{"id":"https://openalex.org/W2976673394","doi":"https://doi.org/10.1137/21m1437457","title":"Benefit of Interpolation in Nearest Neighbor Algorithms","display_name":"Benefit of Interpolation in Nearest Neighbor Algorithms","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W2976673394","doi":"https://doi.org/10.1137/21m1437457","mag":"2976673394"},"language":"en","primary_location":{"id":"doi:10.1137/21m1437457","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1437457","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/21m1437457","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041044132","display_name":"Yue Xing","orcid":"https://orcid.org/0000-0001-7723-0048"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yue Xing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110373518","display_name":"Qifan Song","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qifan Song","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101688179","display_name":"Guang Cheng","orcid":"https://orcid.org/0000-0002-7874-9404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guang Cheng","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":3.95,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.94182791,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"4","issue":"2","first_page":"935","last_page":"956"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12535","display_name":"Machine Learning and Data Classification","score":0.9994000196456909,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9994000196456909,"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9986000061035156,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9983000159263611,"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/interpolation","display_name":"Interpolation (computer graphics)","score":0.6499998569488525},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6489021182060242},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.598040759563446},{"id":"https://openalex.org/keywords/counterintuitive","display_name":"Counterintuitive","score":0.5462174415588379},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4870651066303253},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4725113809108734},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.4634961783885956},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.45314866304397583},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4304353594779968},{"id":"https://openalex.org/keywords/k-nearest-neighbors-algorithm","display_name":"k-nearest neighbors algorithm","score":0.4157072901725769},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.39673811197280884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3847062587738037}],"concepts":[{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6499998569488525},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6489021182060242},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.598040759563446},{"id":"https://openalex.org/C101097943","wikidata":"https://www.wikidata.org/wiki/Q5176983","display_name":"Counterintuitive","level":2,"score":0.5462174415588379},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4870651066303253},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4725113809108734},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.4634961783885956},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.45314866304397583},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4304353594779968},{"id":"https://openalex.org/C113238511","wikidata":"https://www.wikidata.org/wiki/Q1071612","display_name":"k-nearest neighbors algorithm","level":2,"score":0.4157072901725769},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.39673811197280884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3847062587738037},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1437457","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1437457","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/21m1437457","is_oa":true,"landing_page_url":"https://doi.org/10.1137/21m1437457","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","score":0.4099999964237213,"display_name":"Partnerships for the goals"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W107540859","https://openalex.org/W1981276685","https://openalex.org/W2004343933","https://openalex.org/W2043919728","https://openalex.org/W2085988980","https://openalex.org/W2101234009","https://openalex.org/W2108882154","https://openalex.org/W2149894778","https://openalex.org/W2272298386","https://openalex.org/W2298860367","https://openalex.org/W2559655401","https://openalex.org/W2610749375","https://openalex.org/W2612690371","https://openalex.org/W2614119628","https://openalex.org/W2894604724","https://openalex.org/W2895291063","https://openalex.org/W2907127169","https://openalex.org/W2922153390","https://openalex.org/W2923764619","https://openalex.org/W2954975122","https://openalex.org/W2962698540","https://openalex.org/W2962930448","https://openalex.org/W2963038274","https://openalex.org/W2963239103","https://openalex.org/W2963320759","https://openalex.org/W2963376662","https://openalex.org/W2963518130","https://openalex.org/W2963742538","https://openalex.org/W2964161291","https://openalex.org/W3018252856","https://openalex.org/W3042738246","https://openalex.org/W3101477643","https://openalex.org/W3111350549","https://openalex.org/W3118054728","https://openalex.org/W3123231293","https://openalex.org/W4252305909","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2809491669","https://openalex.org/W3005839474","https://openalex.org/W2050235149","https://openalex.org/W4379988549","https://openalex.org/W2139510495","https://openalex.org/W2016376779","https://openalex.org/W2807993762","https://openalex.org/W1992379025","https://openalex.org/W394483113","https://openalex.org/W4287332642"],"abstract_inverted_index":{"In":[0,208],"some":[1],"studies":[2],"(e.g.,":[3,53],"[C.":[4],"Zhang":[5],"et":[6,56],"al.":[7],"in":[8,83,112,124,140,159],"Proceedings":[9,160],"of":[10,20,108,137,161,189,203,213,219],"the":[11,38,113,121,125,135,148,195,204,209,211],"5th":[12],"International":[13],"Conference":[14],"on":[15],"Learning":[16,163],"Representations,":[17],"OpenReview.net,":[18],"2017])":[19],"deep":[21,28],"learning,":[22],"it":[23],"is":[24,41],"observed":[25],"that":[26,170,185],"overparametrized":[27],"neural":[29],"networks":[30],"achieve":[31],"a":[32,99,106,130,182,186],"small":[33],"testing":[34,224],"error":[35,40,95,173],"even":[36],"when":[37],"training":[39,94,172],"almost":[42],"zero.":[43],"Despite":[44],"numerous":[45],"works":[46],"toward":[47],"understanding":[48],"this":[49,84],"so-called":[50],"double-descent":[51],"phenomenon":[52],"[M.":[54,151],"Belkin":[55],"al.,":[57],"Proc.":[58],"Natl.":[59],"Acad.":[60],"Sci.":[61],"USA,":[62],"116":[63],"(2019),":[64],"pp.":[65,81,168],"15849--15854;":[66],"M.":[67],"Belkin,":[68,152],"D.":[69],"Hsu,":[70],"and":[71,143,155,180,198,222],"J.":[72,75],"Xu,":[73],"SIAM":[74],"Math.":[76],"Data":[77],"Sci.,":[78],"2":[79],"(2020),":[80],"1167--1180]),":[82],"paper,":[85],"we":[86,104,128],"turn":[87],"to":[88,91],"another":[89],"way":[90],"enforce":[92],"zero":[93,171],"(without":[96],"overparametrization)":[97],"through":[98],"data":[100,138,190],"interpolation":[101,139,191],"mechanism.":[102],"Specifically,":[103],"consider":[105],"class":[107],"interpolated":[109],"weighting":[110],"schemes":[111],"nearest":[114],"neighbors":[115],"(NN)":[116],"algorithms.":[117],"By":[118],"carefully":[119],"characterizing":[120],"multiplicative":[122],"constant":[123],"statistical":[126,199],"risk,":[127],"reveal":[129],"U-shaped":[131],"performance":[132,197],"curve":[133],"for":[134],"level":[136],"both":[141],"classification":[142],"regression":[144],"setups.":[145],"This":[146],"sharpens":[147],"existing":[149],"result":[150,184],"A.":[153,156],"Rakhlin,":[154],"B.":[157],"Tsybakov,":[158],"Machine":[162],"Research":[164],"89,":[165],"PMLR,":[166],"2019,":[167],"1611--1619]":[169],"does":[174],"not":[175],"necessarily":[176],"jeopardize":[177],"predictive":[178],"performances":[179],"claims":[181],"counterintuitive":[183],"mild":[187],"degree":[188],"actually":[192],"strictly":[193],"improves":[194],"prediction":[196],"stability":[200],"over":[201],"those":[202],"(uninterpolated)":[205],"$k$-NN":[206],"algorithm.":[207],"end,":[210],"universality":[212],"our":[214],"results,":[215],"such":[216],"as":[217],"change":[218],"distance":[220],"measure":[221],"corrupted":[223],"data,":[225],"will":[226],"also":[227],"be":[228],"discussed.":[229]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-03T07:22:36.454288","created_date":"2025-10-10T00:00:00"}
