Causal additive models with unobserved variables
Causal additive models with unobserved variables
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发表时间：
2021
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通讯作者：
Takashi Nicholas Maeda;Shohei Shimizu
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作者：
Takashi Nicholas Maeda;Shohei Shimizu
从受未观测变量影响的数据中发现因果关系是一个重要但难以解决的问题。在非线性情况下，未观测变量对观测变量之间关系的影响比线性情况下更复杂。在这项研究中，我们专注于存在不可观测变量的因果加性模型。因果加性模型展示的结构方程在变量和误差项中是加性的。我们不仅考虑了未观察到的共同原因，而且还考虑了未观察到的中间变量的存在。我们的理论结果表明，当因果关系是非线性的，有未观察到的变量，它是不可能的，以确定所有的因果关系观察变量之间通过回归和独立性测试。然而，我们的理论结果也表明，它是可能的，以避免不正确的推论。我们提出了一种方法来识别所有的因果关系，理论上是可能的，而不会被未观察到的变量的偏见。使用阿尔蒂官方数据和模拟的功能磁共振成像（fMRI）数据的实证结果表明，我们的方法有效地推断因果结构的存在下不可观察的变量。
Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than in linear cases. In this study, we focus on causal additive models in the presence of unobserved variables. Causal additive models exhibit structural equations that are additive in the variables and error terms. We take into account the presence of not only unobserved common causes but also unobserved intermediate variables. Our theoretical results show that, when the causal relationships are nonlinear and there are unobserved variables, it is not possible to identify all the causal relationships between observed variables through regression and independence tests. However, our theoretical results also show that it is possible to avoid incorrect inferences. We propose a method to identify all the causal relationships that are theoretically possible to identify without being biased by unobserved variables. The empirical results using artificial data and simulated functional magnetic resonance imaging (fMRI) data show that our method effectively infers causal structures in the presence of unobserved variables.