Tree cumulants and the geometry of binary tree models

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In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved.

• A novel approach based on the theory of partially ordered sets allows us to obtain a convenient parametrization of this model class.
• The construction of the proposed coordinate system mirrors the combinatorial definition of cumulants.
• A simple product-like form of the resulting parametrization gives insight into identifiability issues associated with this model class.