{"id":"https://openalex.org/W7202231194","doi":"https://doi.org/10.48550/arxiv.2608.07432","title":"Spectral Dependence of Convex Regularization: Fundamental Limits under Right-Rotationally Invariant Designs","display_name":"Spectral Dependence of Convex Regularization: Fundamental Limits under Right-Rotationally Invariant Designs","publication_year":2026,"publication_date":"2026-08-07","ids":{"openalex":"https://openalex.org/W7202231194","doi":"https://doi.org/10.48550/arxiv.2608.07432"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.07432","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.07432","pdf_url":"https://arxiv.org/pdf/2608.07432","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.07432","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5146575908","display_name":"Baichen Tan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tan, Baichen","raw_affiliation_strings":["Department of Statistics , Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5146478344","display_name":"Audrey Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang, Audrey","raw_affiliation_strings":["Department of Statistics , Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069505373","display_name":"Cynthia Rush","orcid":"https://orcid.org/0000-0001-6857-2855","observed_orcids":["https://orcid.org/0000-0001-6857-2855"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rush, Cynthia","raw_affiliation_strings":["Department of Statistics , Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9535999894142151,"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"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9535999894142151,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.035999998450279236,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.002099999925121665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convex-regularization","display_name":"convex regularization","score":0.9860000014305115},{"id":"https://openalex.org/keywords/high-dimensional-linear-regression","display_name":"high-dimensional linear regression","score":0.8429999947547913},{"id":"https://openalex.org/keywords/fundamental-limits","display_name":"fundamental limits","score":0.5479999780654907},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.699999988079071},{"id":"https://openalex.org/keywords/approximate-message-passing","display_name":"approximate message passing","score":0.8299999833106995},{"id":"https://openalex.org/keywords/limiting-spectral-distribution","display_name":"limiting spectral distribution","score":0.8939999938011169},{"id":"https://openalex.org/keywords/singular-value-distribution","display_name":"singular value distribution","score":0.8330000042915344},{"id":"https://openalex.org/keywords/asymptotic-risk","display_name":"asymptotic risk","score":0.7459999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8076000213623047},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7462999820709229},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6184999942779541},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5952000021934509},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.574400007724762},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.46070000529289246},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4415999948978424},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.42719998955726624},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.426800012588501},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.3693000078201294},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3075999915599823},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3019999861717224},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30079999566078186},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2955999970436096},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2703000009059906},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26649999618530273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.07432","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.07432","pdf_url":"https://arxiv.org/pdf/2608.07432","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2608.07432","doi":"https://doi.org/10.48550/arxiv.2608.07432","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.07432","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.07432","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.07432","pdf_url":"https://arxiv.org/pdf/2608.07432","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4603561894","display_name":"Fundamental Limits of High-Dimensional Statistical Estimation","funder_award_id":"2413828","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7202231194.pdf","grobid_xml":"https://content.openalex.org/works/W7202231194.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4402475369"],"related_works":["https://openalex.org/W2922934758","https://openalex.org/W1461441059","https://openalex.org/W2999718746","https://openalex.org/W4414599726","https://openalex.org/W7164043106","https://openalex.org/W2567904107","https://openalex.org/W4387828502","https://openalex.org/W4402475369","https://openalex.org/W4290056447","https://openalex.org/W4407511363"],"abstract_inverted_index":{"We":[0,17],"study":[1],"the":[2,20,32,49,59,68,72,87,103,122,126,130,139,148,153,160,165,168,175],"fundamental":[3],"limits":[4],"of":[5,23,34,61,71,105,110,121,152,164,177],"convex-regularized":[6],"estimation":[7],"in":[8,58,86,89,129,144],"high-dimensional":[9,131],"linear":[10],"regression":[11],"with":[12],"right-rotationally":[13],"invariant":[14],"design":[15,154],"matrices.":[16],"show":[18,137],"that":[19,114,138],"asymptotic":[21,69],"risks":[22],"convex-penalized":[24],"least":[25],"squares":[26],"estimators":[27],"are":[28],"lower":[29,50,63,127,140],"bounded":[30],"by":[31],"risk":[33],"an":[35,145],"approximate":[36],"message":[37],"passing":[38],"algorithm":[39],"known":[40],"as":[41],"Bayes":[42],"VAMP,":[43],"and":[44],"we":[45,66,115,135],"further":[46],"characterize":[47,67],"when":[48],"bound":[51,64,128,141],"is":[52,113,142],"attainable.":[53],"As":[54],"a":[55,84,118],"technical":[56],"ingredient":[57],"proof":[60],"our":[62,111],"theorem,":[65],"performance":[70],"$\\ell_2$-perturbed":[73],"convex":[74,106,178],"estimator":[75],"for":[76],"every":[77],"fixed":[78],"perturbation":[79],"strength":[80],"$\u03bb>0$.":[81],"This":[82],"closes":[83],"gap":[85],"literature,":[88],"which":[90],"$\u03bb$":[91],"was":[92],"required":[93],"to":[94],"be":[95],"sufficiently":[96],"large":[97],"or":[98,171],"restrictions":[99],"were":[100],"imposed":[101],"on":[102,125,147],"class":[104],"estimators.":[107],"The":[108],"benefit":[109],"approach":[112],"can":[116,136],"conduct":[117],"direct":[119],"analysis":[120],"spectrum's":[123],"impact":[124],"limit.":[132],"In":[133],"particular,":[134],"monotone":[143],"ordering":[146],"limiting":[149],"spectral":[150],"distributions":[151],"matrix.":[155],"These":[156],"results":[157],"isolate":[158],"how":[159],"full":[161],"singular-value":[162],"distribution":[163],"design---not":[166],"merely":[167],"aspect":[169],"ratio":[170],"average":[172],"measurement":[173],"strength---governs":[174],"limitations":[176],"regularization.":[179]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-12T00:00:00"}