Missing data are an unavoidable complication frequently encountered in many causal discovery tasks. When a missing process depends on the missing values themselves (known as self-masking missingness), the recovery of the joint distribution becomes unattainable, and detecting the presence of such self-masking missingness remains a perplexing challenge. Consequently, due to the inability to reconstruct the original distribution and to discern the underlying missingness mechanism, simply applying existing causal discovery methods would lead to wrong conclusions. In this work, we found that the recent advances additive noise model has the potential for learning causal structure under the existence of the self-masking missingness. With this observation, we aim to investigate the identification problem of learning causal structure from missing data under an additive noise model with different missingness mechanisms, where the `no self-masking missingness' assumption can be eliminated appropriately. Specifically, we first elegantly extend the scope of identifiability of causal skeleton to the case with weak self-masking missingness (i.e., no other variable could be the cause of self-masking indicators except itself). We further provide the sufficient and necessary identification conditions of the causal direction under additive noise model and show that the causal structure can be identified up to an IN-equivalent pattern. We finally propose a practical algorithm based on the above theoretical results on learning the causal skeleton and causal direction. Extensive experiments on synthetic and real data demonstrate the efficiency and effectiveness of the proposed algorithms.

在存在自我遮蔽缺失情况下，探索从缺失数据中学习因果结构的识别问题是一项具有挑战性的任务，然而我们发现最近引入的加性噪声模型具有潜力用于解决这个问题。本研究通过扩展因果骨架的可识别范围，给出了加性噪声模型下因果方向的充分和必要的识别条件，并提出了一种基于该理论结果的实用算法来学习因果结构。通过对合成数据和真实数据的广泛实验，证明了该算法的高效性和有效性。

缺失数据的加性噪声模型下的因果结构识别