Causal Inference on Discrete Data using Additive Noise Models

Inferring causal relations by analyzing statistical dependences among observed random variables is a challenging task if no controlled randomized experiments are available. Socalled constraint-based approaches to causal discovery (Pearl, 2000; Spirtes et al., 1993) select among all directed acyclic graphs (DAGs) those that satisfy the Markov condition and the faithfulness assumption, i.e., those for which the observed independences are imposed by the structure rather than being a result of specific choices of parameters of the Bayesian network. These approaches are unable to distinguish among causal DAGs that impose the same independences. In particular, it is impossible to distinguish between X Y and Y X. More recently, several methods have been suggested that use not only conditional independences, but also more sophisticated properties of the joint distribution. For simplicity, we explain the ideas for the two variable setting since this case is particularly challenging. Kano & Shimizu (2003) use models Y f(X) N (1) where f is a linear function and N is additive noise that is independent of the hypothetical cause X. This is an example for an additive noise model from X to Y. Apart from trivial