  Bayesian network (BN) structure learning from complete data has been
extensively studied in the literature. However, fewer theoretical results are
available for incomplete data, and most are related to the
Expectation-Maximisation (EM) algorithm. Balov (2013) proposed an alternative
approach called Node-Average Likelihood (NAL) that is competitive with EM but
computationally more efficient; and he proved its consistency and model
identifiability for discrete BNs.
  In this paper, we give general sufficient conditions for the consistency of
NAL; and we prove consistency and identifiability for conditional Gaussian BNs,
which include discrete and Gaussian BNs as special cases. Furthermore, we
confirm our results and the results in Balov (2013) with an independent
simulation study. Hence we show that NAL has a much wider applicability than
originally implied in Balov (2013), and that it is competitive with EM for
conditional Gaussian BNs as well.
