This paper proposes two methods for causal additive models with unobserved variables (CAM-UV). CAM-UV assumes that the causal functions take the form of generalized additive models and that latent confounders are present. First, we propose a method that leverages prior knowledge for efficient causal discovery. Then, we propose an extension of this method for inferring causality in time series data. The original CAM-UV algorithm differs from other existing causal function models in that it does not seek the causal order between observed variables, but rather aims to identify the causes for each observed variable. Therefore, the first proposed method in this paper utilizes prior knowledge, such as understanding that certain variables cannot be causes of specific others. Moreover, by incorporating the prior knowledge that causes precedes their effects in time, we extend the first algorithm to the second method for causal discovery in time series data. We validate the first proposed method by using simulated data to demonstrate that the accuracy of causal discovery increases as more prior knowledge is accumulated. Additionally, we test the second proposed method by comparing it with existing time series causal discovery methods, using both simulated data and real-world data.

翻译：本文提出了两种针对含未观测变量的因果加性模型（CAM-UV）的方法。CAM-UV假设因果函数采用广义加性模型形式，且存在潜在混杂因子。首先，我们提出一种利用先验知识实现高效因果发现的方法。随后，我们将该方法扩展至时间序列数据的因果推断。原始CAM-UV算法与其他现有因果函数模型的不同之处在于，它并非寻求观测变量之间的因果顺序，而是旨在识别每个观测变量的成因。因此，本文提出的第一种方法利用此类先验知识（例如，某些变量不能成为其他特定变量的原因）。此外，通过纳入"原因在时间上先于结果"的先验知识，我们将第一种算法扩展为适用于时间序列数据因果发现的第二种方法。我们通过模拟数据验证了第一种方法，结果表明随着先验知识的累积，因果发现的准确性逐步提升。同时，我们使用模拟数据和真实数据，将第二种方法与现有时间序列因果发现方法进行对比测试。