Determinantal Generalizations of Instrumental Variables

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.authorWeihs, Lucaen_US
dc.contributor.authorRobinson, Billen_US
dc.contributor.authorDufresne, Emilieen_US
dc.contributor.authorKenkel, Jenniferen_US
dc.contributor.authorKubjas, Kaieen_US
dc.contributor.authorMcGee, Reginald L., IIen_US
dc.contributor.authorNguyen, Nhanen_US
dc.contributor.authorRobeva, Elinaen_US
dc.contributor.authorDrton, Mathiasen_US
dc.contributor.departmentUniversity of Washingtonen_US
dc.contributor.departmentDenison Universityen_US
dc.contributor.departmentUniversity of Nottinghamen_US
dc.contributor.departmentUniversity of Utahen_US
dc.contributor.departmentStatistics and Mathematical Data Scienceen_US
dc.contributor.departmentOhio State Universityen_US
dc.contributor.departmentUniversity of Montanaen_US
dc.contributor.departmentMassachusetts Institute of Technology MITen_US
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.date.accessioned2021-05-12T06:35:10Z
dc.date.available2021-05-12T06:35:10Z
dc.date.issued2018-03en_US
dc.description.abstractLinear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the random vector. The graph contains directed edges that represent the linear relationships between components, and bidirected edges that encode unobserved confounding. We study the problem of generic identifiability, that is, whether a generic choice of linear and confounding effects can be uniquely recovered from the joint covariance matrix of the observed random vector. An existing combinatorial criterion for establishing generic identifiability is the half-trek criterion (HTC), which uses the existence of trek systems in the mixed graph to iteratively discover generically invertible linear equation systems in polynomial time. By focusing on edges one at a time, we establish new sufficient and necessary conditions for generic identifiability of edge effects extending those of the HTC. In particular, we show how edge coefficients can be recovered as quotients of subdeterminants of the covariance matrix, which constitutes a determinantal generalization of formulas obtained when using instrumental variables for identification.en
dc.description.versionPeer revieweden
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationWeihs , L , Robinson , B , Dufresne , E , Kenkel , J , Kubjas , K , McGee , R L II , Nguyen , N , Robeva , E & Drton , M 2018 , ' Determinantal Generalizations of Instrumental Variables ' , Journal of causal inference , vol. 6 , no. 1 , 20170009 . https://doi.org/10.1515/jci-2017-0009en
dc.identifier.doi10.1515/jci-2017-0009en_US
dc.identifier.issn2193-3677
dc.identifier.issn2193-3685
dc.identifier.otherPURE UUID: 35e9e8df-066c-42ea-bfdc-09decf4c05dben_US
dc.identifier.otherPURE ITEMURL: https://research.aalto.fi/en/publications/35e9e8df-066c-42ea-bfdc-09decf4c05dben_US
dc.identifier.otherPURE LINK: http://adsabs.harvard.edu/abs/2017arXiv170203884Wen_US
dc.identifier.otherPURE FILEURL: https://research.aalto.fi/files/62502256/Determinantal_Generalizations_of.pdfen_US
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/107402
dc.identifier.urnURN:NBN:fi:aalto-202105126666
dc.language.isoenen
dc.publisherDE GRUYTER
dc.relation.ispartofseriesJournal of causal inferenceen
dc.relation.ispartofseriesVolume 6, issue 1en
dc.rightsopenAccessen
dc.subject.keywordtrek separationen_US
dc.subject.keywordhalf-trek criterionen_US
dc.subject.keywordstructural equation modelsen_US
dc.subject.keywordidentifiabilityen_US
dc.subject.keywordgeneric identifiabilityen_US
dc.titleDeterminantal Generalizations of Instrumental Variablesen
dc.typeA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessäfi
dc.type.versionpublishedVersion
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