期刊
UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
卷 -, 期 -, 页码 735-745出版社
AUAI PRESS
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资金
- American Institute of Mathematics via the SQuaRE program
- EPRSC First Grant
- NIH [R01 AI104459-01A1, R01 AI127271-01A1]
- U.S. Office of Naval Research [N00014-15-1-2672]
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.
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