Causal discovery in the presence of missing data

Missing data are ubiquitous in many domains such as healthcare. Depending on how they are missing, the (conditional) independence relations in the observed data may be different from those for the complete data generated by the underlying causal process and, as a consequence, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. It is then essential to extend existing causal discovery approaches to find true underlying causal structure from such incomplete data. In this paper, we aim at solving this problem for data that are missing with different mechanisms, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness Graph (m-Graph), we analyze conditions under which addition correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose missing value PC (MVPC), which combines additional corrections with traditional causal discovery algorithm, in particular, PC. Our proposed MVPC is shown in theory to give asymptotically correct results even using data that are MAR and MNAR. Experiment results illustrate that the proposed algorithm can correct the conditional independence for values MCAR, MAR and rather general cases of values MNAR both with synthetic data as well as real-life healthcare application.