{"id":"https://openalex.org/W3153900045","doi":"https://doi.org/10.1109/tac.2022.3227907","title":"Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach","display_name":"Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach","publication_year":2022,"publication_date":"2022-12-09","ids":{"openalex":"https://openalex.org/W3153900045","doi":"https://doi.org/10.1109/tac.2022.3227907","mag":"3153900045"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2022.3227907","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3227907","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/handle/20.500.14299/196601","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012155644","display_name":"Paul Scharnhorst","orcid":"https://orcid.org/0000-0003-0942-5032"},"institutions":[{"id":"https://openalex.org/I135218257","display_name":"Swiss Center for Electronics and Microtechnology (Switzerland)","ror":"https://ror.org/05nrrsx06","country_code":"CH","type":"company","lineage":["https://openalex.org/I135218257"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Paul Scharnhorst","raw_affiliation_strings":["CSEM, Neuch&#x00E2;tel, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-0942-5032","affiliations":[{"raw_affiliation_string":"CSEM, Neuch&#x00E2;tel, Switzerland","institution_ids":["https://openalex.org/I135218257"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000850139","display_name":"Emilio T. Maddalena","orcid":"https://orcid.org/0000-0002-5122-1183"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Emilio T. Maddalena","raw_affiliation_strings":["Automatic Control Laboratory, &#x00C9;cole Polytechnique F&#x00E9;d&#x00E9;rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-5122-1183","affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, &#x00C9;cole Polytechnique F&#x00E9;d&#x00E9;rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074655314","display_name":"Yuning Jiang","orcid":"https://orcid.org/0000-0002-7145-0995"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Yuning Jiang","raw_affiliation_strings":["Automatic Control Laboratory, &#x00C9;cole Polytechnique F&#x00E9;d&#x00E9;rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-7145-0995","affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, &#x00C9;cole Polytechnique F&#x00E9;d&#x00E9;rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085117832","display_name":"Colin N. Jones","orcid":"https://orcid.org/0000-0001-7239-4799"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Colin N. Jones","raw_affiliation_strings":["Automatic Control Laboratory, &#x00C9;cole Polytechnique F&#x00E9;d&#x00E9;rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-7239-4799","affiliations":[{"raw_affiliation_string":"Automatic Control Laboratory, &#x00C9;cole Polytechnique F&#x00E9;d&#x00E9;rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8642,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.84149207,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"68","issue":"5","first_page":"2848","last_page":"2861"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11236","display_name":"Control Systems and Identification","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7437726259231567},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6828691363334656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6750053763389587},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6483791470527649},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.6175148487091064},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6168098449707031},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5448985695838928},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.526434063911438},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5188461542129517},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.48395541310310364},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.46210014820098877},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.45740488171577454},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.44229868054389954},{"id":"https://openalex.org/keywords/representer-theorem","display_name":"Representer theorem","score":0.43752962350845337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2917098104953766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2827041447162628},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2597454786300659},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.2267933487892151},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2241053581237793},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22256016731262207},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.13741058111190796},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11484959721565247},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08697330951690674}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7437726259231567},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6828691363334656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6750053763389587},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6483791470527649},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.6175148487091064},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6168098449707031},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5448985695838928},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.526434063911438},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5188461542129517},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.48395541310310364},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.46210014820098877},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.45740488171577454},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.44229868054389954},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.43752962350845337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2917098104953766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2827041447162628},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2597454786300659},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.2267933487892151},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2241053581237793},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22256016731262207},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.13741058111190796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11484959721565247},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08697330951690674},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2022.3227907","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2022.3227907","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:301588","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/196601","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:301588","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/196601","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1536300613","display_name":null,"funder_award_id":"200021 175627","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":81,"referenced_works":["https://openalex.org/W199271301","https://openalex.org/W597932189","https://openalex.org/W1486164486","https://openalex.org/W1560724230","https://openalex.org/W1746819321","https://openalex.org/W1988793248","https://openalex.org/W1994313913","https://openalex.org/W2052398345","https://openalex.org/W2086901931","https://openalex.org/W2087714402","https://openalex.org/W2089245375","https://openalex.org/W2092766760","https://openalex.org/W2112840220","https://openalex.org/W2137796859","https://openalex.org/W2143277772","https://openalex.org/W2161133039","https://openalex.org/W2164009812","https://openalex.org/W2164278908","https://openalex.org/W2166566250","https://openalex.org/W2275150912","https://openalex.org/W2286886577","https://openalex.org/W2320868965","https://openalex.org/W2619551236","https://openalex.org/W2756252287","https://openalex.org/W2780439059","https://openalex.org/W2784084101","https://openalex.org/W2784276140","https://openalex.org/W2880842812","https://openalex.org/W2892521964","https://openalex.org/W2904426420","https://openalex.org/W2913010492","https://openalex.org/W2913243980","https://openalex.org/W2959570737","https://openalex.org/W2962685794","https://openalex.org/W2963271096","https://openalex.org/W2963317682","https://openalex.org/W2963683522","https://openalex.org/W2964915616","https://openalex.org/W2970782456","https://openalex.org/W2990408532","https://openalex.org/W2995486512","https://openalex.org/W3002619089","https://openalex.org/W3009365087","https://openalex.org/W3014803699","https://openalex.org/W3031684975","https://openalex.org/W3081084362","https://openalex.org/W3087397555","https://openalex.org/W3099442372","https://openalex.org/W3104562023","https://openalex.org/W3105252106","https://openalex.org/W3108435811","https://openalex.org/W3109859540","https://openalex.org/W3120459386","https://openalex.org/W3134561541","https://openalex.org/W3142965698","https://openalex.org/W3144619878","https://openalex.org/W3157949100","https://openalex.org/W3200082106","https://openalex.org/W4205734126","https://openalex.org/W4211049957","https://openalex.org/W4220671231","https://openalex.org/W4245558064","https://openalex.org/W4287697272","https://openalex.org/W4288336312","https://openalex.org/W4292363360","https://openalex.org/W4294205985","https://openalex.org/W4294555834","https://openalex.org/W6608099645","https://openalex.org/W6736246758","https://openalex.org/W6738483526","https://openalex.org/W6748028576","https://openalex.org/W6753263680","https://openalex.org/W6758728975","https://openalex.org/W6758804334","https://openalex.org/W6763216130","https://openalex.org/W6781351028","https://openalex.org/W6783123646","https://openalex.org/W6786756798","https://openalex.org/W6786826282","https://openalex.org/W6842469858","https://openalex.org/W7070821404"],"related_works":["https://openalex.org/W1994655188","https://openalex.org/W2392804273","https://openalex.org/W2939134861","https://openalex.org/W2624872425","https://openalex.org/W2964156564","https://openalex.org/W4241777949","https://openalex.org/W2146853797","https://openalex.org/W69532434","https://openalex.org/W2545393543","https://openalex.org/W2148651989"],"abstract_inverted_index":{"The":[0,41],"problem":[1],"of":[2,9,82],"establishing":[3],"out-of-sample":[4],"bounds":[5,70],"for":[6],"the":[7,23,57,80,102],"values":[8],"an":[10,30],"unknown":[11],"ground-truth":[12],"function":[13],"is":[14,93],"considered.":[15],"Kernels":[16],"and":[17,50,87,110],"their":[18],"associated":[19],"Hilbert":[20],"spaces":[21],"are":[22,35,54,85,97],"main":[24],"formalism":[25],"employed":[26],"herein,":[27],"along":[28],"with":[29,90,114],"observational":[31],"model":[32],"where":[33],"outputs":[34],"corrupted":[36],"by":[37],"bounded":[38],"measurement":[39],"noise.":[40],"noise":[42],"can":[43,104],"originate":[44],"from":[45],"any":[46],"compactly":[47],"supported":[48],"distribution,":[49],"no":[51],"independent":[52],"assumptions":[53],"made":[55],"on":[56],"available":[58],"data.":[59],"In":[60],"this":[61],"setting,":[62],"we":[63],"show":[64],"how":[65,101],"computing":[66],"tight,":[67],"finite-sample":[68],"uncertainty":[69],"amounts":[71],"to":[72,99,111],"solving":[73],"parametric":[74],"quadratically":[75],"constrained":[76],"linear":[77],"programs.":[78],"Next,":[79],"properties":[81],"our":[83],"approach":[84],"established,":[86],"its":[88],"relationship":[89],"another":[91],"method":[92],"studied.":[94],"Numerical":[95],"experiments":[96],"presented":[98],"exemplify":[100],"theory":[103],"be":[105],"applied":[106],"in":[107],"various":[108],"scenarios":[109],"contrast":[112],"it":[113],"other":[115],"closed-form":[116],"alternatives.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}
