{"id":"https://openalex.org/W7224739610","doi":"https://doi.org/10.48550/arxiv.2610.39177","title":"Adaptive Bayesian Estimation of Conditional Densities Based on Orthogonal Polynomials","display_name":"Adaptive Bayesian Estimation of Conditional Densities Based on Orthogonal Polynomials","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224739610","doi":"https://doi.org/10.48550/arxiv.2610.39177"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39177","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39177","pdf_url":"https://arxiv.org/pdf/2610.39177","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39177","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052331566","display_name":"Andriy Norets","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Norets, Andriy","raw_affiliation_strings":["Brown University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087652347","display_name":"Marco Stenborg Petterson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210156264","display_name":"Centre for Studies in Economics and Finance","ror":"https://ror.org/052414247","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210156264"]},{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Petterson, Marco Stenborg","raw_affiliation_strings":["University of Naples Federico II and CSEF"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Naples Federico II and CSEF","institution_ids":["https://openalex.org/I4210156264","https://openalex.org/I71267560"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.3463999927043915,"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":0.3463999927043915,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.17499999701976776,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.08139999955892563,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conditional-density-estimation","display_name":"conditional density estimation","score":0.8289999961853027},{"id":"https://openalex.org/keywords/orthogonal-polynomial-series","display_name":"orthogonal polynomial series","score":0.7590000033378601},{"id":"https://openalex.org/keywords/nonparametric-bayesian-inference","display_name":"Bayesian nonparametrics","score":0.8029999732971191},{"id":"https://openalex.org/keywords/posterior-contraction","display_name":"posterior contraction","score":0.7960000038146973},{"id":"https://openalex.org/keywords/minimax-rates","display_name":"minimax rates","score":0.8230000138282776},{"id":"https://openalex.org/keywords/legendre-polynomials","display_name":"Legendre polynomials","score":0.8939999938011169},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":1.0},{"id":"https://openalex.org/keywords/smoothness-prior","display_name":"smoothness prior","score":0.6510000228881836},{"id":"https://openalex.org/keywords/posterior-predictive-distribution","display_name":"posterior predictive distribution","score":0.656000018119812},{"id":"https://openalex.org/keywords/quantile-estimation","display_name":"quantile estimation","score":0.5519999861717224},{"id":"https://openalex.org/keywords/coefficient-recovery","display_name":"coefficient recovery","score":0.7360000014305115},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"uniform convergence","score":0.6320000290870667},{"id":"https://openalex.org/keywords/model-selection","display_name":"model selection","score":0.42500001192092896}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8555999994277954},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.65829998254776},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5472000241279602},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.5368000268936157},{"id":"https://openalex.org/C189508267","wikidata":"https://www.wikidata.org/wiki/Q17088227","display_name":"Density estimation","level":3,"score":0.5199999809265137},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5188999772071838},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.513700008392334},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.44190001487731934},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3847000002861023},{"id":"https://openalex.org/C153024298","wikidata":"https://www.wikidata.org/wiki/Q3030678","display_name":"Hellinger distance","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.35740000009536743},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.3425999879837036},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C68022304","wikidata":"https://www.wikidata.org/wiki/Q842217","display_name":"Bayes estimator","level":3,"score":0.320499986410141},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.31459999084472656},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.296999990940094},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2955999970436096},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.28220000863075256},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2800999879837036},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C117148685","wikidata":"https://www.wikidata.org/wiki/Q6865376","display_name":"Minimax approximation algorithm","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39177","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39177","pdf_url":"https://arxiv.org/pdf/2610.39177","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.2610.39177","doi":"https://doi.org/10.48550/arxiv.2610.39177","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39177","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:2610.39177","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39177","pdf_url":"https://arxiv.org/pdf/2610.39177","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224739610.pdf","grobid_xml":"https://content.openalex.org/works/W7224739610.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1491445643","https://openalex.org/W7095598174","https://openalex.org/W2091157696","https://openalex.org/W7099204431","https://openalex.org/W7095541714","https://openalex.org/W3104787561","https://openalex.org/W7139936023","https://openalex.org/W2125474556","https://openalex.org/W1639765126","https://openalex.org/W2923012342"],"abstract_inverted_index":{"We":[0,15],"study":[1],"Bayesian":[2],"estimation":[3],"of":[4,11,25,33,55,163],"conditional":[5,18,147],"densities":[6],"represented":[7],"by":[8],"normalized":[9,52],"squares":[10],"orthogonal":[12],"polynomial":[13,164],"series.":[14],"specify":[16],"the":[17,22,31,36,43,51,56,73,88,105,120,134,138],"density":[19,58,86,122],"without":[20,46],"modeling":[21],"marginal":[23],"distribution":[24,148],"covariates.":[26],"A":[27,111],"prior":[28,112],"on":[29,137],"smoothness,":[30],"number":[32],"terms,":[34],"and":[35,64,70,100,132,150,154,161],"coefficients":[37],"gives":[38],"adaptive":[39],"posterior":[40,84],"contraction":[41],"at":[42,108],"minimax":[44,90,106],"rate":[45,74,107,136],"a":[47,116,129],"logarithmic":[48,130],"factor":[49,131],"when":[50],"square-root":[53],"representation":[54],"true":[57],"is":[59,81],"bounded":[60,95],"away":[61],"from":[62],"zero":[63],"sufficiently":[65,140],"smooth.":[66],"For":[67,94],"one":[68],"outcome":[69],"$d_x$":[71],"covariates,":[72],"over":[75,124],"classes":[76,126],"with":[77,119],"degree":[78],"smoothness":[79],"$s$":[80],"$n^{-s/(2s+d_x+1)}$.":[82],"The":[83],"predictive":[85],"attains":[87],"corresponding":[89],"squared":[91],"Hellinger":[92],"risk.":[93],"nonnegative":[96],"representations":[97],"in":[98],"Legendre":[99],"Chebyshev":[101],"classes,":[102],"we":[103],"establish":[104],"every":[109],"$s>0$.":[110],"that":[113],"also":[114],"permits":[115],"small":[117],"mixture":[118],"reference":[121],"adapts":[123],"these":[125],"up":[127],"to":[128],"retains":[133],"exact":[135],"positive,":[139],"smooth":[141],"subclass.":[142],"Additional":[143],"results":[144],"concern":[145],"identification,":[146],"functions":[149],"quantiles,":[151],"coefficient":[152,159],"recovery":[153],"uniform":[155],"convergence,":[156],"independent":[157],"Gaussian":[158],"priors,":[160],"selection":[162],"terms.":[165]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}
