  EDML is a recently proposed algorithm for learning MAP parameters in Bayesian
networks. In this paper, we present a number of new advances and insights on
the EDML algorithm. First, we provide the multivalued extension of EDML,
originally proposed for Bayesian networks over binary variables. Next, we
identify a simplified characterization of EDML that further implies a simple
fixed-point algorithm for the convex optimization problem that underlies it.
This characterization further reveals a connection between EDML and EM: a fixed
point of EDML is a fixed point of EM, and vice versa. We thus identify also a
new characterization of EM fixed points, but in the semantics of EDML. Finally,
we propose a hybrid EDML/EM algorithm that takes advantage of the improved
empirical convergence behavior of EDML, while maintaining the monotonic
improvement property of EM.
