{"id":"https://openalex.org/W7148736234","doi":"https://doi.org/10.48550/arxiv.2604.01794","title":"Tree-Adaptive Multiscale Kernel Lasso in Samplet Coordinates","display_name":"Tree-Adaptive Multiscale Kernel Lasso in Samplet Coordinates","publication_year":2026,"publication_date":"2026-04-02","ids":{"openalex":"https://openalex.org/W7148736234","doi":"https://doi.org/10.48550/arxiv.2604.01794"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.01794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01794","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.01794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5121099567","display_name":"Sara Avesani","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Avesani, Sara","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110591603","display_name":"Gaia Fumagalli","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fumagalli, Gaia","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069886499","display_name":"Michael Multerer","orcid":"https://orcid.org/0000-0003-0170-0239"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Multerer, Michael","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5132876030","display_name":"Chiara Segala","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Segala, Chiara","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5121099567"],"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/T11205","display_name":"Numerical methods in inverse problems","score":0.47110000252723694,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.47110000252723694,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.219200000166893,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.05420000106096268,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6633999943733215},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.5995000004768372},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.5120000243186951},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5078999996185303},{"id":"https://openalex.org/keywords/kernel-embedding-of-distributions","display_name":"Kernel embedding of distributions","score":0.4918999969959259},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.48829999566078186},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.444599986076355},{"id":"https://openalex.org/keywords/variable-kernel-density-estimation","display_name":"Variable kernel density estimation","score":0.42879998683929443},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42820000648498535},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.37700000405311584}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6633999943733215},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.5995000004768372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5515999794006348},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5493000149726868},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.5120000243186951},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5078999996185303},{"id":"https://openalex.org/C134517425","wikidata":"https://www.wikidata.org/wiki/Q16000131","display_name":"Kernel embedding of distributions","level":4,"score":0.4918999969959259},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.48829999566078186},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C195699287","wikidata":"https://www.wikidata.org/wiki/Q7915722","display_name":"Variable kernel density estimation","level":4,"score":0.42879998683929443},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42820000648498535},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38929998874664307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37709999084472656},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C2776879701","wikidata":"https://www.wikidata.org/wiki/Q25048660","display_name":"Multiple kernel learning","level":4,"score":0.373199999332428},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35359999537467957},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3433000147342682},{"id":"https://openalex.org/C75866337","wikidata":"https://www.wikidata.org/wiki/Q7280263","display_name":"Radial basis function kernel","level":4,"score":0.33500000834465027},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C172623408","wikidata":"https://www.wikidata.org/wiki/Q7314263","display_name":"Representer theorem","level":5,"score":0.31709998846054077},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.3019999861717224},{"id":"https://openalex.org/C2781170535","wikidata":"https://www.wikidata.org/wiki/Q30587856","display_name":"Noisy data","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C140417398","wikidata":"https://www.wikidata.org/wiki/Q16933942","display_name":"Tree kernel","level":5,"score":0.2791999876499176},{"id":"https://openalex.org/C148483581","wikidata":"https://www.wikidata.org/wiki/Q446488","display_name":"Feature selection","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.26489999890327454},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.2574000060558319},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.2540000081062317},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.01794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01794","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":"doi:10.48550/arxiv.2604.01794","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.01794","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,17,22,83,109,115],"novel":[3],"framework":[4],"for":[5],"sparse":[6],"multiscale":[7],"kernel":[8,35,70,100,134],"approximation":[9],"of":[10,25,34,47,66,86,133],"large":[11],"scattered":[12,48],"data":[13,58,88],"problems":[14],"based":[15,62],"on":[16,51,63,124],"samplet":[18,76],"representation.":[19],"Samplets":[20],"form":[21],"multiresolution":[23],"analysis":[24],"localized":[26],"discrete":[27],"signed":[28],"measures":[29],"and":[30,140,161],"enable":[31],"quasi-sparse":[32],"representations":[33,160],"matrices":[36],"associated":[37],"to":[38,128],"asymptotically":[39],"smooth":[40],"kernels":[41],"as":[42,44],"well":[43],"smoothness":[45],"detection":[46],"data.":[49],"Building":[50],"the":[52,64,67,75,92,97,125,130,151],"latter,":[53],"we":[54,102],"introduce":[55],"an":[56,104,120],"adaptive":[57],"site":[59],"selection":[60,80],"strategy":[61],"localization":[65],"native":[68],"reproducing":[69],"Hilbert":[71],"space":[72],"norm":[73],"in":[74,82,114,138],"expansion":[77],"coefficients.":[78],"The":[79],"results":[81],"small":[84],"set":[85,127],"representative":[87],"sites,":[89],"significantly":[90],"reducing":[91],"effective":[93],"problem":[94,107],"size.":[95],"On":[96],"corresponding":[98],"reduced":[99],"subspace,":[101],"solve":[103],"$\\ell^1$-regularized":[105],"least-squares":[106],"using":[108],"trust-region":[110],"semismooth":[111],"Newton":[112],"method":[113],"normal-map":[116],"formulation,":[117],"stabilized":[118],"by":[119],"online":[121],"low-rank":[122],"SVD":[123],"active":[126],"handle":[129],"notorious":[131],"ill-conditioning":[132],"matrices.":[135],"Numerical":[136],"experiments":[137],"two":[139],"three":[141],"dimensions,":[142],"including":[143],"multi-kernel":[144],"models":[145],"with":[146,157],"varying":[147],"lengthscales,":[148],"demonstrate":[149],"that":[150],"proposed":[152],"approach":[153],"achieves":[154],"accurate":[155],"reconstructions":[156],"considerably":[158],"sparser":[159],"good":[162],"computational":[163],"efficiency.":[164]},"counts_by_year":[],"updated_date":"2026-04-04T06:15:33.020886","created_date":"2026-04-04T00:00:00"}