Identifiability of Discrete Concentration Graphical Models with a Latent Variable

We present an algorithm that can decide whether a graphical model is identifiable. The algorithm is supported with a MATLAB package, iugm. However we presume that the input graphical models are represented by undirected graphs, and the aim is to determine whether they are identifiable or not. Since a distribution P can be completely characterized by its moments, we decide a model as identifiable if it can be uniquely represented in terms of its moments, one-to-one mapping. As for global identifiability, the existence of two different vectors of parameter values that yield the same moments of the distribution of the observed variables negates global identifiability. Therefor, the one-to-one mapping for globally identifiable models is in the whole domain. While local identifiability dictates that the parametrization map has full rank and the one-to-one mapping is satisfied in a neighborhood. For models where the parametrization map does not have full rank, we compute the subset of the parameter space where identifiabilty collapses. The algorithm and the accompanying package are stipulating the existence of only one hidden (latent) variable that is connected to all observed variables. Moreover, all variables have a binary state.