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Paper No. 09-32

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P Zwiernik and Jim Smith

The Geometry of independence tree models with hidden variables

Abstract: In this paper we investigate the geometry of undirected discrete graphical models of trees when all the variables in the system are binary and the inner nodes are unobserved . We obtain a full geometric description of these models which is given by polynomial equations and inequalities. We also give exact formulas for their parameters in terms of the marginal probability over the observed variables. A new system of coordinates is given that is intrinsically related to the defining trees and gives better insight into the underlying geometry.