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.

翻译：因果学习是统计学和科学中的一个基本问题，有助于预测未见干预对系统的影响。尽管该主题近期取得了进展，但现有大多数因果发现算法仍基于两大假设：（i）底层图结构为无环，（ii）可用数据完整。这些假设在实际中可能存在问题，因为许多真实系统包含反馈回路（例如生物系统），且实际场景经常涉及数据缺失。本研究提出了一种名为MissNODAGS的新型框架，用于从部分缺失数据中学习循环因果图。在加性噪声模型下，MissNODAGS遵循期望最大化（EM）框架原理，通过交替进行缺失数据插补和最大化每一步训练中数据可见部分的期望对数似然来学习因果图。通过合成实验和真实单细胞扰动数据，我们证明了与使用最先进插补技术后对部分缺失干预数据进行因果学习相比，本方法具有更优的性能。