{"id":"https://openalex.org/W2906427034","doi":"https://doi.org/10.1137/18m1234461","title":"Learning Finite-Dimensional Coding Schemes with Nonlinear Reconstruction Maps","display_name":"Learning Finite-Dimensional Coding Schemes with Nonlinear Reconstruction Maps","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2906427034","doi":"https://doi.org/10.1137/18m1234461","mag":"2906427034"},"language":"en","primary_location":{"id":"doi:10.1137/18m1234461","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1234461","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1234461","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1234461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jaeho Lee","orcid":"https://orcid.org/0000-0002-1349-8595"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jaeho Lee","raw_affiliation_strings":["***University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"***University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044844161","display_name":"Maxim Raginsky","orcid":"https://orcid.org/0000-0002-5586-9219"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maxim Raginsky","raw_affiliation_strings":["***University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"***University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.3999,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61782734,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"1","issue":"3","first_page":"617","last_page":"642"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.9394000172615051,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9228000044822693,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.545611560344696},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5118655562400818},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4865185618400574},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.48170310258865356},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.479383260011673},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4781016707420349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4760594069957733},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.44189268350601196},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4316028952598572},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.41362589597702026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4039403796195984},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3727315068244934},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.2890329360961914},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0979643166065216}],"concepts":[{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.545611560344696},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5118655562400818},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4865185618400574},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.48170310258865356},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.479383260011673},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4781016707420349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4760594069957733},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.44189268350601196},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4316028952598572},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.41362589597702026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4039403796195984},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3727315068244934},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.2890329360961914},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0979643166065216},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1234461","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1234461","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1234461","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1812.09658","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.09658","pdf_url":"https://arxiv.org/pdf/1812.09658","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":null,"raw_type":"text"},{"id":"mag:2906427034","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1812.09658.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1812.09658","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1812.09658","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"}],"best_oa_location":{"id":"doi:10.1137/18m1234461","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1234461","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1234461","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3790071275","display_name":null,"funder_award_id":"CIF-1302438","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8809490364","display_name":null,"funder_award_id":"1254041","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8853214681","display_name":null,"funder_award_id":"CIF-1527388","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2906427034.pdf","grobid_xml":"https://content.openalex.org/works/W2906427034.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W10765648","https://openalex.org/W27434444","https://openalex.org/W60795585","https://openalex.org/W358045163","https://openalex.org/W568673721","https://openalex.org/W607505555","https://openalex.org/W1542886316","https://openalex.org/W1567180517","https://openalex.org/W1585160083","https://openalex.org/W1608472120","https://openalex.org/W1916828813","https://openalex.org/W1973515330","https://openalex.org/W2013035813","https://openalex.org/W2037468546","https://openalex.org/W2060640288","https://openalex.org/W2092074494","https://openalex.org/W2093011562","https://openalex.org/W2094758240","https://openalex.org/W2099111195","https://openalex.org/W2099471712","https://openalex.org/W2111377143","https://openalex.org/W2112796928","https://openalex.org/W2137216203","https://openalex.org/W2142766915","https://openalex.org/W2144797521","https://openalex.org/W2148603752","https://openalex.org/W2148986322","https://openalex.org/W2163922914","https://openalex.org/W2167349346","https://openalex.org/W2293078015","https://openalex.org/W2502165832","https://openalex.org/W2557283755","https://openalex.org/W2787877872","https://openalex.org/W2790769103","https://openalex.org/W2798836194","https://openalex.org/W2808157231","https://openalex.org/W2889756710","https://openalex.org/W2962857907","https://openalex.org/W2963376432","https://openalex.org/W2963641291","https://openalex.org/W2973214398","https://openalex.org/W3119586787","https://openalex.org/W3148693803","https://openalex.org/W4251232133"],"related_works":["https://openalex.org/W2975585678","https://openalex.org/W2156013511","https://openalex.org/W1994807773","https://openalex.org/W3203777403","https://openalex.org/W3140349852","https://openalex.org/W2120959988","https://openalex.org/W2963806997","https://openalex.org/W1550469414","https://openalex.org/W3203419944","https://openalex.org/W2049892093","https://openalex.org/W2065690007","https://openalex.org/W2945214828","https://openalex.org/W3196891010","https://openalex.org/W1986672109","https://openalex.org/W2963376197","https://openalex.org/W2226303357","https://openalex.org/W2516896396","https://openalex.org/W3118582960","https://openalex.org/W2072224991","https://openalex.org/W2051105796"],"abstract_inverted_index":{"This":[0],"paper":[1],"generalizes":[2],"the":[3,12,37,73,76,84,92,113,117,120],"Maurer--Pontil":[4],"framework":[5],"of":[6,24,28,45,56,78,86,94,98],"finite-dimensional":[7],"lossy":[8],"coding":[9,89],"schemes":[10],"to":[11,21,41,65],"setting":[13,118],"where":[14,119],"a":[15,25,32,42,53,63,88,95],"high-dimensional":[16],"random":[17],"vector":[18],"is":[19],"mapped":[20],"an":[22],"element":[23],"compact":[26],"set":[27],"latent":[29],"representations":[30],"in":[31,116],"lower-dimensional":[33],"Euclidean":[34],"space,":[35],"and":[36,101],"reconstruction":[38,121],"map":[39],"belongs":[40],"given":[43],"class":[44,55],"nonlinear":[46],"maps.":[47],"Under":[48],"this":[49],"setup,":[50],"which":[51],"encompasses":[52],"broad":[54],"unsupervised":[57],"representation":[58],"learning":[59,87],"problems,":[60],"we":[61,82],"establish":[62],"connection":[64],"approximate":[66],"generative":[67],"modeling":[68],"under":[69],"structural":[70],"constraints":[71],"using":[72],"tools":[74],"from":[75],"theory":[77,115],"optimal":[79],"transportation.":[80],"Next,":[81],"consider":[83],"problem":[85],"scheme":[90],"on":[91],"basis":[93],"finite":[96],"collection":[97],"training":[99],"samples":[100],"present":[102],"generalization":[103],"bounds":[104],"that":[105],"hold":[106],"with":[107],"high":[108],"probability.":[109],"We":[110],"then":[111],"illustrate":[112],"general":[114],"maps":[122],"are":[123],"implemented":[124],"by":[125],"deep":[126],"neural":[127],"nets.":[128]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}