  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.
