Nested markov properties for acyclic directed mixed graphs
Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the dseparation criterion), and the local Markov property. Marginals of DAG models also imply equality const...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Institute of Mathematical Statistics
2023
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| _version_ | 1797109242314883072 |
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| author | Richardson, T Robins, JM Evans, RJ Shpitser, I |
| author_facet | Richardson, T Robins, JM Evans, RJ Shpitser, I |
| author_sort | Richardson, T |
| collection | OXFORD |
| description | Conditional independence models associated with directed acyclic
graphs (DAGs) may be characterized in at least three different ways:
via a factorization, the global Markov property (given by the dseparation criterion), and the local Markov property. Marginals of
DAG models also imply equality constraints that are not conditional
independences; the well-known ‘Verma constraint’ is an example.
Constraints of this type are used for testing edges, and in a computationally efficient marginalization scheme via variable elimination.
We show that equality constraints like the ‘Verma constraint’ can
be viewed as conditional independences in kernel objects obtained
from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via
ordered local and global Markov properties, and a factorization, a
graphical model associated with acyclic directed mixed graphs (ADMGs). We prove that marginal distributions of DAG models lie in
this model, and that a set of these constraints given by Tian provides an alternative definition of the model. Finally, we show that
the fixing operation used to define the model leads to a particularly
simple characterization of identifiable causal effects in hidden variable
causal DAG models. |
| first_indexed | 2024-03-07T07:39:02Z |
| format | Journal article |
| id | oxford-uuid:33cf96b3-e75e-4b61-bd54-e446afaf5f91 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:39:02Z |
| publishDate | 2023 |
| publisher | Institute of Mathematical Statistics |
| record_format | dspace |
| spelling | oxford-uuid:33cf96b3-e75e-4b61-bd54-e446afaf5f912023-04-14T09:21:40ZNested markov properties for acyclic directed mixed graphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:33cf96b3-e75e-4b61-bd54-e446afaf5f91EnglishSymplectic ElementsInstitute of Mathematical Statistics2023Richardson, TRobins, JMEvans, RJShpitser, IConditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the dseparation criterion), and the local Markov property. Marginals of DAG models also imply equality constraints that are not conditional independences; the well-known ‘Verma constraint’ is an example. Constraints of this type are used for testing edges, and in a computationally efficient marginalization scheme via variable elimination. We show that equality constraints like the ‘Verma constraint’ can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via ordered local and global Markov properties, and a factorization, a graphical model associated with acyclic directed mixed graphs (ADMGs). We prove that marginal distributions of DAG models lie in this model, and that a set of these constraints given by Tian provides an alternative definition of the model. Finally, we show that the fixing operation used to define the model leads to a particularly simple characterization of identifiable causal effects in hidden variable causal DAG models. |
| spellingShingle | Richardson, T Robins, JM Evans, RJ Shpitser, I Nested markov properties for acyclic directed mixed graphs |
| title | Nested markov properties for acyclic directed mixed graphs |
| title_full | Nested markov properties for acyclic directed mixed graphs |
| title_fullStr | Nested markov properties for acyclic directed mixed graphs |
| title_full_unstemmed | Nested markov properties for acyclic directed mixed graphs |
| title_short | Nested markov properties for acyclic directed mixed graphs |
| title_sort | nested markov properties for acyclic directed mixed graphs |
| work_keys_str_mv | AT richardsont nestedmarkovpropertiesforacyclicdirectedmixedgraphs AT robinsjm nestedmarkovpropertiesforacyclicdirectedmixedgraphs AT evansrj nestedmarkovpropertiesforacyclicdirectedmixedgraphs AT shpitseri nestedmarkovpropertiesforacyclicdirectedmixedgraphs |