{"id":"https://openalex.org/W2101984585","doi":"https://doi.org/10.1109/tit.2014.2353995","title":"Optimal Designs for Lasso and Dantzig Selector Using Expander Codes","display_name":"Optimal Designs for Lasso and Dantzig Selector Using Expander Codes","publication_year":2014,"publication_date":"2014-09-08","ids":{"openalex":"https://openalex.org/W2101984585","doi":"https://doi.org/10.1109/tit.2014.2353995","mag":"2101984585"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2353995","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2353995","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1010.2457","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050991089","display_name":"Yohann de Castro","orcid":"https://orcid.org/0000-0002-9008-7474"},"institutions":[{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]},{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Yohann de Castro","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques d\u2019Orsay, Universit\u00e9 Paris Sud, Orsay, France","Laboratoire de Math\u00e9matiques d'Orsay, Universit\u00e9 Paris-Sud, Orsay, France#TAB#"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques d\u2019Orsay, Universit\u00e9 Paris Sud, Orsay, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I3019441195"]},{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques d'Orsay, Universit\u00e9 Paris-Sud, Orsay, France#TAB#","institution_ids":["https://openalex.org/I102197404"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050991089"],"corresponding_institution_ids":["https://openalex.org/I3019441195","https://openalex.org/I102197404"],"apc_list":null,"apc_paid":null,"fwci":0.63300915,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71023748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"60","issue":"11","first_page":"7293","last_page":"7299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9987999796867371,"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":0.9987999796867371,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9984999895095825,"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/T10207","display_name":"Advanced biosensing and bioanalysis techniques","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/expander-graph","display_name":"Expander graph","score":0.7328602075576782},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7125377655029297},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6271875500679016},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.5941520929336548},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5620661377906799},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5223276019096375},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.513041615486145},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4582587480545044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3910096287727356},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38905227184295654},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3841729760169983},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3502027988433838},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32928597927093506},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2158113718032837},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11807161569595337}],"concepts":[{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.7328602075576782},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7125377655029297},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6271875500679016},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.5941520929336548},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5620661377906799},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5223276019096375},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.513041615486145},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4582587480545044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3910096287727356},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38905227184295654},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3841729760169983},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3502027988433838},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32928597927093506},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2158113718032837},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11807161569595337},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2014.2353995","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2353995","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"},{"id":"pmh:oai:arXiv.org:1010.2457","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1010.2457","pdf_url":"https://arxiv.org/pdf/1010.2457","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:HAL:hal-01027523v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01027523","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2014, 60 (11), &#x27E8;10.1109/TIT.2014.2353995&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1010.2457","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1010.2457","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2101984585","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1010.2457","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1010.2457","pdf_url":"https://arxiv.org/pdf/1010.2457","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W658922830","https://openalex.org/W1499022094","https://openalex.org/W1620362451","https://openalex.org/W1654257729","https://openalex.org/W1812599783","https://openalex.org/W1986931325","https://openalex.org/W2034260606","https://openalex.org/W2090418561","https://openalex.org/W2092058109","https://openalex.org/W2097323375","https://openalex.org/W2115447612","https://openalex.org/W2116581043","https://openalex.org/W2129638195","https://openalex.org/W2133589924","https://openalex.org/W2135046866","https://openalex.org/W2140466267","https://openalex.org/W2164452299","https://openalex.org/W2293231900","https://openalex.org/W2541922030","https://openalex.org/W2963023097","https://openalex.org/W3099944011","https://openalex.org/W3101762025","https://openalex.org/W3105340263","https://openalex.org/W3105703423"],"related_works":["https://openalex.org/W2154441853","https://openalex.org/W2801974316","https://openalex.org/W3098089233","https://openalex.org/W3008352043","https://openalex.org/W2883023885","https://openalex.org/W50956978","https://openalex.org/W2174677872","https://openalex.org/W1986377370","https://openalex.org/W2997453817","https://openalex.org/W2168304473","https://openalex.org/W2398649238","https://openalex.org/W2605569246","https://openalex.org/W3212162729","https://openalex.org/W1482028289","https://openalex.org/W2488984458","https://openalex.org/W2930306418","https://openalex.org/W2402945515","https://openalex.org/W2149896468","https://openalex.org/W2898497065","https://openalex.org/W2408897693"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,19,23,26,29,54,63,66,86,91,102],"high-dimensional":[3,45],"regression":[4],"problem":[5],"using":[6],"adjacency":[7],"matrices":[8,77],"of":[9,25,65,105,122],"unbalanced":[10,106],"expander":[11,107],"graphs.":[12],"In":[13],"this":[14],"frame,":[15],"we":[16,41,72,99],"prove":[17],"that":[18,74],"$\\ell_{2}$-prediction":[20],"error":[21,50],"and":[22,28,90,113],"$\\ell_{1}$-risk":[24],"lasso":[27],"Dantzig":[30],"selector":[31],"are":[32],"optimal":[33],"up":[34],"to":[35,53,110,115],"an":[36,49,79,95],"explicit":[37,80,96],"multiplicative":[38],"constant.":[39,97],"Thus":[40],"can":[42],"estimate":[43],"a":[44,58,117],"target":[46],"vector":[47],"with":[48,94],"term":[51],"similar":[52],"one":[55,61],"obtained":[56],"in":[57,69],"situation":[59],"where":[60],"knows":[62],"support":[64],"largest":[67],"coordinates":[68],"advance.":[70],"Moreover,":[71],"show":[73],"these":[75,123],"design":[76,124],"have":[78],"restricted":[81,87],"eigenvalue.":[82],"Precisely,":[83],"they":[84],"satisfy":[85],"eigenvalue":[88],"assumption":[89],"compatibility":[92],"condition":[93],"Eventually,":[98],"capitalize":[100],"on":[101],"recent":[103],"construction":[104,121],"graphs":[108],"due":[109],"Guruswami,":[111],"Umans,":[112],"Vadhan,":[114],"provide":[116],"deterministic":[118],"polynomial":[119],"time":[120],"matrices.":[125]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
