{"id":"https://openalex.org/W7134054772","doi":"https://doi.org/10.48550/arxiv.2603.05340","title":"On the Statistical Optimality of Optimal Decision Trees","display_name":"On the Statistical Optimality of Optimal Decision Trees","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W7134054772","doi":"https://doi.org/10.48550/arxiv.2603.05340"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.05340","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062709328","display_name":"Zineng Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Zineng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128272416","display_name":"Subhroshekhar Ghosh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ghosh, Subhro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128222622","display_name":"Yan Shuo Tan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tan, Yan Shuo","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":0.18799999356269836,"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":0.18799999356269836,"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/T10136","display_name":"Statistical Methods and Inference","score":0.18559999763965607,"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/T10885","display_name":"Gene expression and cancer classification","score":0.0778999999165535,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.8072999715805054},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5634999871253967},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5202000141143799},{"id":"https://openalex.org/keywords/empirical-risk-minimization","display_name":"Empirical risk minimization","score":0.5062999725341797},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.42309999465942383},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.41679999232292175},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.3763999938964844},{"id":"https://openalex.org/keywords/decision-theory","display_name":"Decision theory","score":0.3628999888896942},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.3571999967098236}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8072999715805054},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6021999716758728},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5634999871253967},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5202000141143799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5098000168800354},{"id":"https://openalex.org/C107321475","wikidata":"https://www.wikidata.org/wiki/Q5374254","display_name":"Empirical risk minimization","level":2,"score":0.5062999725341797},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4287000000476837},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.41679999232292175},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C150325174","wikidata":"https://www.wikidata.org/wiki/Q4335500","display_name":"Optimal decision","level":3,"score":0.289000004529953},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2703999876976013},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2612999975681305},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.2526000142097473},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C2984634286","wikidata":"https://www.wikidata.org/wiki/Q1331926","display_name":"Decision process","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.05340","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},{"id":"doi:10.48550/arxiv.2603.05340","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.05340","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":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.05340","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"While":[0,133],"globally":[1],"optimal":[2,101],"empirical":[3,167],"risk":[4,56],"minimization":[5],"(ERM)":[6],"decision":[7],"trees":[8,36,164],"have":[9],"become":[10],"computationally":[11],"feasible":[12],"and":[13,44,130,165],"empirically":[14,93],"successful,":[15],"rigorous":[16],"theoretical":[17],"guarantees":[18,145],"for":[19,34,159],"their":[20],"statistical":[21,32],"performance":[22],"remain":[23],"limited.":[24],"In":[25],"this":[26],"work,":[27],"we":[28,98,141],"develop":[29],"a":[30,86,104,156],"comprehensive":[31],"theory":[33],"ERM":[35,59,163],"under":[37,139,148],"random":[38],"design":[39],"in":[40,125],"both":[41],"high-dimensional":[42],"regression":[43],"classification.":[45],"We":[46,81],"first":[47],"establish":[48],"sharp":[49],"oracle":[50],"inequalities":[51],"that":[52,146],"bound":[53],"the":[54,58,63,78,108,160],"excess":[55],"of":[57,162],"estimator":[60],"relative":[61],"to":[62,172],"best":[64],"possible":[65],"approximation":[66],"achievable":[67],"by":[68],"any":[69],"tree":[70],"with":[71],"at":[72],"most":[73],"$L$":[74],"leaves,":[75],"thereby":[76],"characterizing":[77],"interpretability-accuracy":[79],"trade-off.":[80],"derive":[82,99],"these":[83,153],"results":[84,136],"using":[85],"novel":[87,105],"uniform":[88],"concentration":[89],"framework":[90],"based":[91],"on":[92],"localized":[94],"Rademacher":[95],"complexity.":[96],"Furthermore,":[97],"minimax":[100],"rates":[102],"over":[103],"function":[106],"class:":[107],"piecewise":[109],"sparse":[110],"heterogeneous":[111],"anisotropic":[112,128],"Besov":[113],"(PSHAB)":[114],"space.":[115],"This":[116],"space":[117],"explicitly":[118],"captures":[119],"three":[120],"key":[121],"structural":[122],"features":[123],"encountered":[124],"practice:":[126],"sparsity,":[127],"smoothness,":[129],"spatial":[131],"heterogeneity.":[132],"our":[134],"main":[135],"are":[137],"established":[138],"sub-Gaussianity,":[140],"also":[142],"provide":[143,155],"robust":[144],"hold":[147],"heavy-tailed":[149],"noise":[150],"settings.":[151],"Together,":[152],"findings":[154],"principled":[157],"foundation":[158],"optimality":[161],"introduce":[166],"process":[168],"tools":[169],"broadly":[170],"applicable":[171],"other":[173],"highly":[174],"adaptive,":[175],"data-driven":[176],"procedures.":[177]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-07T00:00:00"}