{"id":"https://openalex.org/W4417251787","doi":"https://doi.org/10.1109/lsp.2025.3643385","title":"Concentration Inequalities for Semidefinite Least Squares Based on Data","display_name":"Concentration Inequalities for Semidefinite Least Squares Based on Data","publication_year":2025,"publication_date":"2025-12-11","ids":{"openalex":"https://openalex.org/W4417251787","doi":"https://doi.org/10.1109/lsp.2025.3643385"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2025.3643385","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3643385","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5056468963","display_name":"Filippo Fabiani","orcid":"https://orcid.org/0000-0002-9911-4758"},"institutions":[{"id":"https://openalex.org/I127077003","display_name":"IMT School for Advanced Studies Lucca","ror":"https://ror.org/035gh3a49","country_code":"IT","type":"education","lineage":["https://openalex.org/I127077003"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Filippo Fabiani","raw_affiliation_strings":["IMT School for Advanced Studies Lucca, Lucca, Italy","IMT School for Advanced Studies Lucca, Piazza San Francesco, Lucca, Italy"],"raw_orcid":"https://orcid.org/0000-0002-9911-4758","affiliations":[{"raw_affiliation_string":"IMT School for Advanced Studies Lucca, Lucca, Italy","institution_ids":["https://openalex.org/I127077003"]},{"raw_affiliation_string":"IMT School for Advanced Studies Lucca, Piazza San Francesco, Lucca, Italy","institution_ids":["https://openalex.org/I127077003"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019172720","display_name":"Andrea Simonetto","orcid":"https://orcid.org/0000-0003-2923-3361"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrea Simonetto","raw_affiliation_strings":["Unit&#x00E9; de Math&#x00E9;matiques Appliqu&#x00E9;es, ENSTA, Institut Polytechnique de Paris, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Unit&#x00E9; de Math&#x00E9;matiques Appliqu&#x00E9;es, ENSTA, Institut Polytechnique de Paris, Palaiseau, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18588315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":null,"first_page":"326","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.5184999704360962,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.5184999704360962,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.14970000088214874,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.10849999636411667,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/independent-and-identically-distributed-random-variables","display_name":"Independent and identically distributed random variables","score":0.5659999847412109},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.517799973487854},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5044000148773193},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4918999969959259},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4853000044822693},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.48069998621940613},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4571000039577484},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44350001215934753}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684999704360962},{"id":"https://openalex.org/C141513077","wikidata":"https://www.wikidata.org/wiki/Q378542","display_name":"Independent and identically distributed random variables","level":3,"score":0.5659999847412109},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.517799973487854},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5044000148773193},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4918999969959259},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.48069998621940613},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4742000102996826},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4571000039577484},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44350001215934753},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43790000677108765},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.365200012922287},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3160000145435333},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.31189998984336853},{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.30410000681877136},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C126090379","wikidata":"https://www.wikidata.org/wiki/Q6094424","display_name":"Iteratively reweighted least squares","level":4,"score":0.2994000017642975},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.26660001277923584},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2639999985694885}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2025.3643385","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2025.3643385","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05273055v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05273055","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2026, 33, pp.326-330. &#x27E8;10.1109/LSP.2025.3643385&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7835086286","display_name":"Personalized Optimization with Human Feedback","funder_award_id":"ANR-23-CE48-0011","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"data-driven":[2],"least":[3],"squares":[4],"(LS)":[5],"problems":[6],"with":[7,121],"semidefinite":[8],"(SD)":[9],"constraints":[10,24,124],"and":[11,85,89,125],"derive":[12],"finite-sample":[13],"guarantees":[14],"on":[15,108],"the":[16,45,52,55,64,74,95,109,117,126],"spectrum":[17],"of":[18,44,54,60,76],"their":[19],"optimal":[20],"solutions":[21],"when":[22,94],"these":[23],"are":[25,58],"relaxed.":[26],"In":[27],"particular,":[28],"we":[29,105],"provide":[30],"a":[31,39,112],"high":[32],"confidence":[33],"bound":[34],"allowing":[35],"one":[36],"to":[37,81,99],"solve":[38],"simpler":[40],"program":[41],"in":[42],"place":[43],"full":[46],"SDLS":[47,96],"problem,":[48],"while":[49],"ensuring":[50],"that":[51],"eigenvalues":[53],"resulting":[56],"solution":[57],"\u03f5-close":[59],"those":[61],"enforced":[62],"by":[63],"SD":[65,123],"constraints.":[66],"The":[67],"developed":[68],"certificate,":[69],"which":[70],"consistently":[71],"shrinks":[72],"as":[73],"number":[75],"data":[77],"increases,":[78],"turns":[79],"out":[80],"be":[82],"easy-to-compute,":[83],"distribution-free,":[84],"only":[86],"requires":[87],"independent":[88],"identically":[90],"distributed":[91],"samples.":[92],"Moreover,":[93],"is":[97],"used":[98],"learn":[100],"an":[101],"unknown":[102],"quadratic":[103],"function,":[104],"establish":[106],"bounds":[107],"error":[110],"between":[111],"gradient":[113],"descent":[114],"iterate":[115],"minimizing":[116],"surrogate":[118],"cost":[119],"obtained":[120],"no":[122],"true":[127],"minimizer.":[128]},"counts_by_year":[],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-12-11T00:00:00"}
