{"id":"https://openalex.org/W7153350494","doi":"https://doi.org/10.48550/arxiv.2604.07660","title":"Universal, sample-optimal algorithms for recovery of anisotropic functions from i.i.d. samples","display_name":"Universal, sample-optimal algorithms for recovery of anisotropic functions from i.i.d. samples","publication_year":2026,"publication_date":"2026-04-08","ids":{"openalex":"https://openalex.org/W7153350494","doi":"https://doi.org/10.48550/arxiv.2604.07660"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.07660","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07660","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.2604.07660","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065352983","display_name":"Ben Adcock","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Adcock, Ben","raw_affiliation_strings":["Simon Fraser University, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5133355755","display_name":"Avi Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gupta, Avi","raw_affiliation_strings":["Simon Fraser University, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simon Fraser University, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.4799000024795532,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.4799000024795532,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.31929999589920044,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.06040000170469284,"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/smoothness","display_name":"Smoothness","score":0.6380000114440918},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.6159999966621399},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6011999845504761},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5072000026702881},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4860000014305115},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4514999985694885},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.43799999356269836},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.39570000767707825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6521999835968018},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6380000114440918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6305999755859375},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.6159999966621399},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6011999845504761},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5072000026702881},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4860000014305115},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.43799999356269836},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32280001044273376},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26339998841285706},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.07660","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07660","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.2604.07660","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.07660","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"key":[1],"problem":[2,109],"in":[3,25,214],"approximation":[4,74,122],"theory":[5],"is":[6,94,128],"the":[7,17,29,44,95,120,137,141,166,170,180,215,222],"recovery":[8,104,108],"of":[9,19,31,46,58,63,75,97,140,148,173,182,212,224],"high-dimensional":[10],"functions":[11,18,77],"from":[12,209],"samples.":[13],"In":[14,68,204],"many":[15,26],"cases,":[16],"interest":[20],"exhibit":[21],"anisotropic":[22,65,81,85,138],"smoothness,":[23],"and,":[24],"practical":[27],"settings,":[28],"nature":[30],"this":[32,69,126,149,159],"anisotropy":[33],"may":[34],"be":[35],"unknown":[36],"a":[37,61,98,106,153,162,200,210,218],"priori.":[38],"Therefore,":[39],"an":[40],"important":[41],"question":[42],"involves":[43],"development":[45],"universal":[47,73,99,188,228],"algorithms,":[48],"namely,":[49],"algorithms":[50,190,226],"that":[51,78,125,187,194],"simultaneously":[52],"achieve":[53,192],"optimal":[54],"or":[55],"near-optimal":[56],"rates":[57,193],"convergence":[59],"across":[60],"range":[62],"different":[64],"smoothness":[66,88,139],"classes.":[67,176],"work,":[70],"we":[71,178],"consider":[72],"periodic":[76],"belong":[79],"to":[80,118,135,152],"Sobolev":[82,89],"spaces":[83],"and":[84,113],"dominating":[86],"mixed":[87],"spaces.":[90],"Our":[91],"first":[92],"result":[93],"construction":[96],"algorithm.":[100],"This":[101],"recasts":[102],"function":[103,175],"as":[105,130],"sparse":[107],"for":[110,165,169,227],"Fourier":[111],"coefficients":[112],"then":[114,145],"exploits":[115],"compressed":[116],"sensing":[117],"yield":[119],"desired":[121],"rates.":[123],"Note":[124],"algorithm":[127,150],"nonadaptive,":[129],"it":[131],"does":[132],"not":[133],"seek":[134],"learn":[136],"target":[142],"function.":[143],"We":[144,157,185],"demonstrate":[146,179],"optimality":[147],"up":[151],"dimension-independent":[154],"polylogarithmic":[155,202],"factor.":[156,203],"do":[158],"by":[160,199],"presenting":[161],"lower":[163],"bound":[164],"adaptive":[167],"$m$-width":[168],"unit":[171],"balls":[172],"such":[174],"Finally,":[177],"necessity":[181,223],"nonlinear":[183,225],"algorithms.":[184],"show":[186],"linear":[189],"can":[191],"are":[195],"at":[196],"best":[197],"suboptimal":[198],"dimension-dependent":[201],"other":[205],"words,":[206],"they":[207],"suffer":[208],"curse":[211],"dimensionality":[213],"rate":[216],"--":[217],"phenomenon":[219],"which":[220],"justifies":[221],"recovery.":[229]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-11T00:00:00"}