  Incomplete data are a common feature in many domains, from clinical trials to
industrial applications. Bayesian networks (BNs) are often used in these
domains because of their graphical and causal interpretations. BN parameter
learning from incomplete data is usually implemented with the
Expectation-Maximisation algorithm (EM), which computes the relevant sufficient
statistics ("soft EM") using belief propagation. Similarly, the Structural
Expectation-Maximisation algorithm (Structural EM) learns the network structure
of the BN from those sufficient statistics using algorithms designed for
complete data. However, practical implementations of parameter and structure
learning often impute missing data ("hard EM") to compute sufficient statistics
instead of using belief propagation, for both ease of implementation and
computational speed. In this paper, we investigate the question: what is the
impact of using imputation instead of belief propagation on the quality of the
resulting BNs? From a simulation study using synthetic data and reference BNs,
we find that it is possible to recommend one approach over the other in several
scenarios based on the characteristics of the data. We then use this
information to build a simple decision tree to guide practitioners in choosing
the EM algorithm best suited to their problem.
