{"id":"https://openalex.org/W2543920556","doi":"https://doi.org/10.1109/itw.2016.7606829","title":"Learning adaptive multiscale approximations to data and functions near low-dimensional sets","display_name":"Learning adaptive multiscale approximations to data and functions near low-dimensional sets","publication_year":2016,"publication_date":"2016-09-01","ids":{"openalex":"https://openalex.org/W2543920556","doi":"https://doi.org/10.1109/itw.2016.7606829","mag":"2543920556"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2016.7606829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2016.7606829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-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/A5050616963","display_name":"Wenjing Liao","orcid":"https://orcid.org/0000-0003-2309-3839"},"institutions":[{"id":"https://openalex.org/I161057412","display_name":"University of New Hampshire","ror":"https://ror.org/01rmh9n78","country_code":"US","type":"education","lineage":["https://openalex.org/I161057412"]},{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Wenjing Liao","raw_affiliation_strings":["Department of Mathematics, Durham, N.C., U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Durham, N.C., U.S.A","institution_ids":["https://openalex.org/I161057412","https://openalex.org/I190082696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089371996","display_name":"Mauro Maggioni","orcid":"https://orcid.org/0000-0003-3258-9297"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]},{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Mauro Maggioni","raw_affiliation_strings":["Computer Science, Duke University, Durham, N.C., U.S.A","Electrical and Computer Engineering, Durham, N.C., U.S.A"],"affiliations":[{"raw_affiliation_string":"Computer Science, Duke University, Durham, N.C., U.S.A","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Electrical and Computer Engineering, Durham, N.C., U.S.A","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013257932","display_name":"Stefano Vigogna","orcid":"https://orcid.org/0000-0001-9505-8034"},"institutions":[{"id":"https://openalex.org/I161057412","display_name":"University of New Hampshire","ror":"https://ror.org/01rmh9n78","country_code":"US","type":"education","lineage":["https://openalex.org/I161057412"]},{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Stefano Vigogna","raw_affiliation_strings":["Department of Mathematics, Durham, N.C., U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Durham, N.C., U.S.A","institution_ids":["https://openalex.org/I161057412","https://openalex.org/I190082696"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050616963"],"corresponding_institution_ids":["https://openalex.org/I161057412","https://openalex.org/I190082696"],"apc_list":null,"apc_paid":null,"fwci":0.7237,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76694313,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"6","issue":null,"first_page":"226","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9900000095367432,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9900000095367432,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.965499997138977,"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/dimension","display_name":"Dimension (graph theory)","score":0.6523835062980652},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.5719881653785706},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.567815363407135},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.567603588104248},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.556482195854187},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5320730209350586},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.5027141571044922},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4417322874069214},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.43793874979019165},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4201025664806366},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3949074149131775},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3627493977546692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30097225308418274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.291963666677475},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19646567106246948},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.145668625831604}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6523835062980652},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5719881653785706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.567815363407135},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.567603588104248},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.556482195854187},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5320730209350586},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.5027141571044922},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4417322874069214},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.43793874979019165},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4201025664806366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3949074149131775},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3627493977546692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30097225308418274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.291963666677475},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19646567106246948},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.145668625831604},{"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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/itw.2016.7606829","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2016.7606829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"},{"id":"pmh:oai:art.torvergata.it:2108/361045","is_oa":false,"landing_page_url":"https://hdl.handle.net/2108/361045","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1594926678","https://openalex.org/W1680677650","https://openalex.org/W2023989213","https://openalex.org/W2048712744","https://openalex.org/W2129293958","https://openalex.org/W2133296809","https://openalex.org/W2136109306","https://openalex.org/W2963030988","https://openalex.org/W2963674301","https://openalex.org/W2964012263","https://openalex.org/W6635751551","https://openalex.org/W7043940998"],"related_works":["https://openalex.org/W141820298","https://openalex.org/W2049584446","https://openalex.org/W2079781215","https://openalex.org/W4378770497","https://openalex.org/W4308245303","https://openalex.org/W2014033564","https://openalex.org/W2910573937","https://openalex.org/W1986179452","https://openalex.org/W129188671","https://openalex.org/W4300292027"],"abstract_inverted_index":{"In":[0,54,86],"the":[1,55,87,107,128],"setting":[2],"where":[3],"a":[4,16,49,138],"data":[5],"set":[6,27],"in":[7,161,165],"\u211d":[8],"<sup":[9],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</sup>":[11],"consists":[12],"of":[13,40,44,48,64,110,141,145],"samples":[14],"from":[15],"probability":[17],"measure":[18],"\u03c1":[19],"concentrated":[20],"on":[21,52,102,137],"or":[22],"near":[23],"an":[24,146],"unknown":[25,108,147],"d-dimensional":[26],"M,":[28,65,103],"with":[29,157],"D":[30,162],"large":[31],"but":[32],"d":[33],"\u226a":[34],"D,":[35],"we":[36,58,90,126],"consider":[37],"two":[38],"sets":[39],"problems:":[41],"geometric":[42,72,94],"approximation":[43],"M":[45,70],"and":[46,80,82,119,163],"regression":[47],"function":[50],"f":[51,101,111,134],"M.":[53,149],"first":[56],"case":[57,89],"construct":[59,97],"multiscale":[60,98],"low-dimensional":[61],"empirical":[62,93],"approximations":[63,95,99],"which":[66,104],"are":[67],"adaptive":[68],"when":[69,113],"has":[71],"regularity":[73,109],"that":[74,125],"may":[75],"vary":[76],"at":[77,116],"different":[78,117],"locations":[79],"scales,":[81],"give":[83],"performance":[84],"guarantees.":[85],"second":[88],"exploit":[91],"these":[92],"to":[96,100,106],"adapt":[105],"even":[112],"this":[114],"varies":[115],"scales":[118],"locations.":[120],"We":[121],"prove":[122],"guarantees":[123],"showing":[124],"attain":[127],"same":[129],"learning":[130],"rates":[131],"as":[132],"if":[133],"was":[135],"defined":[136],"Euclidean":[139],"domain":[140],"dimension":[142],"d,":[143],"instead":[144],"manifold":[148],"All":[150],"algorithms":[151],"have":[152],"complexity":[153],"O(n":[154],"log":[155],"n),":[156],"constants":[158],"scaling":[159],"linearly":[160],"exponentially":[164],"d.":[166]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}