{"id":"https://openalex.org/W2761184298","doi":"https://doi.org/10.1137/1.9781611975031.173","title":"Improved Coresets for Kernel Density Estimates","display_name":"Improved Coresets for Kernel Density Estimates","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2761184298","doi":"https://doi.org/10.1137/1.9781611975031.173","mag":"2761184298"},"language":"en","primary_location":{"id":"doi:10.1137/1.9781611975031.173","is_oa":true,"landing_page_url":"https://doi.org/10.1137/1.9781611975031.173","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611975031.173","source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"book-chapter"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611975031.173","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017619650","display_name":"Jeff M. Phillips","orcid":"https://orcid.org/0000-0003-1169-2965"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeff M. Phillips","raw_affiliation_strings":["University of Utah"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Utah","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054516039","display_name":"Wai Ming Tai","orcid":"https://orcid.org/0000-0003-4933-7299"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wai Ming Tai","raw_affiliation_strings":["University of Utah"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Utah","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017619650"],"corresponding_institution_ids":["https://openalex.org/I223532165"],"apc_list":null,"apc_paid":null,"fwci":1.2395,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.8137121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"2718","last_page":"2727"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9909999966621399,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.989799976348877,"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/mathematics","display_name":"Mathematics","score":0.7113038301467896},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6434041261672974},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5501710176467896},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5147795677185059},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.48021063208580017},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4639984965324402},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.451494425535202},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4315221905708313},{"id":"https://openalex.org/keywords/kernel-density-estimation","display_name":"Kernel density estimation","score":0.4226102828979492},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.4140707552433014},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32917898893356323},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20899692177772522},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11839106678962708},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11637410521507263},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11206838488578796},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08295834064483643},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.06768864393234253}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7113038301467896},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6434041261672974},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5501710176467896},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5147795677185059},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48021063208580017},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4639984965324402},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.451494425535202},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4315221905708313},{"id":"https://openalex.org/C71134354","wikidata":"https://www.wikidata.org/wiki/Q458825","display_name":"Kernel density estimation","level":3,"score":0.4226102828979492},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.4140707552433014},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32917898893356323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20899692177772522},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11839106678962708},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11637410521507263},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11206838488578796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08295834064483643},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.06768864393234253},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/1.9781611975031.173","is_oa":true,"landing_page_url":"https://doi.org/10.1137/1.9781611975031.173","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611975031.173","source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:1710.04325","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04325","pdf_url":"https://arxiv.org/pdf/1710.04325","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":"","raw_type":"text"},{"id":"mag:2761184298","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.04325.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1710.04325","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.04325","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1137/1.9781611975031.173","is_oa":true,"landing_page_url":"https://doi.org/10.1137/1.9781611975031.173","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/1.9781611975031.173","source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W905619","https://openalex.org/W186585364","https://openalex.org/W1480714498","https://openalex.org/W1560724230","https://openalex.org/W1818863960","https://openalex.org/W1973264045","https://openalex.org/W1975041502","https://openalex.org/W1985142965","https://openalex.org/W1986280275","https://openalex.org/W2025822499","https://openalex.org/W2042294756","https://openalex.org/W2065833332","https://openalex.org/W2072227363","https://openalex.org/W2073020428","https://openalex.org/W2082366275","https://openalex.org/W2097033210","https://openalex.org/W2109706083","https://openalex.org/W2115252011","https://openalex.org/W2118020555","https://openalex.org/W2123602290","https://openalex.org/W2124331852","https://openalex.org/W2129905273","https://openalex.org/W2136885855","https://openalex.org/W2162798864","https://openalex.org/W2163288162","https://openalex.org/W2212660284","https://openalex.org/W2290426984","https://openalex.org/W2328111639","https://openalex.org/W2551238896","https://openalex.org/W2580163882","https://openalex.org/W2952152543","https://openalex.org/W2963154349","https://openalex.org/W2963169589","https://openalex.org/W2963455192","https://openalex.org/W2964181129"],"related_works":["https://openalex.org/W2963982011","https://openalex.org/W2963075731","https://openalex.org/W2888383612","https://openalex.org/W2989721195","https://openalex.org/W3198734116","https://openalex.org/W3087437447","https://openalex.org/W3171084445","https://openalex.org/W3153809844","https://openalex.org/W2995322306","https://openalex.org/W3023160755","https://openalex.org/W3022305391","https://openalex.org/W2613688792","https://openalex.org/W2624941619","https://openalex.org/W2132032691","https://openalex.org/W2140793251","https://openalex.org/W3113827893","https://openalex.org/W2964126381","https://openalex.org/W2952131701","https://openalex.org/W2736964003","https://openalex.org/W2990379149"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,17,49,68,71,73,76,80,83,90,117,146,157,160,172,175,181,198],"construction":[3],"of":[4,67,75,82,116,136,159,174],"coresets":[5],"for":[6,100,163,177,204],"kernel":[7,18,29,53,84,128],"density":[8,19,30,54],"estimates.":[9],"That":[10],"is":[11,92,98,149,169,186],"we":[12,94,151],"show":[13,95],"how":[14],"to":[15,86,122],"approximate":[16],"estimate":[20,31],"described":[21],"by":[22,171,194],"a":[23,33,106,113,133],"large":[24],"point":[25,36,77],"set":[26],"with":[27,32,59],"another":[28],"much":[34,107,153],"smaller":[35],"set.":[37,109],"For":[38],"characteristic":[39],"kernels":[40,102],"(including":[41],"Gaussian":[42,164],"and":[43,143,188],"Laplace":[44],"kernels),":[45],"our":[46],"approximation":[47],"preserves":[48],"L\u221e":[50],"error":[51,57],"between":[52],"estimates":[55],"within":[56],"\u03b5,":[58],"coreset":[60,161,176],"size":[61,158,173],"4/\u03b52,":[62],"but":[63],"no":[64],"other":[65,87],"aspects":[66],"data,":[69],"including":[70],"dimension,":[72],"diameter":[74],"set,":[78],"or":[79],"bandwidth":[81],"common":[85],"approximations.":[88],"When":[89,145],"dimension":[91,147,201],"unrestricted,":[93],"this":[96,123,190],"bound":[97,185],"tight":[99],"these":[101],"as":[103,105],"well":[104],"broader":[108],"This":[110,130,196],"work":[111,137],"provides":[112],"careful":[114],"analysis":[115,131],"iterative":[118],"Frank-Wolfe":[119],"algorithm":[120,126],"adapted":[121],"context,":[124],"an":[125],"called":[127],"herding.":[129],"unites":[132],"broad":[134],"line":[135],"that":[138,167],"spans":[139],"statistics,":[140],"machine":[141],"learning,":[142],"geometry.":[144],"d":[148,205],"constant,":[150],"demonstrate":[152],"tighter":[154],"bounds":[155,202],"on":[156],"specifically":[162],"kernels,":[165],"showing":[166],"it":[168],"bounded":[170],"axis-aligned":[178],"rectangles.":[179],"Currently":[180],"best":[182,199],"known":[183],"constructive":[184],",":[187],"non-constructively,":[189],"can":[191],"be":[192],"improved":[193],".":[195],"improves":[197],"constant":[200],"polynomially":[203],"\u2265":[206],"3.":[207]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-19T21:40:30.786675","created_date":"2025-10-10T00:00:00"}
