Causal discovery in the presence of unobserved common causes from observational data only is a crucial but challenging problem. We categorize all possible causal relationships between two random variables into the following four categories and aim to identify one from observed data: two cases in which either of the direct causality exists, a case that variables are independent, and a case that variables are confounded by latent confounders. Although existing methods have been proposed to tackle this problem, they require unobserved variables to satisfy assumptions on the form of their equation models. In our previous study (Kobayashi et al., 2022), the first causal discovery method without such assumptions is proposed for discrete data and named CLOUD. Using Normalized Maximum Likelihood (NML) Code, CLOUD selects a model that yields the minimum codelength of the observed data from a set of model candidates. This paper extends CLOUD to apply for various data types across discrete, mixed, and continuous. We not only performed theoretical analysis to show the consistency of CLOUD in terms of the model selection, but also demonstrated that CLOUD is more effective than existing methods in inferring causal relationships by extensive experiments on both synthetic and real-world data.

在观测数据中存在未观测共同原因的因果关系发现是一个关键且具有挑战性的问题，本论文通过扩展CLOUD方法来处理不同类型的数据，通过理论分析和广泛实验证明CLOUD在模型选择和推断因果关系方面优于现有方法。

基于离散、混合和连续变量中NML代码的侦测未观察到的共同原因