Being Bayesian about learning Gaussian Bayesian networks from incomplete data

We propose a Bayesian model averaging (BMA) approach for inferring the structure of Gaussian Bayesian networks (BNs) from incomplete data, i.e. from data with missing values. Our method builds on the ‘Bayesian metric for Gaussian networks having score equivalence’ (BGe score) and we make the assumption that the unobserved data points are ‘missing completely at random’. We present a Markov Chain Monte Carlo sampling algorithm that allows for simultaneously sampling directed acyclic graphs (DAGs) as well as the values of the unobserved data points. We empirically cross-compare the network reconstruction accuracy of the new BMA approach with two non-Bayesian approaches for dealing with incomplete BN data, namely the classical structural Expectation Maximisation (EM) approach and the more recently proposed node average likelihood (NAL) method. For the empirical evaluation we use synthetic data from a benchmark Gaussian BN and real wet-lab protein phosphorylation data from the RAF signalling pathway.