{"id":"https://openalex.org/W2306907554","doi":"https://doi.org/10.1162/neco_a_01035","title":"Sufficient Dimension Reduction via Direct Estimation of the Gradients of Logarithmic Conditional Densities","display_name":"Sufficient Dimension Reduction via Direct Estimation of the Gradients of Logarithmic Conditional Densities","publication_year":2017,"publication_date":"2017-11-22","ids":{"openalex":"https://openalex.org/W2306907554","doi":"https://doi.org/10.1162/neco_a_01035","mag":"2306907554","pmid":"https://pubmed.ncbi.nlm.nih.gov/29162006"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01035","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01035","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5047718379","display_name":"Hiroaki Sasaki","orcid":"https://orcid.org/0000-0001-9897-8557"},"institutions":[{"id":"https://openalex.org/I75917431","display_name":"Nara Institute of Science and Technology","ror":"https://ror.org/05bhada84","country_code":"JP","type":"education","lineage":["https://openalex.org/I75917431"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Hiroaki Sasaki","raw_affiliation_strings":["Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Japan","Nara Institute of Science and Technology, Ikoma, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Japan","institution_ids":["https://openalex.org/I75917431"]},{"raw_affiliation_string":"Nara Institute of Science and Technology, Ikoma, Japan","institution_ids":["https://openalex.org/I75917431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055819776","display_name":"Voot Tangkaratt","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Voot Tangkaratt","raw_affiliation_strings":["Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan","Tokyo Institute of Technology, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan","institution_ids":["https://openalex.org/I4210126580"]},{"raw_affiliation_string":"Tokyo Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Gang Niu","orcid":null},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Gang Niu","raw_affiliation_strings":["Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-033, Japan","The University of Tokyo, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-033, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"The University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":null,"display_name":"Masashi Sugiyama","orcid":null},"institutions":[{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masashi Sugiyama","raw_affiliation_strings":["Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan, and Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-033, Japan"],"affiliations":[{"raw_affiliation_string":"Center for Advanced Intelligence Project, RIKEN, Tokyo 103-0027, Japan, and Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-033, Japan","institution_ids":["https://openalex.org/I4210126580","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047718379"],"corresponding_institution_ids":["https://openalex.org/I75917431"],"apc_list":null,"apc_paid":null,"fwci":0.2466,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50586788,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"30","issue":"2","first_page":"477","last_page":"504"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9745000004768372,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9745000004768372,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.963100016117096,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/dimension","display_name":"Dimension (graph theory)","score":0.6867698431015015},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6531335711479187},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6473714113235474},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6031091809272766},{"id":"https://openalex.org/keywords/sufficient-dimension-reduction","display_name":"Sufficient dimension reduction","score":0.484031617641449},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4755104184150696},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.43662557005882263},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.39131417870521545},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3510444462299347},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3387755751609802},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32682472467422485},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1889060139656067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1665675938129425},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12326857447624207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10743087530136108},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06656920909881592}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6867698431015015},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6531335711479187},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6473714113235474},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6031091809272766},{"id":"https://openalex.org/C27931671","wikidata":"https://www.wikidata.org/wiki/Q7634497","display_name":"Sufficient dimension reduction","level":3,"score":0.484031617641449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4755104184150696},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.43662557005882263},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.39131417870521545},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3510444462299347},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3387755751609802},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32682472467422485},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1889060139656067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1665675938129425},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12326857447624207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10743087530136108},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06656920909881592},{"id":"https://openalex.org/C201995342","wikidata":"https://www.wikidata.org/wiki/Q682496","display_name":"Systems engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1162/neco_a_01035","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01035","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:29162006","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29162006","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.714.4419","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.714.4419","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ms.k.u-tokyo.ac.jp/2015/ACML2015e.pdf","raw_type":"text"},{"id":"mag:2306907554","is_oa":false,"landing_page_url":"http://proceedings.mlr.press/v45/Sasaki15.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306417739","display_name":"Asian Conference on Machine Learning","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Asian Conference on Machine Learning","raw_type":null},{"id":"mag:2969813877","is_oa":false,"landing_page_url":"https://www.ieice.org/ken/paper/20151127Xbee/eng/","pdf_url":null,"source":{"id":"https://openalex.org/S4306512848","display_name":"IEICE Technical Report; IEICE Tech. Rep.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IEICE Technical Report; IEICE Tech. Rep.","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/13","score":0.5,"display_name":"Climate action"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1560724230","https://openalex.org/W1855110042","https://openalex.org/W1971901677","https://openalex.org/W1978930294","https://openalex.org/W1997384244","https://openalex.org/W2000125728","https://openalex.org/W2013974460","https://openalex.org/W2022238100","https://openalex.org/W2036163871","https://openalex.org/W2072460512","https://openalex.org/W2087717467","https://openalex.org/W2104320806","https://openalex.org/W2118543192","https://openalex.org/W2144405862","https://openalex.org/W2153635508","https://openalex.org/W2163490846","https://openalex.org/W2171050905","https://openalex.org/W2963815578","https://openalex.org/W4233014035","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2969813877","https://openalex.org/W1972848408","https://openalex.org/W1493751439","https://openalex.org/W2066571230","https://openalex.org/W2507824376","https://openalex.org/W2064480878","https://openalex.org/W2030109712","https://openalex.org/W2801399199","https://openalex.org/W1485843233","https://openalex.org/W1970827259","https://openalex.org/W2070355618","https://openalex.org/W2016292827","https://openalex.org/W2896986837","https://openalex.org/W1559685118","https://openalex.org/W2935535449","https://openalex.org/W1856113194","https://openalex.org/W2082168962","https://openalex.org/W1594158428"],"abstract_inverted_index":{"Sufficient":[0],"dimension":[1],"reduction":[2],"(SDR)":[3],"is":[4,22,33],"aimed":[5],"at":[6],"obtaining":[7],"the":[8,13,36,39,43,46,62,65,76,80,108,116,123,130],"low-rank":[9],"projection":[10],"matrix":[11],"in":[12,95,148],"input":[14],"space":[15],"such":[16],"that":[17,69,115,139],"information":[18],"about":[19],"output":[20,50],"data":[21,161],"maximally":[23],"preserved.":[24],"Among":[25],"various":[26],"approaches":[27,147],"to":[28,75,84],"SDR,":[29],"a":[30,58,72,96,102,155],"promising":[31],"method":[32,105,142],"based":[34,106],"on":[35,107,154],"eigendecomposition":[37],"of":[38,42,45,49,61,64,157],"outer":[40],"product":[41],"gradient":[44,63,78,110,118],"conditional":[47,67],"density":[48,68],"given":[51],"input.":[52],"In":[53],"this":[54,85],"letter,":[55],"we":[56,100,136],"propose":[57],"novel":[59],"estimator":[60],"logarithmic":[66],"directly":[70],"fits":[71],"linear-in-parameter":[73],"model":[74],"true":[77],"under":[79],"squared":[81],"loss.":[82],"Thanks":[83],"simple":[86],"least-squares":[87],"formulation,":[88],"its":[89],"solution":[90,125],"can":[91],"be":[92],"computed":[93],"efficiently":[94],"closed":[97],"form.":[98],"Then":[99],"develop":[101],"new":[103],"SDR":[104,124,141],"proposed":[109,117],"estimator.":[111],"We":[112],"theoretically":[113],"prove":[114],"estimator,":[119],"as":[120,122],"well":[121],"obtained":[126],"from":[127],"it,":[128],"achieves":[129],"optimal":[131],"parametric":[132],"convergence":[133],"rate.":[134],"Finally,":[135],"experimentally":[137],"demonstrate":[138],"our":[140],"compares":[143],"favorably":[144],"with":[145],"existing":[146],"both":[149],"accuracy":[150],"and":[151,159],"computational":[152],"efficiency":[153],"variety":[156],"artificial":[158],"benchmark":[160],"sets.":[162]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}