On Shannon capacity and causal estimation

The problem of estimating causal relationships from purely observational data is studied in this paper. We observe samples from a pair of random variables (X,Y) and wish to estimate whether X causes Y or Y causes X. Any joint distribution can be factored as p_X,Y = p_X p_Y|X = p_Y p_X|Y and therefore the “causal” direction cannot be inferred from the joint distribution without further assumptions. In this paper, we propose and study the utility of Shannon capacity as a metric for causal directionality estimation. This opens up several open questions and directions for future study.