Determinantal generalizations of instrumental variables
Linear 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 repres...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018
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| Online Access: | https://eprints.nottingham.ac.uk/48026/ |
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| author | Weihs, Luca Robinson, Bill Dufresne, Emilie Kenkel, Jennifer Kubjas, Kaie McGee, Reginald L. II Nguyen, Nhan Robeva, Elina Drton, Mathias |
| author_facet | Weihs, Luca Robinson, Bill Dufresne, Emilie Kenkel, Jennifer Kubjas, Kaie McGee, Reginald L. II Nguyen, Nhan Robeva, Elina Drton, Mathias |
| author_sort | Weihs, Luca |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Linear 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. |
| first_indexed | 2025-11-14T20:07:38Z |
| format | Article |
| id | nottingham-48026 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:07:38Z |
| publishDate | 2018 |
| publisher | De Gruyter |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-480262018-12-08T04:30:16Z https://eprints.nottingham.ac.uk/48026/ Determinantal generalizations of instrumental variables Weihs, Luca Robinson, Bill Dufresne, Emilie Kenkel, Jennifer Kubjas, Kaie McGee, Reginald L. II Nguyen, Nhan Robeva, Elina Drton, Mathias Linear 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. De Gruyter 2018-03-26 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/48026/1/1702.03884.pdf Weihs, Luca, Robinson, Bill, Dufresne, Emilie, Kenkel, Jennifer, Kubjas, Kaie, McGee, Reginald L. II, Nguyen, Nhan, Robeva, Elina and Drton, Mathias (2018) Determinantal generalizations of instrumental variables. Journal of Causal Inference, 6 (1). p. 20170009. ISSN 2193-3685 trek separation; half-trek criterion; structural equation models; identifiability generic identifiability https://www.degruyter.com/view/j/jci.ahead-of-print/jci-2017-0009/jci-2017-0009.xml doi:10.1515/jci-2017-0009 doi:10.1515/jci-2017-0009 |
| spellingShingle | trek separation; half-trek criterion; structural equation models; identifiability generic identifiability Weihs, Luca Robinson, Bill Dufresne, Emilie Kenkel, Jennifer Kubjas, Kaie McGee, Reginald L. II Nguyen, Nhan Robeva, Elina Drton, Mathias Determinantal generalizations of instrumental variables |
| title | Determinantal generalizations of instrumental variables |
| title_full | Determinantal generalizations of instrumental variables |
| title_fullStr | Determinantal generalizations of instrumental variables |
| title_full_unstemmed | Determinantal generalizations of instrumental variables |
| title_short | Determinantal generalizations of instrumental variables |
| title_sort | determinantal generalizations of instrumental variables |
| topic | trek separation; half-trek criterion; structural equation models; identifiability generic identifiability |
| url | https://eprints.nottingham.ac.uk/48026/ https://eprints.nottingham.ac.uk/48026/ https://eprints.nottingham.ac.uk/48026/ |