{"id":"https://openalex.org/W7131363750","doi":"https://doi.org/10.1007/s00180-025-01710-6","title":"A framework to efficiently smooth L1 penalties for linear regression","display_name":"A framework to efficiently smooth L1 penalties for linear regression","publication_year":2026,"publication_date":"2026-02-25","ids":{"openalex":"https://openalex.org/W7131363750","doi":"https://doi.org/10.1007/s00180-025-01710-6"},"language":"en","primary_location":{"id":"doi:10.1007/s00180-025-01710-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00180-025-01710-6","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5124759044","display_name":"Georg Hahn","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Georg Hahn","raw_affiliation_strings":["Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA"],"raw_orcid":"https://orcid.org/0000-0001-6008-2720","affiliations":[{"raw_affiliation_string":"Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Sharon M. Lutz","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sharon M. Lutz","raw_affiliation_strings":["Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126776939","display_name":"Nilanjana Laha","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nilanjana Laha","raw_affiliation_strings":["Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126749884","display_name":"Julian Hecker","orcid":null},"institutions":[{"id":"https://openalex.org/I1283280774","display_name":"Brigham and Women's Hospital","ror":"https://ror.org/04b6nzv94","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1283280774","https://openalex.org/I48633490"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julian Hecker","raw_affiliation_strings":["Channing Division of Network Medicine, Brigham and Women\u2019s Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Channing Division of Network Medicine, Brigham and Women\u2019s Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I1283280774","https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019016063","display_name":"Dmitry Prokopenko","orcid":"https://orcid.org/0000-0002-1844-5652"},"institutions":[{"id":"https://openalex.org/I2801315873","display_name":"Somerville Hospital","ror":"https://ror.org/023pf5e38","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I124574311","https://openalex.org/I2801315873"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dmitry Prokopenko","raw_affiliation_strings":["Genetics and Aging Research Unit, Department of Neurology, McCance Center for Brain Health, Massachusetts General Hospital, 399 Revolution Drive, Somerville, MA, 02145, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Genetics and Aging Research Unit, Department of Neurology, McCance Center for Brain Health, Massachusetts General Hospital, 399 Revolution Drive, Somerville, MA, 02145, USA","institution_ids":["https://openalex.org/I2801315873"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126745826","display_name":"Sanghun Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I89015989","display_name":"Dankook University","ror":"https://ror.org/058pdbn81","country_code":"KR","type":"education","lineage":["https://openalex.org/I89015989"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Sanghun Lee","raw_affiliation_strings":["Division of Medicine, Department of Medical Consilience, Graduate school, Dankook University, Yongin-si, 16890, Gyeonggi-do, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Medicine, Department of Medical Consilience, Graduate school, Dankook University, Yongin-si, 16890, Gyeonggi-do, South Korea","institution_ids":["https://openalex.org/I89015989"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124796640","display_name":"Woojoo Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Woojoo Lee","raw_affiliation_strings":["Department of Public Health Science, Graduate School of Public Health, Seoul National University, Gwanak-ro, Gwanak-gu, 08826, South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Public Health Science, Graduate School of Public Health, Seoul National University, Gwanak-ro, Gwanak-gu, 08826, South Korea","institution_ids":["https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126769944","display_name":"Michael H. Cho","orcid":null},"institutions":[{"id":"https://openalex.org/I1283280774","display_name":"Brigham and Women's Hospital","ror":"https://ror.org/04b6nzv94","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1283280774","https://openalex.org/I48633490"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael H. Cho","raw_affiliation_strings":["Channing Division of Network Medicine, Brigham and Women\u2019s Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Channing Division of Network Medicine, Brigham and Women\u2019s Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I1283280774","https://openalex.org/I136199984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126759416","display_name":"Edwin K. Silverman","orcid":null},"institutions":[{"id":"https://openalex.org/I1283280774","display_name":"Brigham and Women's Hospital","ror":"https://ror.org/04b6nzv94","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1283280774","https://openalex.org/I48633490"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edwin K. Silverman","raw_affiliation_strings":["Channing Division of Network Medicine, Brigham and Women\u2019s Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Channing Division of Network Medicine, Brigham and Women\u2019s Hospital and Harvard Medical School, 181 Longwood Avenue, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I1283280774","https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126766433","display_name":"Christoph Lange","orcid":null},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christoph Lange","raw_affiliation_strings":["Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Biostatistics, Harvard T.H. Chan School of Public Health, 677 Huntington Ave, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5124759044"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21165724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.38119998574256897,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.38119998574256897,"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/T10136","display_name":"Statistical Methods and Inference","score":0.25929999351501465,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.07190000265836716,"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":0.6847000122070312},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6498000025749207},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.566100001335144},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.545199990272522},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.5297999978065491},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4765999913215637},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.46799999475479126},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4345000088214874},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.4341000020503998},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43149998784065247}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6847000122070312},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6498000025749207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5838000178337097},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.566100001335144},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.545199990272522},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.5297999978065491},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5024999976158142},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.46799999475479126},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43650001287460327},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4345000088214874},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.4341000020503998},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43149998784065247},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3937999904155731},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.35839998722076416},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.34459999203681946},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3273000121116638},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2825999855995178},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.2784000039100647},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00180-025-01710-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00180-025-01710-6","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4680013325","display_name":null,"funder_award_id":"U01HL089856, U01HL089897, P01HL120839, P01HL132825, 2U01HG008685","funder_id":"https://openalex.org/F4320337338","funder_display_name":"National Heart, Lung, and Blood Institute"},{"id":"https://openalex.org/G744216480","display_name":null,"funder_award_id":"R01HG008976","funder_id":"https://openalex.org/F4320337348","funder_display_name":"National Human Genome Research Institute"}],"funders":[{"id":"https://openalex.org/F4320309944","display_name":"Cure Alzheimer's Fund","ror":"https://ror.org/05ewr7t48"},{"id":"https://openalex.org/F4320337338","display_name":"National Heart, Lung, and Blood Institute","ror":"https://ror.org/012pb6c26"},{"id":"https://openalex.org/F4320337348","display_name":"National Human Genome Research Institute","ror":"https://ror.org/00baak391"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1972010412","https://openalex.org/W1989060270","https://openalex.org/W2056385679","https://openalex.org/W2063978378","https://openalex.org/W2074682976","https://openalex.org/W2082907106","https://openalex.org/W2100556411","https://openalex.org/W2119058682","https://openalex.org/W2119862467","https://openalex.org/W2122825543","https://openalex.org/W2132555912","https://openalex.org/W2138019504","https://openalex.org/W2140514146","https://openalex.org/W2167732364","https://openalex.org/W2416562393","https://openalex.org/W2891479958","https://openalex.org/W2898309436","https://openalex.org/W2964067691","https://openalex.org/W3121832289","https://openalex.org/W3155115410","https://openalex.org/W4294541781","https://openalex.org/W4394641052","https://openalex.org/W4399550443","https://openalex.org/W6910710676"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-02-25T00:00:00"}