In recent years, many methods have been developed for discovering causal relationships from observed data. However, as an important kind of causes existing in many causal systems, combined causes (e.g. multi-factor causes consisting of two or more component variables that individually might not be a cause) have not received enough attention. The existing approach includes both individual and combined variables in the causal discovery process using constraint-based methods, can neither distinguish a set of Markov equivalence classes nor identify a combined cause containing one (or more) individual cause(s), therefore can output only some combined causes, instead of all combined causes. In this paper, we first subsume all possible combined causes into three types and give them formal definitions, then extend the additive noise model (ANM) to infer combined causes. We show that if a candidate variable set X w.r.t. a target Y satisfies: (1) allowing ANM for only the forward direction $X\to Y$, and (2) no disturbance variable is contained in X, i.e., removing any component of X will weaken the causal relationship between X and Y, then X forms a combined cause. Based on this finding, we develop an efficient method to discover combined causes. Furthermore, we also conduct extensive experiments to validate the proposed method on both synthetic and real-world data sets.

近年来，已经开发了许多方法来从观察到的数据中发现因果关系。然而，作为存在于许多因果系统中的一种重要原因，组合原因（例如由两个或多个单独可能不是原因的分量变量组成的多因素原因）并没有得到足够的重视。现有方法使用基于约束的方法在因果发现过程中包括单个变量和组合变量，既不能区分一组马尔可夫等价类，也不能识别包含一个（或多个）单个原因的组合原因，因此只能输出一些综合原因，而不是所有综合原因。在本文中，我们首先将所有可能的组合原因归入三种类型并给出它们的正式定义，然后扩展加性噪声模型 (ANM) 以推断综合原因。我们证明如果一个候选变量集X wrt 目标Y满足： (1) 仅允许正向 ANM$X\to 是$，以及 (2) X 中不包含扰动变量，即去除X 的任何分量都会削弱X和Y之间的因果关系，然后X形成组合原因。基于这一发现，我们开发了一种有效的方法来发现综合原因。此外，我们还进行了广泛的实验，以在合成数据集和真实数据集上验证所提出的方法。