{"id":"https://openalex.org/W3100794795","doi":"https://doi.org/10.1137/20m131727x","title":"Dynamical Systems Approach to Outlier Robust Deep Neural Networks for Regression","display_name":"Dynamical Systems Approach to Outlier Robust Deep Neural Networks for Regression","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3100794795","doi":"https://doi.org/10.1137/20m131727x","mag":"3100794795"},"language":"en","primary_location":{"id":"doi:10.1137/20m131727x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m131727x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"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 Applied Dynamical Systems","raw_type":"journal-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/A5001662366","display_name":"Pavel Gurevich","orcid":"https://orcid.org/0000-0002-8086-4807"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pavel Gurevich","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011184839","display_name":"Hannes Stuke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hannes Stuke","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001662366"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14207426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"4","first_page":"2567","last_page":"2593"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9955999851226807,"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/T10320","display_name":"Neural Networks and Applications","score":0.991100013256073,"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/outlier","display_name":"Outlier","score":0.8205558061599731},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.5863170027732849},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5431380271911621},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5292360782623291},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49117228388786316},{"id":"https://openalex.org/keywords/marginal-distribution","display_name":"Marginal distribution","score":0.45681795477867126},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4559195637702942},{"id":"https://openalex.org/keywords/ground-truth","display_name":"Ground truth","score":0.4541577100753784},{"id":"https://openalex.org/keywords/robust-regression","display_name":"Robust regression","score":0.43730318546295166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43534231185913086},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3487631678581238},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3230752944946289},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.26496511697769165},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07707527279853821}],"concepts":[{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.8205558061599731},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5863170027732849},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5431380271911621},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5292360782623291},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49117228388786316},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.45681795477867126},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4559195637702942},{"id":"https://openalex.org/C146849305","wikidata":"https://www.wikidata.org/wiki/Q370766","display_name":"Ground truth","level":2,"score":0.4541577100753784},{"id":"https://openalex.org/C70259352","wikidata":"https://www.wikidata.org/wiki/Q1847839","display_name":"Robust regression","level":3,"score":0.43730318546295166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43534231185913086},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3487631678581238},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3230752944946289},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26496511697769165},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07707527279853821},{"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/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m131727x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m131727x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"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 Applied Dynamical Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W2029469881","https://openalex.org/W2035641621","https://openalex.org/W2046033161","https://openalex.org/W2054932610","https://openalex.org/W2061933243","https://openalex.org/W2064769840","https://openalex.org/W2117890631","https://openalex.org/W2789595241","https://openalex.org/W2950025868","https://openalex.org/W2951994466","https://openalex.org/W2962952919","https://openalex.org/W2981291347"],"related_works":["https://openalex.org/W3121734683","https://openalex.org/W4210813465","https://openalex.org/W2085680114","https://openalex.org/W1600426151","https://openalex.org/W1974187127","https://openalex.org/W1833314573","https://openalex.org/W3121311879","https://openalex.org/W4380879348","https://openalex.org/W1539940077","https://openalex.org/W2168294724"],"abstract_inverted_index":{"We":[0,23,133],"study":[1],"the":[2,17,27,44,47,51,60,64,69,75,95,104,109,117,122,126,141,144,152,166],"dynamics":[3],"and":[4,67,108,160],"equilibria":[5],"induced":[6],"by":[7,31,72],"training":[8,28,76],"an":[9,55],"artificial":[10],"neural":[11],"network":[12,49,168],"for":[13,58,178],"regression":[14],"based":[15],"on":[16],"gradient":[18],"conjugate":[19],"prior":[20],"(GCP)":[21],"updates.":[22],"show":[24,93],"that":[25,94,165],"contaminating":[26],"data":[29,162],"set":[30],"outliers":[32,73,153],"leads":[33],"to":[34],"bifurcation":[35],"of":[36,46,63,90,103,116,125,140,143,151],"a":[37,79,87,100,114,138,148,171],"stable":[38],"equilibrium":[39],"from":[40],"infinity.":[41],"Furthermore,":[42],"using":[43],"outputs":[45],"GCP":[48,145,167],"at":[50],"equilibrium,":[52],"we":[53,92],"derive":[54],"explicit":[56],"formula":[57],"correcting":[59],"learned":[61],"variance":[62,111,124],"marginal":[65,127],"distribution":[66,84,128],"removing":[68],"bias":[70],"caused":[71],"in":[74,99,113],"set.":[77],"Assuming":[78],"Gaussian":[80],"(input-dependent)":[81],"ground":[82,105,118],"truth":[83,106,119],"contaminated":[85],"with":[86,158,170],"proportion":[88],"$\\varepsilon$":[89],"outliers,":[91],"fitted":[96,169],"mean":[97,107],"is":[98,112],"$c":[101],"e^{-1/\\varepsilon}$-neighborhood":[102],"corrected":[110],"$b\\varepsilon$-neighborhood":[115],"variance,":[120],"whereas":[121],"uncorrected":[123],"can":[129],"even":[130],"be":[131],"infinite.":[132],"explicitly":[134],"find":[135],"$b$":[136],"as":[137],"function":[139],"output":[142],"network,":[146],"without":[147],"priori":[149],"knowledge":[150],"(possibly":[154],"input-dependent)":[155],"distribution.":[156],"Experiments":[157],"synthetic":[159],"real-world":[161],"sets":[163],"indicate":[164],"standard":[172],"optimizer":[173],"outperforms":[174],"other":[175],"robust":[176],"methods":[177],"regression.":[179]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
