{"id":"https://openalex.org/W4413947019","doi":"https://doi.org/10.1109/tit.2025.3605342","title":"Some Facts About the Optimality of the LSE in the Gaussian Sequence Model With Convex Constraint","display_name":"Some Facts About the Optimality of the LSE in the Gaussian Sequence Model With Convex Constraint","publication_year":2025,"publication_date":"2025-09-02","ids":{"openalex":"https://openalex.org/W4413947019","doi":"https://doi.org/10.1109/tit.2025.3605342"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3605342","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3605342","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5093734267","display_name":"Akshay Prasadan","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Akshay Prasadan","raw_affiliation_strings":["Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA","Department of Statistics &#x0026; Data Science, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0009-0000-4143-0929","affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Statistics &#x0026; Data Science, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065273453","display_name":"Matey Neykov","orcid":"https://orcid.org/0000-0002-3320-3889"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matey Neykov","raw_affiliation_strings":["Department of Statistics and Data Science, Northwestern University, Evanston, IL, USA"],"raw_orcid":"https://orcid.org/0000-0002-3320-3889","affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5573,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85061728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"71","issue":"11","first_page":"8928","last_page":"8958"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.8932999968528748,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.8932999968528748,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.8294000029563904,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.8070999979972839,"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/constraint","display_name":"Constraint (computer-aided design)","score":0.6421169638633728},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6218499541282654},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.603854238986969},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5123056173324585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49718979001045227},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4637608528137207},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4283324182033539},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4008343517780304},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.394572913646698},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09029290080070496},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06277930736541748}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6421169638633728},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6218499541282654},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.603854238986969},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5123056173324585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49718979001045227},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4637608528137207},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4283324182033539},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4008343517780304},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.394572913646698},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09029290080070496},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06277930736541748},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3605342","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3605342","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1524622012","https://openalex.org/W1964213467","https://openalex.org/W1969705577","https://openalex.org/W2004853061","https://openalex.org/W2024589123","https://openalex.org/W2055734527","https://openalex.org/W2127991572","https://openalex.org/W2167077875","https://openalex.org/W2488793974","https://openalex.org/W2962735944","https://openalex.org/W2963283829","https://openalex.org/W2965064783","https://openalex.org/W2973002561","https://openalex.org/W3034124940","https://openalex.org/W3049028083","https://openalex.org/W3110679391","https://openalex.org/W3212589533","https://openalex.org/W4211030719","https://openalex.org/W4250954493","https://openalex.org/W4293860921","https://openalex.org/W4312431902","https://openalex.org/W4405603477"],"related_works":["https://openalex.org/W2807251790","https://openalex.org/W2799406489","https://openalex.org/W2049792449","https://openalex.org/W986251431","https://openalex.org/W2884465220","https://openalex.org/W2112284452","https://openalex.org/W563727013","https://openalex.org/W2502468346","https://openalex.org/W1964286703","https://openalex.org/W2169866437"],"abstract_inverted_index":{"We":[0,66,91,107,119],"consider":[1],"a":[2,25,98],"convex":[3,27],"constrained":[4],"Gaussian":[5,85,104],"sequence":[6],"model":[7],"and":[8,11,55,61,148],"characterize":[9,67],"necessary":[10],"sufficient":[12],"conditions":[13],"for":[14,45,114,138],"the":[15,68,73,80,83,102,115,128],"least":[16],"squares":[17],"estimator":[18],"(LSE)":[19],"to":[20,63,97],"be":[21],"minimax":[22],"optimal.":[23],"For":[24],"closed":[26],"set":[28],"<italic":[29,38,48,58,88,139],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[30,34,39,49,51,53,59,89,135,140],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">K</i>":[31,60],"\u2282":[32],"R<sup":[33],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>n</i></sup>":[35],"we":[36],"observe":[37],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Y</i>":[40],"=":[41],"\u03bc":[42,56],"+":[43],"\u03be":[44,46],"~":[47],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>(0,\u03c3<sup":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>I<sub":[52],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>)":[54],"\u2208":[57,142],"aim":[62],"estimate":[64],"\u03bc.":[65],"worst":[69,116],"case":[70,117],"risk":[71],"of":[72,82,101,127,146],"LSE":[74,129],"in":[75],"multiple":[76],"ways":[77],"by":[78],"analyzing":[79],"behavior":[81],"local":[84,103],"width":[86,105],"on":[87,130],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">K</i>.":[90],"demonstrate":[92],"that":[93,112],"optimality":[94,124],"is":[95],"equivalent":[96],"Lipschitz":[99],"property":[100],"mapping.":[106],"also":[108],"provide":[109,121],"theoretical":[110],"algorithms":[111],"search":[113],"risk.":[118],"then":[120],"examples":[122],"showing":[123],"or":[125],"suboptimality":[126],"various":[131],"sets,":[132],"including":[133],"\u2113<sub":[134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><i>p</i></sub>":[136],"balls":[137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</i>":[141],"[1,2],":[143],"pyramids,":[144],"solids":[145],"revolution,":[147],"multivariate":[149],"isotonic":[150],"regression,":[151],"among":[152],"others.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
