Estimating Causal Direction and Confounding of Two Discrete Variables
This work addresses causal inference for researchers in statistics and machine learning, but it appears incremental as it builds on prior identifiability assumptions for continuous variables.
The authors tackled the problem of estimating causal direction between two discrete variables from their joint distribution, proposing a method that achieves classification with an inherent baseline error, though specific numerical results are not provided in the abstract.
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presupposes that the probability distributions $P(C)$ of a cause $C$ is independent from the probability distribution $P(E\mid C)$ of the cause-effect mechanism. While our classifier is trained with a Bayesian assumption of flat hyperpriors, we do not make this assumption about our test data. This work connects to recent developments on the identifiability of causal models over continuous variables under the assumption of "independent mechanisms". Carefully-commented Python notebooks that reproduce all our experiments are available online at http://vision.caltech.edu/~kchalupk/code.html.