A Study of Recently Discovered Equalities about Latent Tree Models Using Inverse Edges

Interesting equalities have recently been discovered about latent tree models. They relate distributions of two or three observed variables with joint distributions of four or more observed variables, and with model parameters that depend on latent variables. The equations are derived by using matrix and tensor decompositions. This paper sheds new light on the equalities by offering an alternative derivation in terms of variable elimination and structure manipulations. The key technique is the introduction of inverse edges.