 The Kirkwood approximation is the probabilistic counterpart of the interaction information.Judea Pearl (1988 §3.2.4) indicates that an expression of this type can be exact in the case of a "decomposable" model, that is, a probability distribution that admits a graph structure whose cliques form a tree.In such cases, the numerator contains the product of the intra-clique joint distributions and the denominator contains the product of the clique intersection distributions.