{"id":"https://openalex.org/W3158840473","doi":"https://doi.org/10.1007/s10994-021-05973-0","title":"Reachable sets of classifiers and regression models: (non-)robustness analysis and robust training","display_name":"Reachable sets of classifiers and regression models: (non-)robustness analysis and robust training","publication_year":2021,"publication_date":"2021-04-28","ids":{"openalex":"https://openalex.org/W3158840473","doi":"https://doi.org/10.1007/s10994-021-05973-0","mag":"3158840473"},"language":"en","primary_location":{"id":"doi:10.1007/s10994-021-05973-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-021-05973-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-021-05973-0.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10994-021-05973-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008486868","display_name":"Anna-Kathrin Kopetzki","orcid":"https://orcid.org/0000-0003-2695-0816"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anna-Kathrin Kopetzki","raw_affiliation_strings":["Department of Informatics, Technical University of Munich, Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2695-0816","affiliations":[{"raw_affiliation_string":"Department of Informatics, Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074504351","display_name":"Stephan G\u00fcnnemann","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stephan G\u00fcnnemann","raw_affiliation_strings":["Department of Informatics, Technical University of Munich, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Informatics, Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008486868"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.28,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62381402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"110","issue":"6","first_page":"1175","last_page":"1197"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/robustness","display_name":"Robustness (evolution)","score":0.8080569505691528},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.717664897441864},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.6666402816772461},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.6420047283172607},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5554797053337097},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5066016912460327},{"id":"https://openalex.org/keywords/training-set","display_name":"Training set","score":0.4974558651447296},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.398398220539093},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.365604430437088},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19413542747497559},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07278597354888916}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.8080569505691528},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.717664897441864},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6666402816772461},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.6420047283172607},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5554797053337097},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5066016912460327},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.4974558651447296},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.398398220539093},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.365604430437088},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19413542747497559},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07278597354888916},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10994-021-05973-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-021-05973-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-021-05973-0.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1634262","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1634262","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s10994-021-05973-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10994-021-05973-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10994-021-05973-0.pdf","source":{"id":"https://openalex.org/S62148650","display_name":"Machine Learning","issn_l":"0885-6125","issn":["0885-6125","1573-0565"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320323383","display_name":"Technische Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/02kkvpp62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3158840473.pdf","grobid_xml":"https://content.openalex.org/works/W3158840473.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W1625941627","https://openalex.org/W1945616565","https://openalex.org/W2001619934","https://openalex.org/W2029469881","https://openalex.org/W2036680769","https://openalex.org/W2051110650","https://openalex.org/W2055734602","https://openalex.org/W2065281378","https://openalex.org/W2282821441","https://openalex.org/W2395317528","https://openalex.org/W2594633041","https://openalex.org/W2594877703","https://openalex.org/W2618235498","https://openalex.org/W2626801932","https://openalex.org/W2640329709","https://openalex.org/W2750384547","https://openalex.org/W2777417342","https://openalex.org/W2794609696","https://openalex.org/W2800473699","https://openalex.org/W2801079363","https://openalex.org/W2803850896","https://openalex.org/W2807040120","https://openalex.org/W2890472662","https://openalex.org/W2892354372","https://openalex.org/W2900153411","https://openalex.org/W2906526011","https://openalex.org/W2909765152","https://openalex.org/W2950183737","https://openalex.org/W2950550894","https://openalex.org/W2963054787","https://openalex.org/W2963207607","https://openalex.org/W2963399829","https://openalex.org/W2963496101","https://openalex.org/W2964153729","https://openalex.org/W2964253222","https://openalex.org/W2990945337","https://openalex.org/W2991226929","https://openalex.org/W3109541805","https://openalex.org/W3120740533","https://openalex.org/W4205950066","https://openalex.org/W6636588491","https://openalex.org/W6637162671","https://openalex.org/W6711870810","https://openalex.org/W6734194636","https://openalex.org/W6739088070","https://openalex.org/W6745136726","https://openalex.org/W6754619240"],"related_works":["https://openalex.org/W1629725936","https://openalex.org/W1896423856","https://openalex.org/W4320472933","https://openalex.org/W2962182036","https://openalex.org/W4379876687","https://openalex.org/W3092161682","https://openalex.org/W3094805729","https://openalex.org/W4302393960","https://openalex.org/W3035729345","https://openalex.org/W4205990285"],"abstract_inverted_index":{"Abstract":[0],"Neural":[1],"networks":[2],"achieve":[3],"outstanding":[4],"accuracy":[5],"in":[6,97],"classification":[7],"and":[8,30,64,84,92,117,145,161],"regression":[9,93],"tasks.":[10],"However,":[11],"understanding":[12],"their":[13],"behavior":[14],"still":[15],"remains":[16],"an":[17],"open":[18],"challenge":[19],"that":[20,60,119],"requires":[21],"questions":[22,37],"to":[23,62,82,99,141,151],"be":[24],"addressed":[25],"on":[26,106,158],"the":[27,67,86,153],"robustness,":[28],"explainability":[29],"reliability":[31],"of":[32,42,47,53,66,89,130,155],"predictions.":[33],"We":[34,55],"answer":[35],"these":[36],"by":[38],"computing":[39],"reachable":[40,68],"sets":[41,46,52],"neural":[43],"networks,":[44],"i.e.":[45],"outputs":[48],"resulting":[49],"from":[50],"continuous":[51],"inputs.":[54],"provide":[56,139],"two":[57],"efficient":[58],"approaches":[59],"lead":[61],"over-":[63],"under-approximations":[65],"set.":[69],"This":[70,95],"principle":[71],"is":[72,96],"highly":[73],"versatile,":[74],"as":[75,125,127],"we":[76,79,109,138],"show.":[77],"First,":[78],"use":[80],"it":[81],"analyze":[83],"enhance":[85],"robustness":[87],"properties":[88],"both":[90],"classifiers":[91,132],"models.":[94],"contrast":[98],"existing":[100],"works,":[101],"which":[102],"are":[103],"mainly":[104],"focused":[105],"classification.":[107],"Specifically,":[108],"verify":[110],"(non-)robustness,":[111],"propose":[112],"a":[113,159,163],"robust":[114],"training":[115],"procedure,":[116],"show":[118],"our":[120],"approach":[121],"outperforms":[122],"adversarial":[123],"attacks":[124],"well":[126],"state-of-the-art":[128],"methods":[129],"verifying":[131],"for":[133,148],"non-norm":[134],"bound":[135],"perturbations.":[136],"Second,":[137],"techniques":[140],"distinguish":[142],"between":[143],"reliable":[144],"non-reliable":[146],"predictions":[147],"unlabeled":[149],"inputs,":[150],"quantify":[152],"influence":[154],"each":[156],"feature":[157,164],"prediction,":[160],"compute":[162],"ranking.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}