  Causal learning is a fundamental problem in statistics and science, offering
insights into predicting the effects of unseen treatments on a system. Despite
recent advances in this topic, most existing causal discovery algorithms
operate under two key assumptions: (i) the underlying graph is acyclic, and
(ii) the available data is complete. These assumptions can be problematic as
many real-world systems contain feedback loops (e.g., biological systems), and
practical scenarios frequently involve missing data. In this work, we propose a
novel framework, named MissNODAGS, for learning cyclic causal graphs from
partially missing data. Under the additive noise model, MissNODAGS learns the
causal graph by alternating between imputing the missing data and maximizing
the expected log-likelihood of the visible part of the data in each training
step, following the principles of the expectation-maximization (EM) framework.
Through synthetic experiments and real-world single-cell perturbation data, we
demonstrate improved performance when compared to using state-of-the-art
imputation techniques followed by causal learning on partially missing
interventional data.
