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：本文针对含未观测变量的因果加性模型（CAM-UV）提出两种方法。CAM-UV假设因果函数形式为广义加性模型，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，将该方法扩展至时间序列数据的因果推断。原始CAM-UV算法区别于现有其他因果函数模型之处在于：它不寻求观测变量间的因果序，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先验知识（例如明确某些变量不可能是其他变量的原因）。此外，通过引入"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第二种方法，用于时间序列数据的因果发现。我们通过模拟数据验证了第一种方法，结果表明因果发现的准确率随先验知识累积而提升。同时，我们采用模拟数据与真实数据，将第二种方法与现有时间序列因果发现方法进行对比验证。