{"id":"https://openalex.org/W4413386210","doi":"https://doi.org/10.1007/s10589-025-00724-6","title":"Probabilistic iterative hard thresholding for sparse learning","display_name":"Probabilistic iterative hard thresholding for sparse learning","publication_year":2025,"publication_date":"2025-08-21","ids":{"openalex":"https://openalex.org/W4413386210","doi":"https://doi.org/10.1007/s10589-025-00724-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-025-00724-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-025-00724-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-025-00724-6.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-025-00724-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045364325","display_name":"Matteo Bergamaschi","orcid":"https://orcid.org/0000-0002-3983-5019"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Matteo Bergamaschi","raw_affiliation_strings":["Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padua, Padova, Italy","Department of Mathematics \"Tullio Levi-Civita\", University of Padua, Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padua, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Department of Mathematics \"Tullio Levi-Civita\", University of Padua, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005501332","display_name":"Andrea Cristofari","orcid":"https://orcid.org/0000-0002-9126-3994"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Cristofari","raw_affiliation_strings":["Department of Civil Engineering and Computer Science Engineering, University of Rome \u201cTor Vergata\u201d, Roma, Italy","Department of Civil Engineering and Computer Science Engineering, University of Rome \"Tor Vergata\", Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Computer Science Engineering, University of Rome \u201cTor Vergata\u201d, Roma, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Civil Engineering and Computer Science Engineering, University of Rome \"Tor Vergata\", Roma, Italy","institution_ids":["https://openalex.org/I116067653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066151990","display_name":"Vyacheslav Kungurtsev","orcid":"https://orcid.org/0000-0003-2229-8824"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Vyacheslav Kungurtsev","raw_affiliation_strings":["Department of Civil Engineering and Computer Science Engineering, Czech Technical University in Prague, Kladno, Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil Engineering and Computer Science Engineering, Czech Technical University in Prague, Kladno, Czechia","institution_ids":["https://openalex.org/I44504214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040000503","display_name":"Francesco Rinaldi","orcid":"https://orcid.org/0000-0001-8978-6027"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Rinaldi","raw_affiliation_strings":["Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padua, Padova, Italy","Department of Mathematics \"Tullio Levi-Civita\", University of Padua, Padova, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8978-6027","affiliations":[{"raw_affiliation_string":"Department of Mathematics \u201cTullio Levi-Civita\u201d, University of Padua, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Department of Mathematics \"Tullio Levi-Civita\", University of Padua, Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045364325"],"corresponding_institution_ids":["https://openalex.org/I138689650"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21685454,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"93","issue":"1","first_page":"57","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9976000189781189,"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/mathematics","display_name":"Mathematics","score":0.7671635150909424},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.6118620038032532},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5842822790145874},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3952253460884094},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3940051198005676},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1856224536895752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17858314514160156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7671635150909424},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.6118620038032532},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5842822790145874},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3952253460884094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3940051198005676},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1856224536895752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17858314514160156},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10589-025-00724-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-025-00724-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-025-00724-6.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:art.torvergata.it:2108/451343","is_oa":true,"landing_page_url":"https://hdl.handle.net/2108/451343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.research.unipd.it:11577/3590785","is_oa":true,"landing_page_url":"https://hdl.handle.net/11577/3590785","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10589-025-00724-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-025-00724-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-025-00724-6.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6129264207","display_name":null,"funder_award_id":"101084642","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8072696303","display_name":null,"funder_award_id":"101084642","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413386210.pdf","grobid_xml":"https://content.openalex.org/works/W4413386210.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W638016179","https://openalex.org/W1875533481","https://openalex.org/W1980454827","https://openalex.org/W2081280387","https://openalex.org/W2083346837","https://openalex.org/W2098840904","https://openalex.org/W2137633966","https://openalex.org/W2187547409","https://openalex.org/W2605323362","https://openalex.org/W2805222821","https://openalex.org/W2912099989","https://openalex.org/W2963465983","https://openalex.org/W2963579802","https://openalex.org/W2963857521","https://openalex.org/W2964152294","https://openalex.org/W2985390828","https://openalex.org/W3112057963","https://openalex.org/W3192244761","https://openalex.org/W3193729844","https://openalex.org/W3201876985","https://openalex.org/W4254313632","https://openalex.org/W4287198943","https://openalex.org/W4391998833"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1542224353","https://openalex.org/W1661087619","https://openalex.org/W2116854923","https://openalex.org/W1979597421","https://openalex.org/W2750730210","https://openalex.org/W2236974868","https://openalex.org/W4312766348","https://openalex.org/W4233939244","https://openalex.org/W2106145857"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"statistical":[2,35],"modeling":[3],"wherein":[4,85],"the":[5,16,23,45,69,89,98,127,133],"data":[6,83],"regime":[7],"is":[8,53,100],"unfavorable":[9],"in":[10,22,31,50,81],"terms":[11],"of":[12,47,58,71,78,88,95,126],"dimensionality":[13],"relative":[14],"to":[15,75],"sample":[17],"size,":[18],"finding":[19],"hidden":[20],"sparsity":[21,60],"relationship":[24],"structure":[25],"between":[26],"variables":[27],"can":[28],"be":[29,92],"critical":[30],"formulating":[32],"an":[33,64,112],"accurate":[34],"model.":[36],"The":[37],"so-called":[38],"\u201c":[39],"$$\\ell":[40],"_0$$":[41],"norm\u201d,":[42],"which":[43],"counts":[44],"number":[46],"non-zero":[48],"components":[49],"a":[51,54,72,76],"vector,":[52],"strong":[55],"reliable":[56],"mechanism":[57],"enforcing":[59],"when":[61],"incorporated":[62],"into":[63],"optimization":[65,118],"problem":[66],"for":[67],"minimizing":[68],"fit":[70],"given":[73],"model":[74],"set":[77],"observations.":[79],"However,":[80],"big":[82],"settings":[84],"noisy":[86],"estimates":[87],"gradient":[90],"must":[91],"evaluated":[93],"out":[94],"computational":[96],"necessity,":[97],"literature":[99],"scant":[101],"on":[102,135],"methods":[103],"that":[104],"reliably":[105],"converge.":[106],"In":[107],"this":[108],"paper,":[109],"we":[110],"present":[111],"approach":[113],"towards":[114],"solving":[115],"expectation":[116],"objective":[117],"problems":[119],"with":[120],"cardinality":[121],"constraints.":[122],"We":[123],"prove":[124],"convergence":[125],"underlying":[128],"stochastic":[129],"process":[130],"and":[131],"demonstrate":[132],"performance":[134],"two":[136],"Machine":[137],"Learning":[138],"problems.":[139]},"counts_by_year":[],"updated_date":"2026-01-10T23:39:48.068659","created_date":"2025-10-10T00:00:00"}