  Learning from data that contain missing values represents a common phenomenon
in many domains. Relatively few Bayesian Network structure learning algorithms
account for missing data, and those that do tend to rely on standard approaches
that assume missing data are missing at random, such as the
Expectation-Maximisation algorithm. Because missing data are often systematic,
there is a need for more pragmatic methods that can effectively deal with data
sets containing missing values not missing at random. The absence of approaches
that deal with systematic missing data impedes the application of BN structure
learning methods to real-world problems where missingness are not random. This
paper describes three variants of greedy search structure learning that utilise
pairwise deletion and inverse probability weighting to maximally leverage the
observed data and to limit potential bias caused by missing values. The first
two of the variants can be viewed as sub-versions of the third and best
performing variant, but are important in their own in illustrating the
successive improvements in learning accuracy. The empirical investigations show
that the proposed approach outperforms the commonly used and state-of-the-art
Structural EM algorithm, both in terms of learning accuracy and efficiency, as
well as both when data are missing at random and not at random.
