Graphical models are a very useful tool with many applications, whereby a joint distribution of a set of random variables is modeled using only pairwise dependencies between the variables, and two variables with a direct causal relationship are connected by an edge, which is associated with their joint distribution.
It makes sense to extend this by looking at "hypergraphical models", where we allow direct causal relationships involving say up to $d$ variables, and the hyperedges connecting them are associated with a $d$-way joint distribution.
I want to know if such models have been studied, and in case they are is there a good survey or reference to learn more about the research that on belief propagation type algorithms on them?
