{"id":"https://openalex.org/W4406230673","doi":"https://doi.org/10.1007/s00180-024-01593-z","title":"Gradient-based smoothing parameter estimation for neural P-splines","display_name":"Gradient-based smoothing parameter estimation for neural P-splines","publication_year":2025,"publication_date":"2025-01-09","ids":{"openalex":"https://openalex.org/W4406230673","doi":"https://doi.org/10.1007/s00180-024-01593-z"},"language":"en","primary_location":{"id":"doi:10.1007/s00180-024-01593-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-024-01593-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-024-01593-z.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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":"Computational Statistics","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/s00180-024-01593-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092148612","display_name":"Lea Maria Dammann","orcid":"https://orcid.org/0000-0002-4142-0277"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lea M. Dammann","raw_affiliation_strings":["University of G\u00f6ttingen, G\u00f6ttingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of G\u00f6ttingen, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103057929","display_name":"Marei Freitag","orcid":"https://orcid.org/0009-0005-0920-2535"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marei Freitag","raw_affiliation_strings":["University of G\u00f6ttingen, G\u00f6ttingen, Germany"],"raw_orcid":"https://orcid.org/0009-0005-0920-2535","affiliations":[{"raw_affiliation_string":"University of G\u00f6ttingen, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063790800","display_name":"Anton Thielmann","orcid":"https://orcid.org/0000-0002-6768-8992"},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Anton Thielmann","raw_affiliation_strings":["Clausthal University of Technology, Clausthal-Zellerfeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clausthal University of Technology, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016630281","display_name":"Benjamin S\u00e4fken","orcid":"https://orcid.org/0000-0003-4702-3333"},"institutions":[{"id":"https://openalex.org/I43980791","display_name":"Clausthal University of Technology","ror":"https://ror.org/04qb8nc58","country_code":"DE","type":"education","lineage":["https://openalex.org/I43980791"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Benjamin S\u00e4fken","raw_affiliation_strings":["Clausthal University of Technology, Clausthal-Zellerfeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Clausthal University of Technology, Clausthal-Zellerfeld, Germany","institution_ids":["https://openalex.org/I43980791"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103057929"],"corresponding_institution_ids":["https://openalex.org/I74656192"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.8209,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62577687,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"40","issue":"7","first_page":"3645","last_page":"3663"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9921000003814697,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9921000003814697,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.98580002784729,"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/smoothing","display_name":"Smoothing","score":0.7020285725593567},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.5436069965362549},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5213845372200012},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5090343356132507},{"id":"https://openalex.org/keywords/smoothing-spline","display_name":"Smoothing spline","score":0.4489981234073639},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4392695128917694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43870511651039124},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36141449213027954},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.34100621938705444},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2188030183315277},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11348050832748413},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.07529410719871521}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7020285725593567},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.5436069965362549},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5213845372200012},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5090343356132507},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.4489981234073639},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4392695128917694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43870511651039124},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36141449213027954},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.34100621938705444},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2188030183315277},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11348050832748413},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.07529410719871521},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00180-024-01593-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-024-01593-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-024-01593-z.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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":"Computational Statistics","raw_type":"journal-article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/147757","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/147757","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00180-024-01593-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-024-01593-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-024-01593-z.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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":"Computational Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7829407014","display_name":"Verteilungsregression mit tiefen k\u00fcnstlichen neuronalen Netzen","funder_award_id":"450330162","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406230673.pdf","grobid_xml":"https://content.openalex.org/works/W4406230673.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1498436455","https://openalex.org/W1990420052","https://openalex.org/W2053197643","https://openalex.org/W2056735347","https://openalex.org/W2063507361","https://openalex.org/W2119160928","https://openalex.org/W2133944729","https://openalex.org/W2154065358","https://openalex.org/W2468874071","https://openalex.org/W2735160842","https://openalex.org/W2919115771","https://openalex.org/W2964155733","https://openalex.org/W3000332379","https://openalex.org/W3047629520","https://openalex.org/W3106414954","https://openalex.org/W3112717819","https://openalex.org/W4229930971","https://openalex.org/W4238404964","https://openalex.org/W4312119985","https://openalex.org/W4401419579","https://openalex.org/W4403298762"],"related_works":["https://openalex.org/W2160550653","https://openalex.org/W1004284732","https://openalex.org/W1833023352","https://openalex.org/W3125802181","https://openalex.org/W2033337756","https://openalex.org/W1980787558","https://openalex.org/W62927482","https://openalex.org/W2158092971","https://openalex.org/W2060934130","https://openalex.org/W1879229833"],"abstract_inverted_index":{"Abstract":[0],"Due":[1],"to":[2,15,20,157,176],"the":[3,33,37,50,69,72,87,112,130,137,162,191],"popularity":[4],"of":[5,39,71,89,114,145,161,174,185],"deep":[6],"learning":[7],"models":[8,19,25,123],"there":[9],"have":[10],"recently":[11],"been":[12],"many":[13],"attempts":[14],"translate":[16],"generalized":[17,62,146],"additive":[18,24,85,122,167],"neural":[21,82,120,177,180,186],"nets.":[22],"Generalized":[23],"are":[26,56,196],"usually":[27],"regularized":[28],"by":[29,43,58],"a":[30,172,199],"penalty":[31],"in":[32,119,198],"loss":[34],"function":[35],"and":[36,79,148,202],"magnitude":[38],"penalization":[40],"is":[41,76,92],"controlled":[42],"one":[44],"or":[45,64,104],"more":[46],"smoothing":[47,54,90,116,139,163,193],"parameters.":[48,164],"In":[49,107],"statistical":[51],"literature":[52],"these":[53],"parameters":[55,91],"estimated":[57,103],"criteria":[59],"such":[60,128],"as":[61,129,188,190],"cross-validation":[63,147],"restricted":[65,149],"maximum":[66,150],"likelihood.":[67,151],"While":[68],"estimation":[70,88,118],"primary":[73],"regression":[74],"coefficients":[75],"well":[77,189],"calibrated":[78],"investigated":[80,197],"for":[81],"net":[83],"based":[84,95],"models,":[86],"often":[93],"either":[94],"on":[96],"testing":[97],"data":[98],"(and":[99],"grid":[100],"search),":[101],"implicitly":[102],"completely":[105],"neglected.":[106],"this":[108],"paper,":[109],"we":[110,153,170],"address":[111],"issue":[113],"explicit":[115],"parameter":[117,140,194],"net-based":[121],"fitted":[124],"via":[125,142],"gradient-based":[126,143,192],"methods,":[127],"well-known":[131],"Adam":[132],"algorithm.":[133],"We":[134],"therefore":[135],"investigate":[136],"data-driven":[138],"selection":[141,195],"optimization":[144],"Thus":[152],"do":[154],"not":[155],"need":[156],"calculate":[158],"Hessian":[159],"information":[160],"As":[165],"an":[166,203],"model":[168],"structure,":[169],"use":[171],"translation":[173],"P-splines":[175,187],"nets,":[178],"so-called":[179],"P-splines.":[181],"The":[182],"fitting":[183],"process":[184],"simulation":[200],"study":[201],"application.":[204]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}
