Hmm. I didn’t encounter this terminology before, but, given a graph and a factor you can consider the convex hull of all probability distributions compatible with this graph and factor (i.e. all probability distributions obtained by assigning other factors to the other cliques in the graph). This is a crisp infradistribution. So, in this sense you can say factors are a special case of infradistributions (although I don’t know how much information this transformation loses).
It’s more natural to consider, instead of a factor, either the marginal probability distribution of a set of variables or the conditional probability distribution of a set of variables on a different set of variables. Specifying one of those is a linear condition on the full distribution so it gives you a crisp infradistribution without having to take convex hull, and no information is lost.
Hmm. I didn’t encounter this terminology before, but, given a graph and a factor you can consider the convex hull of all probability distributions compatible with this graph and factor (i.e. all probability distributions obtained by assigning other factors to the other cliques in the graph). This is a crisp infradistribution. So, in this sense you can say factors are a special case of infradistributions (although I don’t know how much information this transformation loses).
It’s more natural to consider, instead of a factor, either the marginal probability distribution of a set of variables or the conditional probability distribution of a set of variables on a different set of variables. Specifying one of those is a linear condition on the full distribution so it gives you a crisp infradistribution without having to take convex hull, and no information is lost.