{"id":"https://openalex.org/W7162554950","doi":"https://doi.org/10.48550/arxiv.2605.26675","title":"CART Random Forests as Sequential Allocation over Random Opportunity Sets: A Stochastic-Control Theory of Ensemble Risk","display_name":"CART Random Forests as Sequential Allocation over Random Opportunity Sets: A Stochastic-Control Theory of Ensemble Risk","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162554950","doi":"https://doi.org/10.48550/arxiv.2605.26675"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.26675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26675","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.26675","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137141638","display_name":"Tianxing Mei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mei, Tianxing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137155558","display_name":"Yingying Fan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan, Yingying","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016660801","display_name":"Mingming Leng","orcid":"https://orcid.org/0000-0002-3377-2387"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leng, Mingming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034015361","display_name":"Jinchi Lv","orcid":"https://orcid.org/0000-0002-5881-9591"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lv, Jinchi","raw_affiliation_strings":[],"raw_orcid":null,"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":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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.399399995803833,"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"}},"topics":[{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.399399995803833,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.11739999800920486,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.048700001090765,"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/cart","display_name":"Cart","score":0.8762999773025513},{"id":"https://openalex.org/keywords/random-forest","display_name":"Random forest","score":0.6297000050544739},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.45590001344680786},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4505999982357025},{"id":"https://openalex.org/keywords/black-box","display_name":"Black box","score":0.4480000138282776},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.391400009393692},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.37389999628067017}],"concepts":[{"id":"https://openalex.org/C2777275308","wikidata":"https://www.wikidata.org/wiki/Q234668","display_name":"Cart","level":2,"score":0.8762999773025513},{"id":"https://openalex.org/C169258074","wikidata":"https://www.wikidata.org/wiki/Q245748","display_name":"Random forest","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4717000126838684},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4505999982357025},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.4480000138282776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4180999994277954},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.37389999628067017},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.36649999022483826},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3287999927997589},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.2922999858856201},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2863999903202057},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.2842000126838684},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.25850000977516174},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.26675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26675","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.26675","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26675","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,"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"},"sustainable_development_goals":[{"score":0.5126736760139465,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"CART":[0,44,48,71,141,205],"random":[1,45,49,57,65],"forests":[2],"are":[3],"among":[4],"the":[5,18,21,56,70,102,111,121,129,133,140,159,169,174,179,200],"most":[6],"widely":[7],"used":[8],"modern":[9],"predictive":[10],"methods,":[11],"with":[12],"well-documented":[13],"empirical":[14],"success.":[15],"Yet,":[16],"at":[17],"mechanistic":[19],"level,":[20,161],"algorithm":[22],"is":[23,61,143],"often":[24],"treated":[25],"as":[26,63,74],"a":[27,39,64,75,82,193],"black":[28,112],"box":[29,113],"because":[30],"of":[31,59,114,204],"its":[32],"complexity.":[33],"In":[34],"this":[35],"paper,":[36],"we":[37,177],"develop":[38],"stochastic-control":[40],"perspective":[41,190],"on":[42],"feature-subsampled":[43],"forests,":[46],"named":[47],"opportunity-set":[50],"allocation":[51,77],"(CART-ROSA).":[52],"At":[53,158],"each":[54],"node,":[55],"subset":[58],"features":[60],"interpreted":[62],"feasible":[66],"action":[67],"set,":[68],"and":[69,97,128,153],"split":[72,135,151],"rule":[73],"masked-action":[76],"policy.":[78,136],"This":[79],"policy":[80,142],"induces":[81],"controlled":[83],"stochastic":[84],"process":[85],"over":[86],"informative":[87,150],"split-count":[88],"states,":[89],"whose":[90],"terminal":[91,155],"law":[92],"determines":[93],"both":[94],"single-tree":[95],"error":[96,106],"cross-tree":[98],"interaction":[99],"terms":[100],"in":[101,149],"forest":[103,170],"mean":[104],"squared":[105],"(MSE).":[107],"Such":[108],"representation":[109],"opens":[110],"CART-forests":[115],"by":[116,125],"separating":[117],"two":[118],"design":[119],"levers:":[120],"informative-opportunity":[122],"rate":[123],"induced":[124],"feature":[126],"subsampling,":[127],"contraction":[130],"strength":[131],"from":[132,199],"within-mask":[134],"We":[137],"establish":[138],"that":[139],"locally":[144],"stabilizing:":[145],"it":[146,163],"contracts":[147],"imbalances":[148],"allocations":[152],"concentrates":[154],"tree":[156],"geometry.":[157],"system":[160],"however,":[162],"can":[164],"be":[165],"globally":[166],"suboptimal":[167],"for":[168],"objective.":[171],"Specializing":[172],"to":[173,197],"linear":[175],"model,":[176],"derive":[178],"MSE":[180],"risk":[181],"expansion":[182],"explicitly.":[183],"Our":[184],"results":[185],"show":[186],"how":[187],"an":[188],"operations-research":[189],"makes":[191],"tractable":[192],"theoretical":[194],"gap":[195],"difficult":[196],"access":[198],"standard":[201],"algorithmic":[202],"description":[203],"forests.":[206]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-28T00:00:00"}