From DAGs to Essential Graphs through Quasi-Essential Graphs

I discuss work being carried out in collaboration with Jacek Wesolowski and Helene Massam.

A Bayesian network is the factorisation of a probability distribution over Directed Acyclic Graph (DAG). The Markov properties of a DAG are determined by its D-separation statements. The essential graph of a
Markov equivalence class of DAGs is the mixed graph where the edges are directed if and only if they have the same direction for each graph in the equivalence class and undirected otherwise.

This talk describes the concept of quasi-essential (q-essential) graphs.The set of q-essential graphs corresponding to a Markov equivalence class form a po-set of chain graphs where the elements of
lowest order are the DAGs and the (unique) element of highest order is the essential graph.

This characterisation is used to develop an algorithm for learning the essential graph from a DAG