{"id":"https://openalex.org/W7162560874","doi":"https://doi.org/10.48550/arxiv.2605.26408","title":"Function-Valued Causal Influence in Nonlinear Time Series","display_name":"Function-Valued Causal Influence in Nonlinear Time Series","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162560874","doi":"https://doi.org/10.48550/arxiv.2605.26408"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.26408","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26408","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.26408","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069790131","display_name":"Valentina Kuskova","orcid":"https://orcid.org/0000-0003-4716-2544"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kuskova, Valentina V.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130448665","display_name":"Dmitry Zaytsev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zaytsev, Dmitry","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137175311","display_name":"Michael Coppedge","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Coppedge, Michael","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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.7315999865531921,"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":0.7315999865531921,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.048500001430511475,"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/T10656","display_name":"Child and Animal Learning Development","score":0.03370000049471855,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.6380000114440918},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6194000244140625},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6079999804496765},{"id":"https://openalex.org/keywords/causal-structure","display_name":"Causal structure","score":0.5356000065803528},{"id":"https://openalex.org/keywords/causal-model","display_name":"Causal model","score":0.48899999260902405},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4334999918937683},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.41440001130104065},{"id":"https://openalex.org/keywords/conditional-expectation","display_name":"Conditional expectation","score":0.3806000053882599}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.6380000114440918},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6194000244140625},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6079999804496765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.544700026512146},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.5356000065803528},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.41760000586509705},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.41440001130104065},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.3806000053882599},{"id":"https://openalex.org/C158600405","wikidata":"https://www.wikidata.org/wiki/Q5054566","display_name":"Causal inference","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C2987525970","wikidata":"https://www.wikidata.org/wiki/Q96374569","display_name":"Causal analysis","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.36910000443458557},{"id":"https://openalex.org/C133029050","wikidata":"https://www.wikidata.org/wiki/Q385593","display_name":"Vector autoregression","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.36010000109672546},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3467000126838684},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33880001306533813},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3061999976634979},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2849999964237213},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C42536954","wikidata":"https://www.wikidata.org/wiki/Q7049462","display_name":"Nonlinear autoregressive exogenous model","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.26408","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26408","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":"doi:10.48550/arxiv.2605.26408","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26408","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":"Preprint"},"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":{"Causal":[0],"discovery":[1],"in":[2],"time":[3],"series":[4],"is":[5],"increasingly":[6],"performed":[7],"using":[8],"nonlinear":[9,36],"machine-learning":[10],"models,":[11],"yet":[12],"the":[13,31],"resulting":[14],"causal":[15,53,63,98,146],"relationships":[16],"are":[17],"almost":[18],"always":[19],"summarized":[20],"by":[21,35,150],"scalar":[22,62,115],"edge":[23],"scores.":[24],"We":[25,50],"argue":[26],"that":[27,61,111,139],"this":[28],"practice":[29],"obscures":[30],"true":[32],"object":[33],"learned":[34],"autoregressive":[37],"models:":[38],"a":[39,66,83,88],"state-dependent":[40],"function":[41],"whose":[42],"effect":[43],"varies":[44],"across":[45],"regimes,":[46],"magnitudes,":[47],"and":[48,59,127,144],"contexts.":[49],"formalize":[51],"function-valued":[52,140],"influence":[54],"for":[55,96],"additive,":[56],"contribution-decomposable":[57],"architectures":[58],"show":[60],"scores":[64,116],"constitute":[65],"severe":[67],"information":[68],"bottleneck,":[69],"conflating":[70],"between-state":[71],"variation":[72],"with":[73,113],"within-state":[74],"residual":[75],"noise.":[76],"Using":[77],"Neural":[78],"Additive":[79],"Vector":[80],"Autoregression":[81],"as":[82],"representative":[84],"architecture,":[85],"we":[86,109],"introduce":[87],"practical":[89],"framework":[90],"based":[91],"on":[92,134],"Individual":[93],"Conditional":[94],"Expectation":[95],"estimating":[97],"response":[99],"functions":[100],"directly":[101],"from":[102],"trained":[103],"models.":[104],"Through":[105],"controlled":[106],"synthetic":[107],"experiments,":[108],"demonstrate":[110],"edges":[112],"indistinguishable":[114],"can":[117],"exhibit":[118],"qualitatively":[119],"different":[120],"functional":[121],"behaviors,":[122],"including":[123],"monotonic,":[124],"thresholded,":[125],"saturating,":[126],"sign-changing":[128],"effects.":[129],"An":[130],"applied":[131],"case":[132],"study":[133],"democratic":[135],"development":[136],"further":[137],"shows":[138],"analysis":[141],"reveals":[142],"regime-specific":[143],"asymmetric":[145],"structure":[147],"systematically":[148],"missed":[149],"score-centric":[151],"approaches.":[152]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-28T00:00:00"}
