{"id":"https://openalex.org/W3027650860","doi":"https://doi.org/10.1137/20m1330634","title":"The Trimmed Lasso: Sparse Recovery Guarantees and Practical Optimization by the Generalized Soft-Min Penalty","display_name":"The Trimmed Lasso: Sparse Recovery Guarantees and Practical Optimization by the Generalized Soft-Min Penalty","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3027650860","doi":"https://doi.org/10.1137/20m1330634","mag":"3027650860"},"language":"en","primary_location":{"id":"doi:10.1137/20m1330634","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1330634","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1330634","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1330634","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058139643","display_name":"Tal Amir","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tal Amir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101453970","display_name":"Ronen Basri","orcid":"https://orcid.org/0000-0001-8053-2151"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronen Basri","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034942163","display_name":"Boaz Nadler","orcid":"https://orcid.org/0000-0002-9777-4576"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boaz Nadler","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9777-4576","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058139643"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.178,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.41955504,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"3","first_page":"900","last_page":"929"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9994000196456909,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.8078358173370361},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.587242603302002},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5671414732933044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5203206539154053},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5153881311416626},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5058512687683105},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5047239065170288},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49051254987716675},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.46398165822029114},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.4194175899028778},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40185102820396423},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.377579003572464}],"concepts":[{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.8078358173370361},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.587242603302002},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5671414732933044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5203206539154053},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5153881311416626},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5058512687683105},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5047239065170288},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49051254987716675},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.46398165822029114},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.4194175899028778},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40185102820396423},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.377579003572464},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1330634","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1330634","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1330634","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2005.09021","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.09021","pdf_url":"https://arxiv.org/pdf/2005.09021","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3027650860","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2005.09021","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2005.09021","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.09021","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1137/20m1330634","is_oa":true,"landing_page_url":"https://doi.org/10.1137/20m1330634","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/20M1330634","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308316","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3027650860.pdf","grobid_xml":"https://content.openalex.org/works/W3027650860.grobid-xml"},"referenced_works_count":88,"referenced_works":["https://openalex.org/W18203565","https://openalex.org/W143004564","https://openalex.org/W228380312","https://openalex.org/W340244495","https://openalex.org/W1523985187","https://openalex.org/W1583497301","https://openalex.org/W1591116419","https://openalex.org/W1620362451","https://openalex.org/W1916786071","https://openalex.org/W1965125844","https://openalex.org/W1969423031","https://openalex.org/W1974478886","https://openalex.org/W1975377467","https://openalex.org/W1976709621","https://openalex.org/W1980079540","https://openalex.org/W1980454827","https://openalex.org/W1989009613","https://openalex.org/W1996287810","https://openalex.org/W1996352909","https://openalex.org/W1998615394","https://openalex.org/W2004544971","https://openalex.org/W2012961725","https://openalex.org/W2015418199","https://openalex.org/W2018429487","https://openalex.org/W2020390700","https://openalex.org/W2021302824","https://openalex.org/W2025666718","https://openalex.org/W2028781966","https://openalex.org/W2031906930","https://openalex.org/W2032618720","https://openalex.org/W2039094757","https://openalex.org/W2040912306","https://openalex.org/W2041781650","https://openalex.org/W2050968963","https://openalex.org/W2065829287","https://openalex.org/W2069959554","https://openalex.org/W2074682976","https://openalex.org/W2075506710","https://openalex.org/W2077925928","https://openalex.org/W2078204800","https://openalex.org/W2090963365","https://openalex.org/W2095978736","https://openalex.org/W2097360283","https://openalex.org/W2100068253","https://openalex.org/W2100556411","https://openalex.org/W2101675075","https://openalex.org/W2105630053","https://openalex.org/W2107861471","https://openalex.org/W2111067490","https://openalex.org/W2116148865","https://openalex.org/W2119883478","https://openalex.org/W2122189635","https://openalex.org/W2122340891","https://openalex.org/W2125151258","https://openalex.org/W2127271355","https://openalex.org/W2128659236","https://openalex.org/W2129131372","https://openalex.org/W2131074607","https://openalex.org/W2135046866","https://openalex.org/W2145096794","https://openalex.org/W2149414429","https://openalex.org/W2151693816","https://openalex.org/W2155628440","https://openalex.org/W2157434051","https://openalex.org/W2160396672","https://openalex.org/W2160979406","https://openalex.org/W2161765392","https://openalex.org/W2164452299","https://openalex.org/W2166029977","https://openalex.org/W2168745297","https://openalex.org/W2289917018","https://openalex.org/W2395430402","https://openalex.org/W2536620281","https://openalex.org/W2584565348","https://openalex.org/W2588776893","https://openalex.org/W2738241071","https://openalex.org/W2748514054","https://openalex.org/W2963351303","https://openalex.org/W2963423191","https://openalex.org/W2963452074","https://openalex.org/W2963564348","https://openalex.org/W2963696951","https://openalex.org/W3006889477","https://openalex.org/W3048822613","https://openalex.org/W3101767848","https://openalex.org/W3105034597","https://openalex.org/W4205337121","https://openalex.org/W4294541781"],"related_works":["https://openalex.org/W2748514054","https://openalex.org/W2113328646","https://openalex.org/W2788943234","https://openalex.org/W2014475680","https://openalex.org/W2469129780","https://openalex.org/W2888231103","https://openalex.org/W3197657182","https://openalex.org/W3097759136","https://openalex.org/W3098707346","https://openalex.org/W2913088541","https://openalex.org/W3213019012","https://openalex.org/W1983956809","https://openalex.org/W2010282149","https://openalex.org/W2949340155","https://openalex.org/W3100817920","https://openalex.org/W2985353144","https://openalex.org/W3015894195","https://openalex.org/W2964224255","https://openalex.org/W2950919203","https://openalex.org/W2944731954"],"abstract_inverted_index":{"We":[0,32,59],"present":[1],"a":[2,17,34,100,142,152],"new":[3],"approach":[4],"to":[5,145,169],"solve":[6],"the":[7,24,43,49,62,81,103,107,115,119,156,173],"sparse":[8,74,158],"approximation":[9,159],"or":[10],"best":[11],"subset":[12],"selection":[13],"problem,":[14],"namely":[15],"find":[16],"$k$-sparse":[18,128],"vector":[19],"${\\bf":[20,52],"x}\\in\\mathbb{R}^d$":[21],"that":[22,61,88],"minimizes":[23],"$\\ell_2$":[25],"residual":[26,39],"$\\lVert":[27],"A{\\bf":[28],"x}-{\\bf":[29],"y}":[30],"\\rVert_2$.":[31],"consider":[33],"regularized":[35],"approach,":[36],"whereby":[37],"this":[38,91],"is":[40],"penalized":[41,82],"by":[42],"non-convex":[44],"$\\textit{trimmed":[45],"lasso}$,":[46],"defined":[47],"as":[48],"$\\ell_1$-norm":[50],"of":[51,80,172],"x}$":[53],"excluding":[54],"its":[55,165],"$k$":[56],"largest-magnitude":[57],"entries.":[58],"prove":[60],"trimmed":[63,104,120],"lasso":[64,117],"has":[65],"several":[66],"appealing":[67],"theoretical":[68],"properties,":[69],"and":[70,118],"in":[71,149],"particular":[72],"derive":[73,141],"recovery":[75],"guarantees":[76],"assuming":[77],"successful":[78],"optimization":[79],"objective.":[83],"Next,":[84],"we":[85,98,140,163],"show":[86],"empirically":[87],"directly":[89],"optimizing":[90],"objective":[92],"can":[93],"be":[94],"quite":[95],"challenging.":[96],"Instead,":[97],"propose":[99],"surrogate":[101],"for":[102,155],"lasso,":[105,121],"called":[106],"$\\textit{generalized":[108],"soft-min}$.":[109],"This":[110],"penalty":[111,133],"smoothly":[112],"interpolates":[113],"between":[114],"classical":[116],"while":[122],"taking":[123],"into":[124],"account":[125],"all":[126],"possible":[127],"patterns.":[129],"The":[130],"generalized":[131],"soft-min":[132],"involves":[134],"summation":[135],"over":[136],"$\\binom{d}{k}$":[137],"terms,":[138],"yet":[139],"polynomial-time":[143],"algorithm":[144],"compute":[146],"it.":[147],"This,":[148],"turn,":[150],"yields":[151],"practical":[153],"method":[154],"original":[157],"problem.":[160],"Via":[161],"simulations,":[162],"demonstrate":[164],"competitive":[166],"performance":[167],"compared":[168],"current":[170],"state":[171],"art.":[174]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
