{"id":"https://openalex.org/W7129244081","doi":"https://doi.org/10.48550/arxiv.2602.14020","title":"Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation","display_name":"Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation","publication_year":2026,"publication_date":"2026-02-15","ids":{"openalex":"https://openalex.org/W7129244081","doi":"https://doi.org/10.48550/arxiv.2602.14020"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.14020","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121036563","display_name":"Even He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Even","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5126194271","display_name":"Zaizai Yan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yan, Zaizai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.4627000093460083,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.4627000093460083,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.03799999877810478,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11236","display_name":"Control Systems and Identification","score":0.03720000013709068,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.7354999780654907},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6675000190734863},{"id":"https://openalex.org/keywords/clipping","display_name":"Clipping (morphology)","score":0.5659999847412109},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4684000015258789},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.4287000000476837},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.4041999876499176},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.400299996137619},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.382999986410141},{"id":"https://openalex.org/keywords/estimation-of-covariance-matrices","display_name":"Estimation of covariance matrices","score":0.37540000677108765}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7354999780654907},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6675000190734863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5976999998092651},{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.5659999847412109},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5112000107765198},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4684000015258789},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.4287000000476837},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37950000166893005},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.37540000677108765},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36469998955726624},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3303999900817871},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.32499998807907104},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.3215000033378601},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30889999866485596},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2892000079154968},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C157286648","wikidata":"https://www.wikidata.org/wiki/Q846780","display_name":"Kalman filter","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.14020","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.14020","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.14020","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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.14020","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,37],"study":[1],"operator-norm":[2],"covariance":[3,42],"estimation":[4],"from":[5],"heavy-tailed":[6],"samples":[7],"that":[8,59],"may":[9],"include":[10],"a":[11,39,56,65],"small":[12],"fraction":[13],"of":[14],"arbitrary":[15],"outliers.":[16],"A":[17],"simple":[18],"and":[19,64,88,105],"widely":[20],"used":[21],"safeguard":[22],"is":[23],"\\emph{Euclidean":[24],"norm":[25],"clipping},":[26],"but":[27],"its":[28],"accuracy":[29,107],"depends":[30],"critically":[31],"on":[32,98],"an":[33],"unknown":[34],"clipping":[35,70],"level.":[36],"propose":[38],"cross-fitted":[40],"clipped":[41],"estimator":[43],"equipped":[44],"with":[45],"\\emph{fully":[46],"computable}":[47],"Bernstein-type":[48],"deviation":[49],"certificates,":[50],"enabling":[51],"principled":[52],"data-driven":[53],"tuning":[54],"via":[55],"selector":[57],"(\\emph{MinUpper})":[58],"balances":[60],"certified":[61],"stochastic":[62],"error":[63],"robust":[66],"hold-out":[67],"proxy":[68],"for":[69],"bias.":[71],"The":[72],"resulting":[73],"procedure":[74],"adapts":[75],"to":[76],"intrinsic":[77],"complexity":[78],"measures":[79],"such":[80],"as":[81],"effective":[82],"rank":[83],"under":[84,92],"mild":[85],"tail":[86],"regularity":[87],"retains":[89],"meaningful":[90],"guarantees":[91],"only":[93],"finite":[94],"fourth":[95],"moments.":[96],"Experiments":[97],"contaminated":[99],"spiked-covariance":[100],"benchmarks":[101],"illustrate":[102],"stable":[103],"performance":[104],"competitive":[106],"across":[108],"regimes.":[109]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-18T00:00:00"}
