Detection of Unobserved Common Causes based on NML Code in Discrete,
  Mixed, and Continuous Variables
Masatoshi Kobayashi Kohei Miyagichi Shin Matsushima
Causal discovery in the presence of unobserved common causes from
observational data only is a crucial but challenging problem. We categorize all
possible causal relationships between two random variables into the following
four categories and aim to identify one from observed data: two cases in which
either of the direct causality exists, a case that variables are independent,
and a case that variables are confounded by latent confounders. Although
existing methods have been proposed to tackle this problem, they require
unobserved variables to satisfy assumptions on the form of their equation
models. In our previous study (Kobayashi et al., 2022), the first causal
discovery method without such assumptions is proposed for discrete data and
named CLOUD. Using Normalized Maximum Likelihood (NML) Code, CLOUD selects a
model that yields the minimum codelength of the observed data from a set of
model candidates. This paper extends CLOUD to apply for various data types
across discrete, mixed, and continuous. We not only performed theoretical
analysis to show the consistency of CLOUD in terms of the model selection, but
also demonstrated that CLOUD is more effective than existing methods in
inferring causal relationships by extensive experiments on both synthetic and
real-world data.