{"id":"https://openalex.org/W7101814417","doi":"https://doi.org/10.48550/arxiv.2510.22157","title":"Stochastic Trace and Diagonal Estimator for Tensors","display_name":"Stochastic Trace and Diagonal Estimator for Tensors","publication_year":2025,"publication_date":"2025-10-25","ids":{"openalex":"https://openalex.org/W7101814417","doi":"https://doi.org/10.48550/arxiv.2510.22157"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2510.22157","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.22157","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2510.22157","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Verma, Bhisham Dev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Verma, Bhisham Dev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Pratap, Rameshwar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pratap, Rameshwar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Kang, Keegan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kang, Keegan","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":true,"primary_topic":{"id":"https://openalex.org/T12828","display_name":"Plant Genetic and Mutation Studies","score":0.10339999943971634,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12828","display_name":"Plant Genetic and Mutation Studies","score":0.10339999943971634,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12834","display_name":"Flowering Plant Growth and Cultivation","score":0.07249999791383743,"subfield":{"id":"https://openalex.org/subfields/1110","display_name":"Plant Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11237","display_name":"Plant Gene Expression Analysis","score":0.061500001698732376,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.9057000279426575},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.861299991607666},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8342000246047974},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6758000254631042},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6292999982833862},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.3440000116825104}],"concepts":[{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.9057000279426575},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.861299991607666},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8342000246047974},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6877999901771545},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6758000254631042},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6292999982833862},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5353999733924866},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.3440000116825104},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.3285999894142151},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3102000057697296},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29820001125335693},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.28610000014305115},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2510.22157","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.22157","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":"doi:10.48550/arxiv.2510.22157","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.22157","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":false,"raw_source_name":null,"raw_type":"Preprint"},"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":[0,151],"consider":[1],"the":[2,6,20,23,37,45,68,83,95,116],"problem":[3],"of":[4,11,47,53,67,73,85,100,121,135,157],"estimating":[5,94],"trace":[7,42,69,96,117],"and":[8,41,55,70,97,111,118,137,142,160],"diagonal":[9,39,71,98,119],"entries":[10,40,99,120],"an":[12],"N-order":[13],"tensor":[14,24,123],"(where":[15],"$N":[16],"\\geq":[17],"2$)":[18],"under":[19,124],"framework":[21],"where":[22],"can":[25,130],"only":[26],"be":[27,131],"accessed":[28],"through":[29],"tensor-vector":[30,48,104],"multiplication.":[31],"The":[32,50],"aim":[33],"is":[34],"to":[35,60,82,144],"estimate":[36],"tensor's":[38],"by":[43],"minimizing":[44],"number":[46],"queries.":[49,80,105],"seminal":[51],"work":[52],"Hutchinson":[54],"its":[56],"extended":[57],"version":[58],"due":[59],"Bekas":[61,138],"et":[62,139],"al.":[63],"give":[64],"unbiased":[65,113],"estimates":[66],"elements":[72],"a":[74,122,153],"given":[75],"matrix,":[76],"respectively,":[77],"using":[78,103],"matrix-vector":[79],"However,":[81],"best":[84],"our":[86,158],"knowledge,":[87],"no":[88],"analogous":[89],"results":[90],"are":[91],"known":[92],"for":[93,115],"higher-order":[101],"tensors":[102],"This":[106],"paper":[107],"addresses":[108],"this":[109,125],"gap":[110],"presents":[112],"estimators":[114,141,146],"model.":[126],"Our":[127],"proposed":[128],"methods":[129],"seen":[132],"as":[133],"generalizations":[134],"Hutchinson's":[136],"al.'s":[140],"reduce":[143],"their":[145],"when":[147],"N":[148],"=":[149],"2.":[150],"provide":[152],"rigorous":[154],"theoretical":[155],"analysis":[156],"proposals":[159],"complement":[161],"it":[162],"with":[163],"supporting":[164],"simulations.":[165]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2025-10-29T00:00:00"}