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Title: A unified approach to marginal and conditional independencies of binary variables based on Moebius inversion Authors:  Luca La Rocca - University of Modena and Reggio Emilia (Italy) [presenting]
Alberto Roverato - University of Bologna (Italy)
Abstract: A novel parameterization is presented for the joint distribution of a binary vector, based on partitioning the vector in two sets of variables. This parameterization, which we name hybrid parameterization, provides us with a unified expression for all conditional and marginal independencies implied by a class of bipartite regression graphs. Both undirected and bidirected graphical models belong to this class, as extreme cases, and the hybrid parameterization specializes to the traditional log-linear parameterization and the more recent log-mean linear parameterization, respectively, in these cases. We illustrate the role the hybrid parameterization can play in the study of relationships among binary variables.