I'm working on structural learning in Bayesian Networks.
Assume two types of random variables are given. class I: $x_1, x_2,\dots, x_n$ and class II: $y_1, y_2, \dots, y_n$.
Generally, we can have a directed arc from $x_i$ to $y_j$ and vice versa.
Is there any application in which we know there is only one possible direction i.e., either we can go from $x_i$ variables to $y_j$ variables or we can only go from $y_j$ variables to $x_i$ variable?
Note, we don't know the direction a priori. The only thing we can assume is that there is one directional relationship (if any relationship exists) among two set of variables i.e., $x \rightarrow y$ or $y \rightarrow x$.
Can anyone give me some suggestions where I can find case studies in real world with such properties. I very much appreciate it.