{"id":"https://openalex.org/W7140161982","doi":"https://doi.org/10.48550/arxiv.2603.21844","title":"On the Number of Conditional Independence Tests in Constraint-based Causal Discovery","display_name":"On the Number of Conditional Independence Tests in Constraint-based Causal Discovery","publication_year":2026,"publication_date":"2026-03-23","ids":{"openalex":"https://openalex.org/W7140161982","doi":"https://doi.org/10.48550/arxiv.2603.21844"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2603.21844","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.21844","pdf_url":"https://arxiv.org/pdf/2603.21844","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2603.21844","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127881749","display_name":"Marc Franquesa Mon\u00e9s","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mon\u00e9s, Marc Franquesa","raw_affiliation_strings":["Centre de Formaci\u00f3 Interdisciplin\u00e0ria Superior , Universitat Polit\u00e8cnica de Catalunya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de Formaci\u00f3 Interdisciplin\u00e0ria Superior , Universitat Polit\u00e8cnica de Catalunya","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043426218","display_name":"Jiaqi Zhang","orcid":"https://orcid.org/0000-0001-9039-6843","observed_orcids":["https://orcid.org/0000-0001-9039-6843"]},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhang, Jiaqi","raw_affiliation_strings":["Laboratory for Information and Decision Systems , Massachusetts Institute of Technology \u2020 Equal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems , Massachusetts Institute of Technology \u2020 Equal","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008891620","display_name":"Caroline Uhler","orcid":"https://orcid.org/0000-0002-7008-0216","observed_orcids":["https://orcid.org/0000-0002-7008-0216"]},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Uhler, Caroline","raw_affiliation_strings":["Laboratory for Information and Decision Systems , Massachusetts Institute of Technology \u2020 Equal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems , Massachusetts Institute of Technology \u2020 Equal","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":1.0,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":1.0,"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":0.0,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/causal-discovery","display_name":"causal discovery","score":0.7279999852180481},{"id":"https://openalex.org/keywords/constraint-based-causal-discovery","display_name":"constraint-based causal discovery","score":0.7739999890327454},{"id":"https://openalex.org/keywords/conditional-independence-tests","display_name":"conditional independence testing","score":0.9850000143051147},{"id":"https://openalex.org/keywords/pc-algorithm","display_name":"PC algorithm","score":0.8289999961853027},{"id":"https://openalex.org/keywords/computational-complexity","display_name":"computational complexity","score":0.8809999823570251},{"id":"https://openalex.org/keywords/essential-graphs","display_name":"essential graphs","score":0.8140000104904175},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.7549999952316284},{"id":"https://openalex.org/keywords/observational-data","display_name":"observational data","score":0.621999979019165},{"id":"https://openalex.org/keywords/gene-expression-data","display_name":"gene expression data","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.7592999935150146},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.6717000007629395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5541999936103821},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4584999978542328},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4564000070095062},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3871999979019165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3806999921798706},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3578999936580658},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35269999504089355},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3231000006198883},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C193244246","wikidata":"https://www.wikidata.org/wiki/Q5432696","display_name":"False discovery rate","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.2842000126838684},{"id":"https://openalex.org/C183905921","wikidata":"https://www.wikidata.org/wiki/Q1038757","display_name":"Multiple comparisons problem","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.275299996137619},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.262800008058548},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2603.21844","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.21844","pdf_url":"https://arxiv.org/pdf/2603.21844","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2603.21844","doi":"https://doi.org/10.48550/arxiv.2603.21844","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.21844","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2603.21844","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2603.21844","pdf_url":"https://arxiv.org/pdf/2603.21844","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7243662210","display_name":"M2DT: MULTIFACETED MATHEMATICS FOR PREDICTIVE DIGITAL TWINS","funder_award_id":"DESC0023187","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8684072693","display_name":null,"funder_award_id":"1DP2AT012345","funder_id":"https://openalex.org/F4320337593","funder_display_name":"National Center for Complementary and Integrative Health"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320314070","display_name":"Broad Institute","ror":"https://ror.org/05a0ya142"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337593","display_name":"National Center for Complementary and Integrative Health","ror":"https://ror.org/00190t495"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7140161982.pdf","grobid_xml":"https://content.openalex.org/works/W7140161982.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Learning":[0],"causal":[1,21,59],"relations":[2],"from":[3],"observational":[4],"data":[5],"is":[6,51,92],"a":[7,40,84,139],"fundamental":[8],"problem":[9],"with":[10,71],"wide-ranging":[11],"applications":[12],"across":[13],"many":[14],"fields.":[15],"Constraint-based":[16],"methods":[17,176],"infer":[18],"the":[19,33,48,54,58,93,98,103,109,145,168],"underlying":[20,110],"structure":[22],"by":[23],"performing":[24],"conditional":[25,127,148,182],"independence":[26,44,128,149,183],"tests.":[27],"However,":[28],"existing":[29,175],"algorithms":[30,70],"such":[31],"as":[32],"prominent":[34],"PC":[35],"algorithm":[36,81,121,134,172],"need":[37],"to":[38,138,174],"perform":[39,123],"large":[41],"number":[42,94,146,180],"of":[43,57,87,95,108,144,147,170,179,181],"tests,":[45,89,129],"which":[46],"in":[47,53,97,142,177],"worst":[49],"case":[50],"exponential":[52],"maximum":[55,104],"degree":[56],"graph.":[60,112],"Despite":[61],"extensive":[62],"research,":[63],"it":[64],"remains":[65],"unclear":[66],"if":[67],"there":[68],"exist":[69],"better":[72,85],"complexity":[73,86],"without":[74],"additional":[75],"assumptions.":[76],"Here,":[77],"we":[78,116,153],"establish":[79],"an":[80],"that":[82,118,131],"achieves":[83,135],"$p^{\\mathcal{O}(s)}$":[88],"where":[90],"$p$":[91],"nodes":[96],"graph":[99],"and":[100,164],"$s$":[101],"denotes":[102],"undirected":[105],"clique":[106],"size":[107],"essential":[111],"Complementing":[113],"this":[114],"result,":[115],"prove":[117],"any":[119],"constraint-based":[120],"must":[122],"at":[124],"least":[125],"$2^{\u03a9(s)}$":[126],"establishing":[130],"our":[132,155,171],"proposed":[133],"exponent-optimality":[136],"up":[137],"logarithmic":[140],"factor":[141],"terms":[143,178],"tests":[150,184],"needed.":[151,185],"Finally,":[152],"validate":[154],"theoretical":[156],"findings":[157],"through":[158],"simulations,":[159],"on":[160],"semi-synthetic":[161],"gene-expression":[162],"data,":[163,166],"real-world":[165],"demonstrating":[167],"efficiency":[169],"compared":[173]},"counts_by_year":[],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2026-03-25T00:00:00"}
