{"id":"https://openalex.org/W4401396978","doi":"https://doi.org/10.1145/3686794","title":"Fast Algorithms for <i> \u2113 <sub>p</sub> </i> -Regression","display_name":"Fast Algorithms for <i> \u2113 <sub>p</sub> </i> -Regression","publication_year":2024,"publication_date":"2024-08-07","ids":{"openalex":"https://openalex.org/W4401396978","doi":"https://doi.org/10.1145/3686794"},"language":"en","primary_location":{"id":"doi:10.1145/3686794","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3686794","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3686794","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3686794","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016937106","display_name":"Deeksha Adil","orcid":"https://orcid.org/0009-0004-7520-0696"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Deeksha Adil","raw_affiliation_strings":["Institute for Theoretical Studies, ETH Z\u00fcrich, Zurich, Switzerland"],"raw_orcid":"https://orcid.org/0009-0004-7520-0696","affiliations":[{"raw_affiliation_string":"Institute for Theoretical Studies, ETH Z\u00fcrich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053449713","display_name":"Rasmus Kyng","orcid":"https://orcid.org/0000-0002-8268-6258"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Rasmus Kyng","raw_affiliation_strings":["ETH Zurich Department of Computer Science, Zurich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-8268-6258","affiliations":[{"raw_affiliation_string":"ETH Zurich Department of Computer Science, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102611578","display_name":"Richard Peng","orcid":"https://orcid.org/0000-0002-5407-7965"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Richard Peng","raw_affiliation_strings":["Department of Computer Science, University of Waterloo, Waterloo, Canada"],"raw_orcid":"https://orcid.org/0000-0002-5407-7965","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067464936","display_name":"Sushant Sachdeva","orcid":"https://orcid.org/0000-0002-5393-9324"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sushant Sachdeva","raw_affiliation_strings":["University of Toronto, Toronto, Canada"],"raw_orcid":"https://orcid.org/0000-0002-5393-9324","affiliations":[{"raw_affiliation_string":"University of Toronto, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016937106"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12981387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"5","first_page":"1","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9990000128746033,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.5930224657058716},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5517404675483704},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5506172776222229},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5383272171020508},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5359476804733276},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.444404661655426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3707994818687439},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15474724769592285},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15095701813697815},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10234656929969788}],"concepts":[{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.5930224657058716},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5517404675483704},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5506172776222229},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5383272171020508},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5359476804733276},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.444404661655426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3707994818687439},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15474724769592285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15095701813697815},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10234656929969788}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3686794","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3686794","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3686794","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1145/3686794","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3686794","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3686794","source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the ACM","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4401396978.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W171428496","https://openalex.org/W1597020313","https://openalex.org/W1632601927","https://openalex.org/W1826824261","https://openalex.org/W1968307589","https://openalex.org/W2037848057","https://openalex.org/W2096633276","https://openalex.org/W2113642685","https://openalex.org/W2122315118","https://openalex.org/W2129131372","https://openalex.org/W2401415512","https://openalex.org/W2604292070","https://openalex.org/W2730726820","https://openalex.org/W2912973156","https://openalex.org/W2949083732","https://openalex.org/W2963388608","https://openalex.org/W2963595145","https://openalex.org/W2992402078","https://openalex.org/W3143835353","https://openalex.org/W3209193315","https://openalex.org/W4297952928","https://openalex.org/W4313203312","https://openalex.org/W6674103528","https://openalex.org/W6685958430"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W238609530","https://openalex.org/W2051487156","https://openalex.org/W2734192830","https://openalex.org/W3016395638","https://openalex.org/W1636163329","https://openalex.org/W3045121788","https://openalex.org/W3201655533","https://openalex.org/W3134442314","https://openalex.org/W2281248943"],"abstract_inverted_index":{"The":[0,23],"\\(\\ell":[1,102],"_p\\)":[2,103],"-norm":[3],"regression":[4],"problem":[5,9,71],"is":[6,25,167],"a":[7,106,115,128,175],"classic":[8],"in":[10,16,76,118,174,191],"optimization":[11],"with":[12],"wide":[13],"ranging":[14],"applications":[15],"machine":[17],"learning":[18],"and":[19,62,78,80],"theoretical":[20],"computer":[21],"science.":[22],"goal":[24],"to":[26,137,169,171],"compute":[27],"\\(\\boldsymbol":[28,47],"{\\mathit":[29,35,37,39,42,48,53,58],"{x}}^{\\star":[30,49],"}":[31],"=\\arg":[32],"\\min":[33],"_{\\boldsymbol":[34],"{A}}\\boldsymbol":[36],"{x}}=\\boldsymbol":[38],"{b}}}\\Vert":[40],"\\boldsymbol":[41],"{x}}\\Vert":[43],"_p^p\\)":[44],",":[45],"where":[46,142],"}\\in":[50],"\\mathbb":[51,55,60],"{R}^n,\\boldsymbol":[52],"{A}}\\in":[54],"{R}^{d\\times":[56],"n},\\boldsymbol":[57],"{b}}\\in":[59],"{R}^d\\)":[61],"\\(d\\le":[63],"n\\)":[64,153],".":[65,93],"Efficient":[66],"high-accuracy":[67,116],"algorithms":[68,83,100],"for":[69,90,101,149],"the":[70,81,111,146,158,187],"have":[72],"been":[73],"challenging":[74],"both":[75],"theory":[77],"practice":[79],"state-of-the-art":[82],"require":[84],"\\(poly(p)\\cdot":[85],"n^{\\frac{1}{2}-\\frac{1}{p}}\\)":[86],"linear":[87,122],"system":[88,123],"solves":[89],"\\(p\\ge":[91],"2\\)":[92],"In":[94],"this":[95],"article,":[96],"we":[97,156],"provide":[98],"new":[99,129],"-regression":[104],"(and":[105],"more":[107],"general":[108],"formulation":[109],"of":[110],"problem)":[112],"that":[113,133,166],"obtain":[114],"solution":[117],"\\(O(p":[119],"n^{":[120],"{(p-2)}{(3p-2)}})\\)":[121],"solves.":[124],"We":[125],"further":[126],"propose":[127],"inverse":[130],"maintenance":[131],"procedure":[132],"speeds-up":[134],"our":[135],"algorithm":[136,165,180],"\\(\\widetilde{O}(n^{\\omega":[138],"})\\)":[139,144],"total":[140],"runtime,":[141],"\\(O(n^{\\omega":[143],"denotes":[145],"running":[147],"time":[148],"multiplying":[150],"\\(n":[151],"\\times":[152],"matrices.":[154],"Additionally,":[155],"give":[157],"first":[159],"Iteratively":[160],"Reweighted":[161],"Least":[162],"Squares":[163],"(IRLS)":[164],"guaranteed":[168],"converge":[170],"an":[172],"optimum":[173],"few":[176],"iterations.":[177],"Our":[178],"IRLS":[179],"has":[181],"shown":[182],"exceptional":[183],"practical":[184],"performance,":[185],"beating":[186],"currently":[188],"available":[189],"implementations":[190],"MATLAB/CVX":[192],"by":[193],"10\u201350\u00d7.":[194]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2024-08-08T00:00:00"}