Inferring the causal decomposition under the presence of deterministic relations

The presence of deterministic relations pose problems for current algorithms that learn the causal structure of a system based on the observed conditional independencies. Deterministic variables lead to information equivalences; two sets of variables have the same information about a third variable. Based on information content, one cannot decide on the direct causes. Several edges model equally well the dependencies. We call them equivalent edges. We propose to select among the equivalent edges the one with the simplest descriptive complexity. This approach assumes that the descriptive complexity increases along a causal path. As confirmed by our experimental results, the accuracy of the method depends on the chance of accidental matches of complexities.