Abstract

Hidden variable DAGs can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. Knowing the complete set of observable constraints is ideal, but this can be difficult to determine in many settings. In models with categorical observed variables we define a class of models where our proposed systematic method for deriving constraints provides the complete set of observable constraints. Although this provides the complete set of observable constraints, there are still some practical issues. We have a method for reducing the candidate non-trivial constraints, but determining which constraints are actually non-trivial and thus useful can still be the challenge. Additionally, the method, although scalable in the number of districts, does not scale well in the complexity of any given district. Finally, the class of models where the method can be applied is well-defined but, to our knowledge, it is not yet known what models outside the class have equivalent constraints to ones inside the class. We illustrate the method in several new settings, including ones that imply both inequality and equality constraints.