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 "hypergraph 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 am interested in whether people have looked at such things, and analyzed the behavior of belief propagation type algorithms for them.
