(eng): Multidimensional probability distributions that are too large to be stored in computer memory can be represented by a compositional model - a sequence of low-dimensional probability distributions that when composed together try to faithfully estimate the original multidimensional distribution. The decomposition to the compositional model is not satisfactorily resolved. We offer an approach based on search traversal through the decomposable model class using likelihood-test statistics. The paper is a work sketch of the current research.