{"id":"https://openalex.org/W2185411978","doi":null,"title":"A New Computational Approach to Density Estimation with Semidefinite Programming","display_name":"A New Computational Approach to Density Estimation with Semidefinite Programming","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2185411978","mag":"2185411978"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.399.8356","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.399.8356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2003/11/783.pdf","raw_type":"text"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5085043629","display_name":"Tadayoshi Fushiki","orcid":"https://orcid.org/0000-0002-1115-4692","observed_orcids":["https://orcid.org/0000-0002-1115-4692"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tadayoshi Fushiki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114067893","display_name":"Shingo Horiuchi","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shingo Horiuchi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020790231","display_name":"Takashi Tsuchiya","orcid":"https://orcid.org/0000-0002-6950-6160","observed_orcids":["https://orcid.org/0000-0002-6950-6160"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Takashi Tsuchiya","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6950-6160","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3279,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48494845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9160000085830688,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9160000085830688,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.022600000724196434,"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/T10136","display_name":"Statistical Methods and Inference","score":0.01269999984651804,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/density-estimation","display_name":"density estimation","score":0.9980000257492065},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"semidefinite programming","score":0.9990000128746033},{"id":"https://openalex.org/keywords/non-negativity-constraints","display_name":"nonnegativity constraints","score":0.8169999718666077},{"id":"https://openalex.org/keywords/maximum-likelihood-estimation","display_name":"maximum likelihood estimation","score":0.9660000205039978},{"id":"https://openalex.org/keywords/interior-point-methods","display_name":"interior point methods","score":0.8889999985694885},{"id":"https://openalex.org/keywords/primal-dual-algorithm","display_name":"primal-dual algorithm","score":0.7749999761581421},{"id":"https://openalex.org/keywords/unimodal-density","display_name":"unimodal density","score":0.6809999942779541},{"id":"https://openalex.org/keywords/akaike-information-criterion","display_name":"Akaike information criterion","score":0.9120000004768372},{"id":"https://openalex.org/keywords/model-selection","display_name":"model selection","score":0.734000027179718}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.8115192651748657},{"id":"https://openalex.org/C21596040","wikidata":"https://www.wikidata.org/wiki/Q2896771","display_name":"Unimodality","level":2,"score":0.7877427935600281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.757545530796051},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6553902626037598},{"id":"https://openalex.org/C126674687","wikidata":"https://www.wikidata.org/wiki/Q1662573","display_name":"Akaike information criterion","level":2,"score":0.6532489657402039},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6119391918182373},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.5152652263641357},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5005345344543457},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44199851155281067},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.4171587824821472},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1867573857307434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09070444107055664},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.07947543263435364},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.399.8356","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.399.8356","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2003/11/783.pdf","raw_type":"text"},{"id":"mag:2185411978","doi":null,"is_oa":false,"landing_page_url":"http://www.optimization-online.org/DB_FILE/2003/11/783.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W16952281","https://openalex.org/W45917502","https://openalex.org/W171686316","https://openalex.org/W204885769","https://openalex.org/W813566965","https://openalex.org/W1568307856","https://openalex.org/W1579271636","https://openalex.org/W1806104592","https://openalex.org/W1963753244","https://openalex.org/W1967073510","https://openalex.org/W1983768315","https://openalex.org/W1993000710","https://openalex.org/W1993566124","https://openalex.org/W2006043936","https://openalex.org/W2024318675","https://openalex.org/W2024424774","https://openalex.org/W2025486357","https://openalex.org/W2028570814","https://openalex.org/W2058815839","https://openalex.org/W2066459185","https://openalex.org/W2067244657","https://openalex.org/W2075379600","https://openalex.org/W2077274614","https://openalex.org/W2077866122","https://openalex.org/W2084622916","https://openalex.org/W2095734615","https://openalex.org/W2117065890","https://openalex.org/W2128202699","https://openalex.org/W2142635246","https://openalex.org/W2167641446","https://openalex.org/W2481044684","https://openalex.org/W2495457432","https://openalex.org/W2795536332","https://openalex.org/W2912522929"],"related_works":["https://openalex.org/W1968333654","https://openalex.org/W7096506027","https://openalex.org/W3212971401","https://openalex.org/W1965731860","https://openalex.org/W2100647910","https://openalex.org/W2026452695","https://openalex.org/W3033864370","https://openalex.org/W2905464459","https://openalex.org/W2004191624","https://openalex.org/W172848683"],"abstract_inverted_index":{"Density":[0],"estimation":[1,24,90],"is":[2,15,72,85,97,131,144,184,208],"a":[3,18,30,42,48,52,75,100],"classical":[4],"and":[5,51,61,193,226],"important":[6],"problem":[7],"in":[8,34,36,108],"statistics.":[9],"The":[10,64,169,181],"aim":[11],"of":[12,47,91,94,102,151,179,223,228],"this":[13],"paper":[14],"to":[16,22,136,146,164,175,187,210,217],"develop":[17],"new":[19,31],"computational":[20],"approach":[21],"density":[23,43,54,84,119,167,202],"based":[25],"on":[26,69,200],"semidefinite":[27,76],"programming":[28],"(SDP),":[29],"technology":[32],"developed":[33,113],"optimization":[35],"the":[37,45,70,79,82,87,92,95,111,117,128,137,148,152,158,165,177,201,212,224,229],"last":[38],"decade.":[39],"We":[40],"express":[41,188],"as":[44,56,74,99,191],"product":[46],"nonnegative":[49],"polynomial":[50,71,96,138],"base":[53,83,118,166],"such":[55,189],"normal":[57],"distribution,":[58],"exponential":[59],"distribution":[60],"uniform":[62],"distribution.":[63],"difficult":[65],"nonnegativity":[66],"constraint":[67],"imposed":[68,199],"expressed":[73],"constraint.":[77],"Under":[78],"condition":[80],"that":[81],"specified,":[86],"maximum":[88,150],"likelihood":[89,129,153,160],"coefficients":[93],"formulated":[98],"variant":[101,178],"SDP":[103],"which":[104,195],"can":[105],"be":[106,197],"solved":[107],"polynomial-time":[109],"with":[110,134,162],"recently":[112],"interior-point":[114,171],"methods.":[115],"Since":[116],"typically":[120],"contains":[121],"just":[122],"one":[123],"or":[124],"two":[125],"parameters,":[126],"if":[127],"function":[130,154,161],"easily":[132],"maximized":[133],"respect":[135,163],"part":[139],"by":[140,155],"SDP,":[141],"then":[142],"it":[143],"possible":[145],"compute":[147],"global":[149],"further":[156],"maximizing":[157],"partially-maximized":[159],"parameter.":[168],"primal-dual":[170],"algorithms":[172],"are":[173],"used":[174,209],"solve":[176],"SDP.":[180],"proposed":[182,230],"model":[183,225],"flexible":[185],"enough":[186],"properties":[190],"unimodality":[192],"symmetry":[194],"would":[196],"reasonably":[198],"function.":[203],"AIC":[204],"(Akaike":[205],"information":[206],"criterion)":[207],"choose":[211],"best":[213],"model.":[214],"Through":[215],"applications":[216],"several":[218],"instances":[219],"we":[220],"demonstrate":[221],"flexibility":[222],"performance":[227],"procedure.":[231]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}