{"id":"https://openalex.org/W3091802565","doi":"https://doi.org/10.1145/3417994","title":"Near-optimal Sample Complexity Bounds for Robust Learning of Gaussian Mixtures via Compression Schemes","display_name":"Near-optimal Sample Complexity Bounds for Robust Learning of Gaussian Mixtures via Compression Schemes","publication_year":2020,"publication_date":"2020-10-06","ids":{"openalex":"https://openalex.org/W3091802565","doi":"https://doi.org/10.1145/3417994","mag":"3091802565"},"language":"en","primary_location":{"id":"doi:10.1145/3417994","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3417994","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051338636","display_name":"Hassan Ashtiani","orcid":"https://orcid.org/0000-0003-1758-7330"},"institutions":[{"id":"https://openalex.org/I4210127509","display_name":"Vector Institute","ror":"https://ror.org/03kqdja62","country_code":"CA","type":"facility","lineage":["https://openalex.org/I4210127509"]},{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Hassan Ashtiani","raw_affiliation_strings":["McMaster University, Canada and Vector Institute, Toronto, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McMaster University, Canada and Vector Institute, Toronto, Ontario, Canada","institution_ids":["https://openalex.org/I4210127509","https://openalex.org/I98251732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112193907","display_name":"Shai Ben-David","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shai Ben-David","raw_affiliation_strings":["University of Waterloo, Waterloo, Ontario, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102957872","display_name":"Nicholas J. A. Harvey","orcid":"https://orcid.org/0000-0001-5593-9785"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nicholas J. A. Harvey","raw_affiliation_strings":["University of British Columbia, British Columbia, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of British Columbia, British Columbia, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076085270","display_name":"Christopher Liaw","orcid":"https://orcid.org/0000-0001-5373-9229"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Christopher Liaw","raw_affiliation_strings":["University of British Columbia, British Columbia, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of British Columbia, British Columbia, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089076722","display_name":"Abbas Mehrabian","orcid":"https://orcid.org/0000-0002-0658-7709"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Abbas Mehrabian","raw_affiliation_strings":["McGill University, Montr\u00e9al, Qu\u00e9bec Canada"],"raw_orcid":"https://orcid.org/0000-0002-0658-7709","affiliations":[{"raw_affiliation_string":"McGill University, Montr\u00e9al, Qu\u00e9bec Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018866413","display_name":"Yaniv Plan","orcid":"https://orcid.org/0000-0002-9930-0980"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yaniv Plan","raw_affiliation_strings":["University of British Columbia, Vancouver, British Columbia, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of British Columbia, Vancouver, British Columbia, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8957,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.8899354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"67","issue":"6","first_page":"1","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9936000108718872,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9866999983787537,"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/mixture-model","display_name":"Mixture model","score":0.7876343727111816},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7531620264053345},{"id":"https://openalex.org/keywords/compression","display_name":"Compression (physics)","score":0.7045219540596008},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6914387941360474},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.620982825756073},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.587828516960144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46817702054977417},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.447353720664978},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.445472776889801},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.441249281167984},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42401111125946045},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42292749881744385},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4196428656578064},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23165175318717957},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1428426206111908},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0851275622844696},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0797635018825531}],"concepts":[{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.7876343727111816},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7531620264053345},{"id":"https://openalex.org/C180016635","wikidata":"https://www.wikidata.org/wiki/Q2712821","display_name":"Compression (physics)","level":2,"score":0.7045219540596008},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6914387941360474},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.620982825756073},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.587828516960144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46817702054977417},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.447353720664978},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.445472776889801},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.441249281167984},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42401111125946045},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42292749881744385},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4196428656578064},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23165175318717957},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1428426206111908},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0851275622844696},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0797635018825531},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3417994","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3417994","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6870196779","display_name":null,"funder_award_id":"22R23068","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W44213566","https://openalex.org/W124167277","https://openalex.org/W786265215","https://openalex.org/W1511694993","https://openalex.org/W1533335487","https://openalex.org/W1560153690","https://openalex.org/W1585566614","https://openalex.org/W1594991866","https://openalex.org/W1746819321","https://openalex.org/W1796325169","https://openalex.org/W1956647075","https://openalex.org/W1965555277","https://openalex.org/W1974088667","https://openalex.org/W1999370902","https://openalex.org/W2010072035","https://openalex.org/W2014569888","https://openalex.org/W2026302946","https://openalex.org/W2063178190","https://openalex.org/W2095374884","https://openalex.org/W2129905273","https://openalex.org/W2143122862","https://openalex.org/W2154952480","https://openalex.org/W2231267930","https://openalex.org/W2340736170","https://openalex.org/W2496316373","https://openalex.org/W2601251344","https://openalex.org/W2753338564","https://openalex.org/W2808660397","https://openalex.org/W2896292273","https://openalex.org/W2900689674","https://openalex.org/W2902088824","https://openalex.org/W2939797295","https://openalex.org/W2950664431","https://openalex.org/W2957821713","https://openalex.org/W2990138404","https://openalex.org/W3037947134","https://openalex.org/W4205818646","https://openalex.org/W4236653259","https://openalex.org/W4238284510","https://openalex.org/W4240981432","https://openalex.org/W4248289108","https://openalex.org/W4249716558","https://openalex.org/W4250589301","https://openalex.org/W4250954493","https://openalex.org/W6756188728"],"related_works":["https://openalex.org/W4376639527","https://openalex.org/W1991417304","https://openalex.org/W2132876566","https://openalex.org/W1967080779","https://openalex.org/W1969276875","https://openalex.org/W4323706382","https://openalex.org/W2612632602","https://openalex.org/W2788738055","https://openalex.org/W2950049300","https://openalex.org/W4299895404"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,10,23,34,40,77,123,147,168],"novel":[3],"technique":[4],"for":[5,75,104],"distribution":[6,143],"learning":[7,76,134],"based":[8],"on":[9],"notion":[11],"of":[12,18,36,48,52,58,79,109,149,162],"sample":[13],"compression":[14,24,41,170],".":[15],"Any":[16],"class":[17,35,161],"distributions":[19,37],"that":[20,63,114,159],"allows":[21],"such":[22,39],"scheme":[25],"can":[26],"be":[27],"learned":[28],"with":[29],"few":[30],"samples.":[31],"Moreover,":[32,127],"if":[33],"has":[38],"scheme,":[42],"then":[43],"so":[44],"do":[45],"the":[46,97,141,160],"classes":[47],"products":[49],"and":[50,73,101],"mixtures":[51,108],"those":[53],"distributions.":[54],"As":[55],"an":[56,132],"application":[57],"this":[59,105],"technique,":[60],"we":[61,112],"prove":[62],"\u02dc\u0398(":[64],"kd":[65,116],"2":[66,68,118],"/\u03b5":[67,117],")":[69,119],"samples":[70,120],"are":[71],"necessary":[72],"sufficient":[74],"mixture":[78,148],"k":[80],"Gaussians":[81,163],"in":[82,90,131,139,164],"R":[83,165],"d":[84,166],",":[85],"up":[86],"to":[87],"error":[88],"\u03b5":[89],"total":[91],"variation":[92],"distance.":[93],"This":[94],"improves":[95],"both":[96],"known":[98,124],"upper":[99,153],"bounds":[100,103],"lower":[102,125],"problem.":[106],"For":[107],"axis-aligned":[110],"Gaussians,":[111],"show":[113],"\u00d5(":[115],"suffice,":[121],"matching":[122],"bound.":[126],"these":[128],"results":[129],"hold":[130],"agnostic":[133],"(or":[135],"robust":[136],"estimation)":[137],"setting,":[138],"which":[140],"target":[142],"is":[144,155],"only":[145],"approximately":[146],"Gaussians.":[150],"Our":[151],"main":[152],"bound":[154],"proven":[156],"by":[157],"showing":[158],"admits":[167],"small":[169],"scheme.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
