{"id":"https://openalex.org/W4225432521","doi":"https://doi.org/10.1109/tpami.2022.3172282","title":"On the Optimality of Sufficient Statistics-based Quantizers","display_name":"On the Optimality of Sufficient Statistics-based Quantizers","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4225432521","doi":"https://doi.org/10.1109/tpami.2022.3172282","pmid":"https://pubmed.ncbi.nlm.nih.gov/35503822"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2022.3172282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3172282","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","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/A5026166103","display_name":"Berkan D\u00fclek","orcid":"https://orcid.org/0000-0003-2126-7356"},"institutions":[{"id":"https://openalex.org/I66514158","display_name":"Hacettepe University","ror":"https://ror.org/04kwvgz42","country_code":"TR","type":"education","lineage":["https://openalex.org/I66514158"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Berkan Dulek","raw_affiliation_strings":["Electrical and Electronics Engineering, Hacettepe University, 37515 Ankara, Ankara, Turkey, 06800"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Electronics Engineering, Hacettepe University, 37515 Ankara, Ankara, Turkey, 06800","institution_ids":["https://openalex.org/I66514158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026166103"],"corresponding_institution_ids":["https://openalex.org/I66514158"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04269733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"3","first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9993000030517578,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7512633800506592},{"id":"https://openalex.org/keywords/exponential-family","display_name":"Exponential family","score":0.6769788861274719},{"id":"https://openalex.org/keywords/sufficient-statistic","display_name":"Sufficient statistic","score":0.5992954969406128},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.550887942314148},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5322228670120239},{"id":"https://openalex.org/keywords/fisher-information","display_name":"Fisher information","score":0.509895920753479},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.49165040254592896},{"id":"https://openalex.org/keywords/multivariate-random-variable","display_name":"Multivariate random variable","score":0.48337239027023315},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.45047032833099365},{"id":"https://openalex.org/keywords/order-statistic","display_name":"Order statistic","score":0.4389096796512604},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.4257635474205017},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42398571968078613},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.42050036787986755},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3649015426635742},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36198633909225464},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.351692795753479},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2087951898574829},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1942143440246582}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7512633800506592},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.6769788861274719},{"id":"https://openalex.org/C178197554","wikidata":"https://www.wikidata.org/wiki/Q1099110","display_name":"Sufficient statistic","level":2,"score":0.5992954969406128},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.550887942314148},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5322228670120239},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.509895920753479},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.49165040254592896},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.48337239027023315},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.45047032833099365},{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.4389096796512604},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.4257635474205017},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42398571968078613},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.42050036787986755},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3649015426635742},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36198633909225464},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.351692795753479},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2087951898574829},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1942143440246582},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2022.3172282","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3172282","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:35503822","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35503822","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":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W979878732","https://openalex.org/W1903172032","https://openalex.org/W1987719797","https://openalex.org/W2010683218","https://openalex.org/W2033497516","https://openalex.org/W2080037086","https://openalex.org/W2092977764","https://openalex.org/W2102909445","https://openalex.org/W2109808436","https://openalex.org/W2113111284","https://openalex.org/W2124509324","https://openalex.org/W2140405352","https://openalex.org/W2143059729","https://openalex.org/W2148620777","https://openalex.org/W2150472020","https://openalex.org/W2150593711","https://openalex.org/W2158336584","https://openalex.org/W2161160262","https://openalex.org/W2164996087","https://openalex.org/W2171801319","https://openalex.org/W2789716288","https://openalex.org/W3133603318","https://openalex.org/W3164441165","https://openalex.org/W4234494334","https://openalex.org/W4244017338","https://openalex.org/W4250589301","https://openalex.org/W4301459447","https://openalex.org/W4302561155"],"related_works":["https://openalex.org/W2050515813","https://openalex.org/W4256537608","https://openalex.org/W2010974761","https://openalex.org/W4312840083","https://openalex.org/W3209622190","https://openalex.org/W4254043250","https://openalex.org/W2042999809","https://openalex.org/W2045939383","https://openalex.org/W2779683126","https://openalex.org/W4225432521"],"abstract_inverted_index":{"Let":[0],"<inline-formula><tex-math":[1,12,18,36,43,50,59,83,133,147],"notation=\"LaTeX\">$X$</tex-math></inline-formula>":[2],"be":[3,26,87],"a":[4,10,27,41,57,90,173,180],"random":[5,48],"variable":[6,49],"taking":[7,38],"values":[8,39],"in":[9,40],"set":[11,42,76],"notation=\"LaTeX\">$\\mathcal":[13],"{X}$</tex-math></inline-formula>":[14],",":[15],"and":[16,185],"let":[17],"notation=\"LaTeX\">$\\lbrace":[19,148],"P_{\\theta":[20,149],"};":[21,150],"\\theta":[22,151],"\\in":[23,152],"\\Theta":[24,153],"\\rbrace$</tex-math></inline-formula>":[25,154],"family":[28],"of":[29,74,77,82,106,116,129,141,163,175],"distributions":[30,81],"indexed":[31],"by":[32,55,89],"the":[33,75,98,114,139,142,157,161],"parameter":[34,117,183],"vector":[35],"notation=\"LaTeX\">$\\theta$</tex-math></inline-formula>":[37],"notation=\"LaTeX\">$\\Theta$</tex-math></inline-formula>":[44],".":[45,66],"A":[46],"quantized":[47],"notation=\"LaTeX\">$\\gamma":[51,60,84],"(X)$</tex-math></inline-formula>":[52,85],"is":[53,68,120],"obtained":[54],"employing":[56],"quantizer":[58,92],":":[61],"\\mathcal":[62],"{X}\\rightarrow":[63],"\\lbrace":[64],"1,\\ldots,K\\rbrace$</tex-math></inline-formula>":[65],"It":[67,119],"shown":[69],"that":[70,93,122],"any":[71],"extreme":[72],"point":[73],"all":[78],"possible":[79],"probability":[80],"can":[86],"achieved":[88],"deterministic":[91,107],"decides":[94],"based":[95],"only":[96],"on":[97],"sufficient":[99,108,130],"statistics.":[100],"Using":[101],"this":[102,176],"fact,":[103],"optimality":[104,162],"properties":[105],"statistics-based":[109],"quantizers":[110],"are":[111],"established":[112],"for":[113,167],"problem":[115],"estimation.":[118],"proven":[121],"there":[123],"always":[124],"exists":[125],"an":[126],"optimal":[127],"partitioning":[128],"statistics":[131],"into":[132],"notation=\"LaTeX\">$K$</tex-math></inline-formula>":[134],"convex":[135],"polytopes":[136],"which":[137],"maximizes":[138],"trace":[140],"Fisher":[143],"information":[144],"matrix":[145],"when":[146],"belongs":[155],"to":[156],"exponential":[158],"family.":[159],"Furthermore,":[160],"likelihood":[164],"ratio":[165],"statistic":[166],"simple":[168],"hypothesis":[169,186],"testing":[170],"follows":[171],"as":[172],"consequence":[174],"result,":[177],"thereby":[178],"demonstrating":[179],"link":[181],"between":[182],"estimation":[184],"testing.":[187]},"counts_by_year":[],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}