{"id":"https://openalex.org/W4392121002","doi":"https://doi.org/10.48550/arxiv.2402.14645","title":"Sparse Linear Regression and Lattice Problems","display_name":"Sparse Linear Regression and Lattice Problems","publication_year":2024,"publication_date":"2024-02-22","ids":{"openalex":"https://openalex.org/W4392121002","doi":"https://doi.org/10.48550/arxiv.2402.14645"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2402.14645","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.14645","pdf_url":"https://arxiv.org/pdf/2402.14645","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2402.14645","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015434599","display_name":"Aparna Gupte","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gupte, Aparna","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009532062","display_name":"Neekon Vafa","orcid":"https://orcid.org/0000-0002-0555-4200"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vafa, Neekon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000240220","display_name":"Vinod Vaikuntanathan","orcid":"https://orcid.org/0000-0002-2666-0045"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vaikuntanathan, Vinod","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015434599"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.805400013923645,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.805400013923645,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5300949215888977},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5071508884429932},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.49543464183807373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37741920351982117},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.36067265272140503},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3427296280860901},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.34122204780578613},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18651044368743896}],"concepts":[{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5300949215888977},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5071508884429932},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.49543464183807373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37741920351982117},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36067265272140503},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3427296280860901},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.34122204780578613},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18651044368743896},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2402.14645","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.14645","pdf_url":"https://arxiv.org/pdf/2402.14645","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2402.14645","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.14645","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2402.14645","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.14645","pdf_url":"https://arxiv.org/pdf/2402.14645","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392121002.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2040944759","https://openalex.org/W2015645585","https://openalex.org/W2054730750","https://openalex.org/W1985063657","https://openalex.org/W3103093651","https://openalex.org/W31220157","https://openalex.org/W2288557197","https://openalex.org/W4233024177","https://openalex.org/W2101914902","https://openalex.org/W3174613421"],"abstract_inverted_index":{"Sparse":[0],"linear":[1,174],"regression":[2],"(SLR)":[3],"is":[4,12,41,75,80,83,152,223],"a":[5,14,20,25,44,126,193],"well-studied":[6,256],"problem":[7,134],"in":[8,90,209,228,240],"statistics":[9],"where":[10,139,221,244],"one":[11],"given":[13],"design":[15,73,162,200,219],"matrix":[16,74],"$X\\in\\mathbb{R}^{m\\times":[17],"n}$":[18],"and":[19,33,38,65,255],"response":[21],"vector":[22,27],"$y=X\u03b8^*+w$":[23],"for":[24,172,192,214],"$k$-sparse":[26,45],"$\u03b8^*$":[28],"(that":[29],"is,":[30],"$\\|\u03b8^*\\|_0\\leq":[31],"k$)":[32],"small,":[34],"arbitrary":[35],"noise":[36],"$w$,":[37],"the":[39,51,66,72,113,129,140,144,149,156,161,168,185,199,204,210,229,241,250],"goal":[40],"to":[42,96,137,155,179,181,225],"find":[43],"$\\widehat\u03b8":[46],"\\in":[47],"\\mathbb{R}^n$":[48],"that":[49,147],"minimizes":[50],"mean":[52],"squared":[53],"prediction":[54],"error":[55],"$\\frac{1}{m}\\|X\\widehat\u03b8-X\u03b8^*\\|^2_2$.":[56],"While":[57],"$\\ell_1$-relaxation":[58],"methods":[59],"such":[60],"as":[61],"basis":[62,146],"pursuit,":[63],"Lasso,":[64],"Dantzig":[67],"selector":[68],"solve":[69],"SLR":[70,107,196,206],"when":[71],"well-conditioned,":[76],"no":[77],"general":[78],"algorithm":[79],"known,":[81],"nor":[82],"there":[84,245],"any":[85,237],"formal":[86],"evidence":[87,102],"of":[88,103,106,116,128,143,160,167,187,195,235,253],"hardness":[89,105,115,191,234,252],"an":[91,122],"average-case":[92,104,182],"setting":[93],"with":[94],"respect":[95],"all":[97,109],"efficient":[98,110],"algorithms.":[99],"We":[100],"give":[101,121],"w.r.t.":[108],"algorithms":[111],"assuming":[112,249],"worst-case":[114,180,251],"lattice":[117,145,257],"problems.":[118,258],"Specifically,":[119],"we":[120,232],"instance-by-instance":[123],"reduction":[124],"from":[125,184],"variant":[127],"bounded":[130],"distance":[131],"decoding":[132],"(BDD)":[133],"on":[135],"lattices":[136],"SLR,":[138],"condition":[141,159],"number":[142],"defines":[148],"BDD":[150],"instance":[151],"directly":[153],"related":[154],"restricted":[157],"eigenvalue":[158],"matrix,":[163],"which":[164],"characterizes":[165],"some":[166],"classical":[169],"statistical-computational":[170],"gaps":[171],"sparse":[173],"regression.":[175],"Also,":[176],"by":[177],"appealing":[178],"reductions":[183],"world":[186],"lattices,":[188],"this":[189],"shows":[190],"distribution":[194],"instances;":[197],"while":[198],"matrices":[201],"are":[202,208,246],"ill-conditioned,":[203],"resulting":[205],"instances":[207],"identifiable":[211,230],"regime.":[212],"Furthermore,":[213],"well-conditioned":[215],"(essentially)":[216],"isotropic":[217],"Gaussian":[218],"matrices,":[220],"Lasso":[222],"known":[224],"behave":[226],"well":[227],"regime,":[231],"show":[233],"outputting":[236],"good":[238],"solution":[239],"unidentifiable":[242],"regime":[243],"many":[247],"solutions,":[248],"standard":[254]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
