{"id":"https://openalex.org/W2771022413","doi":"https://doi.org/10.1109/allerton.2018.8635825","title":"Parameter Estimation in Gaussian Mixture Models with Malicious Noise, without Balanced Mixing Coefficients","display_name":"Parameter Estimation in Gaussian Mixture Models with Malicious Noise, without Balanced Mixing Coefficients","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2771022413","doi":"https://doi.org/10.1109/allerton.2018.8635825","mag":"2771022413"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2018.8635825","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2018.8635825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.08082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101560666","display_name":"Jing Xu","orcid":"https://orcid.org/0000-0002-0848-2361"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]},{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jing Xu","raw_affiliation_strings":["Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I4210131439","https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003656133","display_name":"Jakub Mare\u010dek","orcid":"https://orcid.org/0000-0003-0839-0691"},"institutions":[{"id":"https://openalex.org/I4210145784","display_name":"IBM Research - Ireland","ror":"https://ror.org/04jnxr720","country_code":"IE","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210145784"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Jakub Marecek","raw_affiliation_strings":["IBM Research \u2013 Ireland, Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research \u2013 Ireland, Dublin, Ireland","institution_ids":["https://openalex.org/I4210145784"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"abs 1711 8082","issue":null,"first_page":"446","last_page":"453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9965999722480774,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9965999722480774,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mahalanobis-distance","display_name":"Mahalanobis distance","score":0.7506368160247803},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.6307544112205505},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.6241836547851562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.611499547958374},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5972443222999573},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.587312638759613},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5706946849822998},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5654646158218384},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5489205121994019},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5270453095436096},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5159995555877686},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5053487420082092},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4133090376853943},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33320504426956177},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3263947367668152},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2722461223602295},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18555426597595215},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14528179168701172},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10128393769264221}],"concepts":[{"id":"https://openalex.org/C1921717","wikidata":"https://www.wikidata.org/wiki/Q1334846","display_name":"Mahalanobis distance","level":2,"score":0.7506368160247803},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.6307544112205505},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.6241836547851562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.611499547958374},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5972443222999573},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.587312638759613},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5706946849822998},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5654646158218384},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5489205121994019},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5270453095436096},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5159995555877686},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5053487420082092},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4133090376853943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33320504426956177},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3263947367668152},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2722461223602295},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18555426597595215},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14528179168701172},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10128393769264221},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":2,"locations":[{"id":"doi:10.1109/allerton.2018.8635825","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2018.8635825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1711.08082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.08082","pdf_url":"https://arxiv.org/pdf/1711.08082","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.08082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.08082","pdf_url":"https://arxiv.org/pdf/1711.08082","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1524622012","https://openalex.org/W1540596182","https://openalex.org/W1560153690","https://openalex.org/W2022852240","https://openalex.org/W2026593911","https://openalex.org/W2030991582","https://openalex.org/W2046033161","https://openalex.org/W2052044664","https://openalex.org/W2062817469","https://openalex.org/W2098288588","https://openalex.org/W2099020507","https://openalex.org/W2111992537","https://openalex.org/W2138967244","https://openalex.org/W2140956445","https://openalex.org/W2464464020","https://openalex.org/W2488678869","https://openalex.org/W2601154487","https://openalex.org/W2605817644","https://openalex.org/W2768353504","https://openalex.org/W2771022413","https://openalex.org/W2797746357","https://openalex.org/W2911742394","https://openalex.org/W2962737134","https://openalex.org/W2962856918","https://openalex.org/W2963351358","https://openalex.org/W2964207716","https://openalex.org/W4249736682","https://openalex.org/W6631330567","https://openalex.org/W6633707392","https://openalex.org/W6680662047","https://openalex.org/W6680776171","https://openalex.org/W6735559455","https://openalex.org/W6746041533"],"related_works":["https://openalex.org/W4382795578","https://openalex.org/W2355463328","https://openalex.org/W2402648945","https://openalex.org/W1431147547","https://openalex.org/W2771741613","https://openalex.org/W2055761197","https://openalex.org/W2053213469","https://openalex.org/W2886934452","https://openalex.org/W1489099099","https://openalex.org/W2024369332"],"abstract_inverted_index":{"We":[0,28],"consider":[1],"the":[2,6,21,35,42,48,52,57,61,64,67,80,87,103],"problem":[3],"of":[4,8,24,44,60,66,72,79,110,114],"estimating":[5],"means":[7],"components":[9],"in":[10,70,112],"a":[11,30,76],"noisy":[12],"2-Gaussian":[13],"Mixture":[14],"Model":[15],"(2-GMM)":[16],"without":[17],"balanced":[18],"weights,":[19],"where":[20,51],"noise":[22],"is":[23,86],"an":[25],"arbitrary":[26],"distribution.":[27],"present":[29],"robust":[31],"algorithm":[32,101,107],"to":[33],"estimate":[34],"parameters,":[36],"together":[37],"with":[38],"upper":[39],"bounds":[40,53],"on":[41],"numbers":[43],"samples":[45],"required":[46],"for":[47,91],"good":[49],"estimates,":[50],"are":[54],"parametrised":[55],"by":[56,95,108],"dimension,":[58],"ratio":[59],"mixing":[62],"coefficients,":[63],"separation":[65],"two":[68],"Gaussians":[69],"terms":[71,113],"Mahalanobis":[73],"distance,":[74],"and":[75],"condition":[77],"number":[78],"covariance":[81],"matrix.":[82],"In":[83,98],"theory,":[84],"this":[85],"first":[88],"sample-complexity":[89],"result":[90],"Gaussian":[92],"mixtures":[93],"corrupted":[94],"adversarial":[96],"noise.":[97],"practice,":[99],"our":[100],"outperforms":[102],"vanilla":[104],"Expectation-Maximisation":[105],"(EM)":[106],"orders":[109],"magnitude":[111],"estimation":[115],"error.":[116]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
