The constraints arising from DAG models with latent variables can be
naturally represented by means of acyclic directed mixed graphs (ADMGs).
Such graphs contain directed (→) and bidirected (↔)
arrows, and contain no directed cycles. DAGs with latent variables imply
independence constraints in the distribution resulting from a 'fixing'
operation, in which a joint distribution is divided by a conditional. This
operation generalizes marginalizing and conditioning. Some of these
constraints correspond to identifiable 'dormant' independence
constraints, with the well known 'Verma constraint' as one example.
Recently, models defined by a set of the constraints arising after fixing
from a DAG with latents, were characterized via a recursive factorization
and a nested Markov property. In addition, a parameterization was given in
the discrete case. In this paper we use this parameterization to describe
a parameter fitting algorithm, and a search and score structure learning
algorithm for these nested Markov models. We apply our algorithms to a
variety of datasets.
[ Paper ]