"Imsets, introduced by Studený (see Studený, 2005 for details), are an algebraic method for representing conditional independence models. They have many attractive properties when applied to such models, and they are particularly nice when applied to directed acyclic graph (DAG) models. In particular, the standard imset for a DAG is in one-to-one correspondence with the independence model it induces, and hence is a label for its Markov equivalence class. We present a proposed extension to standard imsets for maximal ancestral graph (MAG) models, which have directed and bidirected edges, using the parameterizing set representation of Hu and Evans (2020). By construction, our imset also represents the Markov equivalence class of the MAG.
We show that for many such graphs our proposed imset defines the model, though there is a subclass of graphs for which the representation does not. We prove that it does work for MAGs that include models with no adjacent bidirected edges, as well as for a large class of purely bidirected models. If there is time, we will also discuss applications of imsets to structure learning in MAGs.
This is joint work with Zhongyi Hu (Oxford).
Z. Hu and R.J. Evans, Faster algorithms for Markov equivalence, In Proceedings for the 36th Conference on Uncertainty in Artificial Intelligence (UAI-2020), 2020.
M. Studený, Probabilistic Conditional Independence Structures, Springer-Verlag, 2005."