{"id":"https://openalex.org/W4415329696","doi":"https://doi.org/10.48550/arxiv.2505.16713","title":"Improved generalization bounds for binary linear classification via isoperimetry","display_name":"Improved generalization bounds for binary linear classification via isoperimetry","publication_year":2025,"publication_date":"2025-05-22","ids":{"openalex":"https://openalex.org/W4415329696","doi":"https://doi.org/10.48550/arxiv.2505.16713"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2505.16713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.16713","pdf_url":"https://arxiv.org/pdf/2505.16713","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2505.16713","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010801333","display_name":"Shogo Nakakita","orcid":"https://orcid.org/0000-0002-5961-0562","observed_orcids":["https://orcid.org/0000-0002-5961-0562"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nakakita, Shogo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5010801333"],"corresponding_institution_ids":[],"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7788000106811523,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7788000106811523,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.15610000491142273,"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/T10320","display_name":"Neural Networks and Applications","score":0.006200000178068876,"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/generalization-bounds","display_name":"generalization bounds","score":0.8259999752044678},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"isoperimetric inequality","score":0.8709999918937683},{"id":"https://openalex.org/keywords/poincare-inequality","display_name":"Poincar\u00e9 inequality","score":0.9769999980926514},{"id":"https://openalex.org/keywords/logarithmic-sobolev-inequality","display_name":"logarithmic Sobolev inequality","score":0.9959999918937683},{"id":"https://openalex.org/keywords/concentration-of-measure","display_name":"concentration of measure","score":0.8349999785423279},{"id":"https://openalex.org/keywords/logistic-regression","display_name":"logistic regression","score":0.7409999966621399},{"id":"https://openalex.org/keywords/high-dimensional-asymptotics","display_name":"high-dimensional asymptotics","score":0.6729999780654907},{"id":"https://openalex.org/keywords/uniform-law-of-large-numbers","display_name":"uniform law of large numbers","score":0.9039999842643738}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8391000032424927},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.788100004196167},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6430000066757202},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6220999956130981},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.6115999817848206},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49959999322891235},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48100000619888306},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.44449999928474426},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.42340001463890076},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.40119999647140503},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.3718999922275543},{"id":"https://openalex.org/C66905080","wikidata":"https://www.wikidata.org/wiki/Q17005494","display_name":"Binary classification","level":3,"score":0.3714999854564667},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3199000060558319},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2838999927043915},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.2833999991416931},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2824000120162964},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C2779190172","wikidata":"https://www.wikidata.org/wiki/Q4913888","display_name":"Binary data","level":3,"score":0.2606000006198883},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2505.16713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.16713","pdf_url":"https://arxiv.org/pdf/2505.16713","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.2505.16713","doi":"https://doi.org/10.48550/arxiv.2505.16713","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2505.16713","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2505.16713","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2505.16713","pdf_url":"https://arxiv.org/pdf/2505.16713","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415329696.pdf","grobid_xml":"https://content.openalex.org/works/W4415329696.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"examine":[1],"the":[2,29,33,37],"concentration":[3,46],"of":[4,32,80,104],"uniform":[5,81,102],"generalization":[6,82],"errors":[7,83],"around":[8],"their":[9,85],"expectation":[10,86],"in":[11,88],"binary":[12],"linear":[13],"classification":[14],"problems":[15],"via":[16],"an":[17],"isoperimetric":[18],"argument.":[19],"In":[20,70],"particular,":[21],"we":[22,42,73,100],"establish":[23,101],"Poincar\u00e9":[24],"and":[25,36],"log-Sobolev":[26],"inequalities":[27],"for":[28],"joint":[30],"distribution":[31],"output":[34],"labels":[35],"label-weighted":[38],"input":[39],"vectors,":[40],"which":[41],"apply":[43],"to":[44,67,84],"derive":[45],"bounds.":[47],"The":[48],"derived":[49],"results":[50],"improve":[51],"upon":[52],"existing":[53],"bounds":[54],"obtained":[55],"from":[56],"general":[57],"unbounded":[58],"empirical":[59],"processes,":[60],"as":[61,63,93],"well":[62],"that":[64,76],"tailored":[65],"specifically":[66],"logistic":[68],"regression.":[69],"asymptotic":[71],"analysis,":[72],"also":[74],"show":[75],"almost":[77],"sure":[78],"convergence":[79],"occurs":[87],"very":[89],"broad":[90],"settings,":[91],"such":[92],"proportionally":[94],"high-dimensional":[95],"regimes.":[96],"Using":[97],"this":[98],"convergence,":[99],"laws":[103],"large":[105],"numbers":[106],"under":[107],"dimension-free":[108],"conditions.":[109]},"counts_by_year":[],"updated_date":"2026-10-09T09:14:12.587421","created_date":"2025-10-19T00:00:00"}