  This paper provides a graphical characterization of Markov blankets in chain
graphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The
characterization is different from the well-known one for Bayesian networks and
generalizes it. We provide a novel scalable and sound algorithm for Markov
blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB
algorithm, and its variants are still correct for Markov blanket discovery in
LWF CGs under the same assumptions as for Bayesian networks. We provide a sound
and scalable constraint-based framework for learning the structure of LWF CGs
from faithful causally sufficient data and prove its correctness when the
Markov blanket discovery algorithms in this paper are used. Our proposed
algorithms compare positively/competitively against the state-of-the-art LCD
(Learn Chain graphs via Decomposition) algorithm, depending on the algorithm
that is used for Markov blanket discovery. Our proposed algorithms make a broad
range of inference/learning problems computationally tractable and more
reliable because they exploit locality.
