{"id":"https://openalex.org/W7135237706","doi":"https://doi.org/10.48550/arxiv.2603.11304","title":"Worst-case low-rank approximations","display_name":"Worst-case low-rank approximations","publication_year":2026,"publication_date":"2026-03-11","ids":{"openalex":"https://openalex.org/W7135237706","doi":"https://doi.org/10.48550/arxiv.2603.11304"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.11304","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11304","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"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":"https://doi.org/10.48550/arxiv.2603.11304","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112995049","display_name":"A. Fries","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fries, Anya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129057715","display_name":"Markus Reichstein","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Reichstein, Markus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129067448","display_name":"David Blei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blei, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5002127148","display_name":"Jonas Peters","orcid":"https://orcid.org/0000-0002-1487-7511"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peters, Jonas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.3596000075340271,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.3596000075340271,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.1388999968767166,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.09849999845027924,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/estimator","display_name":"Estimator","score":0.7163000106811523},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.5907999873161316},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.4715999960899353},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4449999928474426},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4429999887943268},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4237000048160553},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.40880000591278076},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4075999855995178}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7163000106811523},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.5907999873161316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5569999814033508},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5052000284194946},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.4715999960899353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46619999408721924},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4449999928474426},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4237000048160553},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.396699994802475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3912000060081482},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3061000108718872},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.11304","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11304","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.11304","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.11304","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.6454399824142456,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Real-world":[0],"data":[1],"in":[2,31,44,48,83,133,188,195],"health,":[3],"economics,":[4],"and":[5,90,102,146,168,178],"environmental":[6],"sciences":[7],"are":[8,93,114],"often":[9],"collected":[10],"across":[11,66],"heterogeneous":[12,99],"domains":[13,46,123,129],"(such":[14,54],"as":[15,55,88],"hospitals,":[16],"regions,":[17],"or":[18],"time":[19],"periods).":[20],"In":[21],"such":[22,87],"settings,":[23],"distributional":[24],"shifts":[25],"can":[26],"make":[27],"standard":[28],"PCA":[29],"unreliable,":[30],"that,":[32],"for":[33,96,109,173],"example,":[34],"the":[35,49,84,112,120,134,138],"leading":[36],"principal":[37],"components":[38],"may":[39],"explain":[40],"substantially":[41],"less":[42],"variance":[43],"unseen":[45],"than":[47,63],"training":[50],"domains.":[51,68],"Existing":[52],"approaches":[53],"FairPCA)":[56],"have":[57],"proposed":[58],"to":[59,79,157],"consider":[60],"worst-case":[61,115,148,171,189],"(rather":[62],"average)":[64],"performance":[65],"multiple":[67],"This":[69],"work":[70],"develops":[71],"a":[72],"unified":[73],"framework,":[74],"called":[75],"wcPCA,":[76],"applies":[77],"it":[78],"other":[80],"objectives":[81],"(resulting":[82],"novel":[85],"estimators":[86,113],"norm-minPCA":[89],"norm-maxregret,":[91],"which":[92],"better":[94],"suited":[95],"applications":[97,181],"with":[98,191],"total":[100],"variance)":[101],"analyzes":[103],"their":[104],"relationship.":[105],"We":[106,143,153],"prove":[107,169],"that":[108,162],"all":[110,127],"objectives,":[111],"optimal":[116],"not":[117],"only":[118,192],"over":[119,126],"observed":[121],"source":[122,141],"but":[124],"also":[125],"target":[128],"whose":[130],"covariance":[131],"lies":[132],"convex":[135],"hull":[136],"of":[137,150,165],"(possibly":[139],"normalized)":[140],"covariances.":[142],"establish":[144],"consistency":[145],"asymptotic":[147],"guarantees":[149],"empirical":[151],"estimators.":[152],"extend":[154],"our":[155],"methodology":[156],"matrix":[158,175],"completion,":[159],"another":[160],"problem":[161],"makes":[163],"use":[164],"low-rank":[166],"approximations,":[167],"approximate":[170],"optimality":[172],"inductive":[174],"completion.":[176],"Simulations":[177],"two":[179],"real-world":[180],"on":[182],"ecosystem-atmosphere":[183],"fluxes":[184],"demonstrate":[185],"marked":[186],"improvements":[187],"performance,":[190],"minor":[193],"losses":[194],"average":[196],"performance.":[197]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-14T00:00:00"}
