{"id":"https://openalex.org/W3012324700","doi":"https://doi.org/10.1109/jsait.2020.2980676","title":"Information-Theoretic Lower Bounds for Compressive Sensing With Generative Models","display_name":"Information-Theoretic Lower Bounds for Compressive Sensing With Generative Models","publication_year":2020,"publication_date":"2020-03-13","ids":{"openalex":"https://openalex.org/W3012324700","doi":"https://doi.org/10.1109/jsait.2020.2980676","mag":"3012324700"},"language":"en","primary_location":{"id":"doi:10.1109/jsait.2020.2980676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsait.2020.2980676","pdf_url":null,"source":{"id":"https://openalex.org/S4210211895","display_name":"IEEE Journal on Selected Areas in Information Theory","issn_l":"2641-8770","issn":["2641-8770"],"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 Journal on Selected Areas in Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://scholarbank.nus.edu.sg/handle/10635/171882","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089855005","display_name":"Zhaoqiang Liu","orcid":"https://orcid.org/0000-0002-0392-6648"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Zhaoqiang Liu","raw_affiliation_strings":["Department of Computer Science, School of Computing, National University of Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, School of Computing, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046337437","display_name":"Jonathan Scarlett","orcid":"https://orcid.org/0000-0003-1403-9160"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Jonathan Scarlett","raw_affiliation_strings":["Department of Computer Science, School of Computing, National University of Singapore, Singapore","Department of Mathematics, National University of Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, School of Computing, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089855005"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":3.6972,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94021099,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"1","issue":"1","first_page":"292","last_page":"303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.7873821258544922},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7204919457435608},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6721493005752563},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.659936785697937},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6575121879577637},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6067089438438416},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6021860837936401},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.5772907733917236},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5723885297775269},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5447514653205872},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.5425184369087219},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5012891292572021},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4743686616420746},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4512537717819214},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35763612389564514},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32524800300598145},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22139081358909607},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21544361114501953},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19966039061546326},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15520146489143372}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.7873821258544922},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7204919457435608},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6721493005752563},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.659936785697937},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6575121879577637},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6067089438438416},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6021860837936401},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.5772907733917236},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5723885297775269},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5447514653205872},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.5425184369087219},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5012891292572021},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4743686616420746},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4512537717819214},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35763612389564514},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32524800300598145},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22139081358909607},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21544361114501953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19966039061546326},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15520146489143372},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/jsait.2020.2980676","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsait.2020.2980676","pdf_url":null,"source":{"id":"https://openalex.org/S4210211895","display_name":"IEEE Journal on Selected Areas in Information Theory","issn_l":"2641-8770","issn":["2641-8770"],"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 Journal on Selected Areas in Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/171882","is_oa":true,"landing_page_url":"https://scholarbank.nus.edu.sg/handle/10635/171882","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/171882","is_oa":true,"landing_page_url":"https://scholarbank.nus.edu.sg/handle/10635/171882","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4457590956","display_name":null,"funder_award_id":"R-252-000-A74-281","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"}],"funders":[{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W2003045459","https://openalex.org/W2025223969","https://openalex.org/W2091482891","https://openalex.org/W2104357403","https://openalex.org/W2106586162","https://openalex.org/W2109379066","https://openalex.org/W2116148865","https://openalex.org/W2125680629","https://openalex.org/W2127300249","https://openalex.org/W2137198385","https://openalex.org/W2141556672","https://openalex.org/W2147656689","https://openalex.org/W2161610387","https://openalex.org/W2208555118","https://openalex.org/W2478708596","https://openalex.org/W2510244936","https://openalex.org/W2557873547","https://openalex.org/W2571527823","https://openalex.org/W2595294663","https://openalex.org/W2787438119","https://openalex.org/W2787898208","https://openalex.org/W2807256526","https://openalex.org/W2808361645","https://openalex.org/W2809866471","https://openalex.org/W2898001268","https://openalex.org/W2945068291","https://openalex.org/W2962692462","https://openalex.org/W2962782102","https://openalex.org/W2962886646","https://openalex.org/W2962990163","https://openalex.org/W2963031612","https://openalex.org/W2963861702","https://openalex.org/W2964253263","https://openalex.org/W2994196995","https://openalex.org/W3014022300","https://openalex.org/W3101990100","https://openalex.org/W3125402404","https://openalex.org/W3125735862","https://openalex.org/W4211030719","https://openalex.org/W4295597720","https://openalex.org/W4297795180","https://openalex.org/W4300303470","https://openalex.org/W4301028776","https://openalex.org/W6695533872","https://openalex.org/W6729999211","https://openalex.org/W6735307612","https://openalex.org/W6738155126","https://openalex.org/W6752579191","https://openalex.org/W6755694737","https://openalex.org/W6762568018"],"related_works":["https://openalex.org/W2726819869","https://openalex.org/W2224648581","https://openalex.org/W2053374910","https://openalex.org/W2994196995","https://openalex.org/W4297795180","https://openalex.org/W3173850332","https://openalex.org/W3082706992","https://openalex.org/W3036291575","https://openalex.org/W3012324700","https://openalex.org/W2971117199"],"abstract_inverted_index":{"It":[0],"has":[1],"recently":[2],"been":[3],"shown":[4,45],"that":[5,134,184],"for":[6,54,158],"compressive":[7],"sensing,":[8],"significantly":[9],"fewer":[10],"measurements":[11,52,71,140,164],"may":[12],"be":[13],"required":[14],"if":[15],"the":[16,22,24,29,58,74,98,110,135,160,185,199],"sparsity":[17],"assumption":[18,23],"is":[19,61,77,141],"replaced":[20],"by":[21],"unknown":[25],"vector":[26],"lies":[27],"near":[28],"range":[30],"of":[31,128,139,163,201],"a":[32,78,180],"suitably-chosen":[33],"generative":[34,59,75,125],"model.":[35],"In":[36,88,107],"particular,":[37],"in":[38,174,189,198],"(Bora":[39,190],"et":[40,191],"al.,":[41,192],"2017)":[42,193],"it":[43],"was":[44],"roughly":[46],"O(k":[47],"log":[48],"L)":[49],"random":[50],"Gaussian":[51],"suffice":[53,72],"accurate":[55],"recovery":[56],"when":[57,73],"model":[60,76,126],"an":[62,123],"L-Lipschitz":[63,124],"function":[64],"with":[65,82,109,152],"bounded":[66],"k-dimensional":[67],"inputs,":[68],"and":[69,85,132,173],"O(kdlogw)":[70],"k-input":[79],"ReLU":[80,150],"network":[81],"depth":[83,154,157],"d":[84],"width":[86],"w.":[87],"this":[89],"paper,":[90],"we":[91,148,182],"establish":[92,183],"corresponding":[93],"algorithm-independent":[94],"lower":[95],"bounds":[96],"on":[97],"sample":[99],"complexity":[100],"using":[101],"tools":[102],"from":[103],"minimax":[104],"statistical":[105],"analysis.":[106],"accordance":[108],"above":[111],"upper":[112],"bounds,":[113],"our":[114],"results":[115],"are":[116,194],"summarized":[117],"as":[118,166],"follows:":[119],"(i)":[120],"We":[121],"construct":[122,149],"capable":[127],"generating":[129],"group-sparse":[130],"signals,":[131],"show":[133],"resulting":[136],"necessary":[137,161],"number":[138,162],"\u03a9(k":[142],"logL);":[143],"(ii)":[144],"Using":[145],"similar":[146],"ideas,":[147],"networks":[151],"high":[153,156],"and/or":[155],"which":[159],"scales":[165],"\u03a9(kd":[167,177],"logw/logn)":[168],"(with":[169],"output":[170],"dimension":[171],"n),":[172],"some":[175],"cases":[176],"logw).":[178],"As":[179],"result,":[181],"scaling":[186],"laws":[187],"derived":[188],"optimal":[195],"or":[196],"near-optimal":[197],"absence":[200],"further":[202],"assumptions.":[203]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
