Identifiability of an Integer Modular Acyclic Additive Noise Model and its Causal Structure Discovery

The notion of causality is used in many situations dealing with uncertainty. We consider the problem whether causality can be identified given data set generated by discrete random variables rather than continuous ones. In particular, for non-binary data, thus far it was only known that causality can be identified except rare cases. In this paper, we present necessary and sufficient condition for an integer modular acyclic additive noise (IMAN) of two variables. In addition, we relate bivariate and multivariate causal identifiability in a more explicit manner, and develop a practical algorithm to find the order of variables and their parent sets. We demonstrate its performance in applications to artificial data and real world body motion data with comparisons to conventional methods.