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State-of-the-art causal discovery methods usually assume that theobservational data is complete. However, the missing data problem is pervasivein many practical scenarios such as clinical trials, economics, and biology.One straightforward way to address the missing data problem is first to imputethe data using off-the-shelf imputation methods and then apply existing causaldiscovery methods. However, such a two-step method may suffer fromsuboptimality, as the imputation algorithm may introduce bias for modeling theunderlying data distribution. In this paper, we develop a general method, whichwe call MissDAG, to perform causal discovery from data with incompleteobservations. Focusing mainly on the assumptions of ignorable missingness andthe identifiable additive noise models (ANMs), MissDAG maximizes the expectedlikelihood of the visible part of observations under theexpectation-maximization (EM) framework. In the E-step, in cases wherecomputing the posterior distributions of parameters in closed-form is notfeasible, Monte Carlo EM is leveraged to approximate the likelihood. In theM-step, MissDAG leverages the density transformation to model the noisedistributions with simpler and specific formulations by virtue of the ANMs anduses a likelihood-based causal discovery algorithm with directed acyclic graphconstraint. We demonstrate the flexibility of MissDAG for incorporating variouscausal discovery algorithms and its efficacy through extensive simulations andreal data experiments.

MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models