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.

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