2122111042","https://openalex.org/W4403706448","https://openalex.org/W4407237124","https://openalex.org/W4414448594"],"related_works":["https://openalex.org/W4407237124","https://openalex.org/W7159689059","https://openalex.org/W4317528894","https://openalex.org/W4406318854","https://openalex.org/W3174365326","https://openalex.org/W4387323498","https://openalex.org/W7222817367","https://openalex.org/W7171646593","https://openalex.org/W3041995706","https://openalex.org/W2799653600"],"abstract_inverted_index":{"This":[0,102],"paper":[1],"studies":[2],"the":[3,16,21,26,48,64,80,84],"construction":[4],"of":[5,69,79],"an":[6],"explanatory":[7,77],"space":[8],"for":[9],"a":[10,36,58,75,98,105,117],"weighted":[11],"naive":[12],"Bayes":[13],"classifier":[14],"from":[15,25,94,116],"supervised":[17,28,91,109],"representation":[18,56],"induced":[19,82],"by":[20,83],"model.":[22,85],"We":[23,51],"start":[24],"classical":[27],"distance":[29,59,66],"based":[30,39],"on":[31,40],"conditional":[32],"log-likelihoods":[33],"and":[34,113],"introduce":[35],"discriminative":[37],"reformulation":[38],"log-odds,":[41],"which":[42],"is":[43],"more":[44],"directly":[45],"related":[46],"to":[47],"classification":[49],"decision.":[50],"then":[52],"show":[53],"that":[54,60],"this":[55],"induces":[57],"exactly":[61],"coincides":[62],"with":[63],"$\\ell_1$":[65],"between":[67,108],"vectors":[68],"analytical":[70],"Shapley":[71],"values,":[72],"thereby":[73],"providing":[74],"formal":[76],"interpretation":[78],"geometry":[81],"Finally,":[86],"we":[87],"empirically":[88],"compare":[89],"several":[90],"distances":[92],"derived":[93],"these":[95],"representations":[96],"using":[97],"$k$-nearest":[99],"neighbors":[100],"classifier.":[101],"work":[103],"highlights":[104],"close":[106],"link":[107],"distance,":[110],"local":[111],"explanation,":[112],"predictive":[114],"behavior,":[115],"primarily":[118],"methodological":[119],"perspective.":[120]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}