293 research outputs found
Towards standard imsets for maximal ancestral graphs
The imsets of Studen\'y (2005) are an algebraic method for representing
conditional independence models. They have many attractive properties when
applied to such models, and they are particularly nice for working with
directed acyclic graph (DAG) models. In particular, the 'standard' imset for a
DAG is in one-to-one correspondence with the independences it induces, and
hence is a label for its Markov equivalence class. We first present a proposed
extension to standard imsets for maximal ancestral graph (MAG) models, using
the parameterizing set representation of Hu and Evans (2020). In these cases
the imset provides a scoring criteria by measuring the discrepancy for a list
of independences that define the model; this gives an alternative to the usual
BIC score that is also consistent, and much easier to compute. We also show
that, of independence models that do represent the MAG, the imset we give is
minimal. Unfortunately, for some graphs the representation does not represent
all the independences in the model, and in certain cases does not represent any
at all. For these general MAGs, we refine the reduced ordered local Markov
property Richardson (2003) by a novel graphical tool called _power DAGs_, and
this results in an imset that induces the correct model and which, under a mild
condition, can be constructed in polynomial time.Comment: Accepted to Bernoulli, 58 pages, 17 figure
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