A factorization criterion for acyclic directed mixed graphs
This work provides a theoretical tool for modeling latent variable structures in graphical models, but it appears incremental as it extends existing d-separation concepts to a specific graph type.
The paper tackles the problem of representing conditional independence structures in acyclic directed mixed graphs (semi-Markov models) by presenting a factorization criterion that is equivalent to the global Markov property based on d-separation.
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present a factorization criterion for these models that is equivalent to the global Markov property given by (the natural extension of) d-separation.