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# Identifiability and Consistency of Bayesian Network Structure Learning from Incomplete Data

*Proceedings of the 10th International Conference on Probabilistic Graphical Models*, PMLR 138:29-40, 2020.

#### Abstract

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 based on the use of 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 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. Hence NAL
has a wider applicability than originally stated in Balov (2013).