In the face of sparsity, statistical models are often interpolated with lower order (backoff) models, particularly in Language Modeling. In this paper, we argue that there is a relation between the higher order and the backoff model that must be satisfied in order for the interpolation to be effective. We show that in n-gram models, the relation is trivially held, but in models that allow arbitrary clustering of context (such as decision tree models), this relation is generally not satisfied. .
