{"id":"https://openalex.org/W2920084148","doi":null,"title":"High-Dimensional Learning under Approximate Sparsity: A Unifying Framework for Nonsmooth Learning and Regularized Neural Networks","display_name":"High-Dimensional Learning under Approximate Sparsity: A Unifying Framework for Nonsmooth Learning and Regularized Neural Networks","publication_year":2019,"publication_date":"2019-03-02","ids":{"openalex":"https://openalex.org/W2920084148","mag":"2920084148"},"language":"en","primary_location":{"id":"mag:2920084148","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.00616","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.00616","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100778698","display_name":"Hongcheng Liu","orcid":"https://orcid.org/0000-0003-2451-5204","observed_orcids":["https://orcid.org/0000-0003-2451-5204"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongcheng Liu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2451-5204","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041526408","display_name":"Yinyu Ye","orcid":"https://orcid.org/0009-0001-3239-2622","observed_orcids":["https://orcid.org/0009-0001-3239-2622"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yinyu Ye","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0001-3239-2622","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"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":0.9707000255584717,"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":0.9707000255584717,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.019700000062584877,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.005900000222027302,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/restricted-strong-convexity","display_name":"restricted strong convexity","score":0.7940000295639038},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"sample complexity","score":0.6890000104904175},{"id":"https://openalex.org/keywords/regularized-neural-networks","display_name":"regularized neural networks","score":0.8849999904632568},{"id":"https://openalex.org/keywords/m-estimation","display_name":"M-estimation","score":0.906000018119812},{"id":"https://openalex.org/keywords/excess-risk","display_name":"excess risk","score":0.8669999837875366},{"id":"https://openalex.org/keywords/generalization-performance","display_name":"generalization performance","score":0.6759999990463257},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.49399998784065247}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.7308773994445801},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6886733174324036},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6767603158950806},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6157500743865967},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5830060839653015},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.565708339214325},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5503284335136414},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5011718273162842},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4903576374053955},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.44298073649406433},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4350033700466156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42597806453704834},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4220791161060333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40334075689315796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3799549639225006},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2920084148","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.00616","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2920084148","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.00616","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1618978521","https://openalex.org/W2269440111","https://openalex.org/W2384495648","https://openalex.org/W2513671774","https://openalex.org/W2771655537","https://openalex.org/W2789829558","https://openalex.org/W2807299122","https://openalex.org/W2889756710","https://openalex.org/W2950220847","https://openalex.org/W2962698540","https://openalex.org/W3119586787"],"related_works":["https://openalex.org/W3208461153","https://openalex.org/W4394591213","https://openalex.org/W4398150900","https://openalex.org/W2785619321","https://openalex.org/W2770888898","https://openalex.org/W3009328655","https://openalex.org/W2889756710","https://openalex.org/W3007580751","https://openalex.org/W4408092960","https://openalex.org/W4380490515"],"abstract_inverted_index":{"High-dimensional":[0],"statistical":[1],"learning":[2,126],"(HDSL)":[3],"has":[4],"been":[5],"widely":[6],"applied":[7],"in":[8,105,196],"data":[9,98],"analysis,":[10],"operations":[11],"research,":[12],"and":[13,39,78,127,192],"stochastic":[14],"optimization.":[15],"Despite":[16],"the":[17,27,37,41,52,55,69,75,80,85,93,96,106,123,128,139,149,152,154,162,166,174,179,184,189,193],"availability":[18],"of":[19,54,95,157],"multiple":[20],"theoretical":[21,181],"frameworks,":[22],"most":[23],"HDSL":[24],"theories":[25],"stipulate":[26],"following":[28],"two":[29,116],"conditions,":[30],"which":[31],"are":[32],"sometimes":[33],"overly":[34],"critical:":[35],"(a)":[36],"sparsity,":[38],"(b)":[40],"restricted":[42],"strong":[43],"convexity":[44],"(RSC).":[45],"This":[46,109],"paper":[47],"generalizes":[48],"both":[49,134],"conditions":[50],"via":[51,147],"use":[53],"folded":[56],"concave":[57],"penalty":[58],"(FCP);":[59],"we":[60,136],"show":[61,137],"that,":[62],"for":[63,165,183],"an":[64,198],"M-estimation":[65],"problem":[66,107],"where":[67],"(i)":[68],"(conventional)":[70],"sparsity":[71,77],"is":[72,82,99,168],"relaxed":[73],"into":[74],"approximate":[76],"(ii)":[79],"RSC":[81],"completely":[83],"absent,":[84],"FCP-based":[86],"regularization":[87],"leads":[88],"to":[89,102,113,161,173],"poly-logarithmic":[90,104,140],"sample":[91,141],"complexity:":[92],"size":[94],"training":[97,163,197],"only":[100],"required":[101],"be":[103,144],"dimensionality.":[108],"finding":[110],"allows":[111],"us":[112],"further":[114],"understand":[115],"important":[117],"paradigms":[118],"much":[119],"less":[120],"discussed":[121],"formerly:":[122],"high-dimensional":[124],"nonsmooth":[125],"(deep)":[129],"neural":[130],"networks":[131],"(NN).":[132],"For":[133],"problems,":[135],"that":[138],"complexity":[142],"can":[143],"maintained.":[145],"Furthermore,":[146],"integrating":[148],"NN":[150,167],"with":[151,171],"FCP,":[153],"excess":[155],"risk":[156],"a":[158],"stationary":[159],"point":[160],"formulation":[164],"strictly":[169],"monotonic":[170],"respect":[172],"solution's":[175],"suboptimality":[176],"gap,":[177],"providing":[178],"first":[180],"evidence":[182],"empirically":[185],"observed":[186],"consistency":[187],"between":[188],"generalization":[190],"performance":[191],"optimization":[194],"quality":[195],"NN.":[199]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2019-03-11T00:00:00"}
