Acyclic linear SEMs obey the nested Markov property
The conditional independence structure induced on the observed marginal distribution by a hidden variable directed acyclic graph (DAG) may be represented by a graphical model represented by mixed graphs called maximal ancestral graphs (MAGs). This model has a number of desirable properties, in parti...
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| Format: | Conference item |
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AUAI Press
2018
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| _version_ | 1797091620291608576 |
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| author | Shpitser, I Evans, R Richardson, T |
| author_facet | Shpitser, I Evans, R Richardson, T |
| author_sort | Shpitser, I |
| collection | OXFORD |
| description | The conditional independence structure induced on the observed marginal distribution by a hidden variable directed acyclic graph (DAG) may be represented by a graphical model represented by mixed graphs called maximal ancestral graphs (MAGs). This model has a number of desirable properties, in particular the set of Gaussian distributions can be parameterized by viewing the graph as a path diagram. Models represented by MAGs have been used for causal discovery [22], and identification theory for causal effects [28]. In addition to ordinary conditional independence constraints, hidden variable DAGs also induce generalized independence constraints. These constraints form the nested Markov property [20]. We first show that acyclic linear SEMs obey this property. Further we show that a natural parameterization for all Gaussian distributions obeying the nested Markov property arises from a generalization of maximal ancestral graphs that we call maximal arid graphs (MArG). We show that every nested Markov model can be associated with a MArG; viewed as a path diagram this MArG parametrizes the Gaussian nested Markov model. This leads directly to methods for ML fitting and computing BIC scores for Gaussian nested models. |
| first_indexed | 2024-03-07T03:35:39Z |
| format | Conference item |
| id | oxford-uuid:bc320c77-7a69-487b-b94b-ab85fc26c353 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:35:39Z |
| publishDate | 2018 |
| publisher | AUAI Press |
| record_format | dspace |
| spelling | oxford-uuid:bc320c77-7a69-487b-b94b-ab85fc26c3532022-03-27T05:22:37ZAcyclic linear SEMs obey the nested Markov propertyConference itemhttp://purl.org/coar/resource_type/c_5794uuid:bc320c77-7a69-487b-b94b-ab85fc26c353Symplectic Elements at OxfordAUAI Press2018Shpitser, IEvans, RRichardson, TThe conditional independence structure induced on the observed marginal distribution by a hidden variable directed acyclic graph (DAG) may be represented by a graphical model represented by mixed graphs called maximal ancestral graphs (MAGs). This model has a number of desirable properties, in particular the set of Gaussian distributions can be parameterized by viewing the graph as a path diagram. Models represented by MAGs have been used for causal discovery [22], and identification theory for causal effects [28]. In addition to ordinary conditional independence constraints, hidden variable DAGs also induce generalized independence constraints. These constraints form the nested Markov property [20]. We first show that acyclic linear SEMs obey this property. Further we show that a natural parameterization for all Gaussian distributions obeying the nested Markov property arises from a generalization of maximal ancestral graphs that we call maximal arid graphs (MArG). We show that every nested Markov model can be associated with a MArG; viewed as a path diagram this MArG parametrizes the Gaussian nested Markov model. This leads directly to methods for ML fitting and computing BIC scores for Gaussian nested models. |
| spellingShingle | Shpitser, I Evans, R Richardson, T Acyclic linear SEMs obey the nested Markov property |
| title | Acyclic linear SEMs obey the nested Markov property |
| title_full | Acyclic linear SEMs obey the nested Markov property |
| title_fullStr | Acyclic linear SEMs obey the nested Markov property |
| title_full_unstemmed | Acyclic linear SEMs obey the nested Markov property |
| title_short | Acyclic linear SEMs obey the nested Markov property |
| title_sort | acyclic linear sems obey the nested markov property |
| work_keys_str_mv | AT shpitseri acycliclinearsemsobeythenestedmarkovproperty AT evansr acycliclinearsemsobeythenestedmarkovproperty AT richardsont acycliclinearsemsobeythenestedmarkovproperty |