Bayesian partitioning is utilised simultaneously on subjects and categorical variables to reveal complex dependence structures. Clusters of variables are referred to as views. Variable selection highlights the variables that drive the clustering of the subjects within each view. We derive theoretical results on the relation between the variables' dependence structure and the inferences derived from bi-clustering. The results relate to marginal independence and conditional independence. Using simulated and real data, we demonstrate the applicability of bi-clustering results in assisting log-linear graphical model determination, leading to the efficient exploration of typically vast model spaces. This work sheds light on the relation between two very different but equally popular Bayesian approaches; mixture modelling, that benefits from a large number of variables, and graphical log-linear modelling, which describes explicitly the variables' dependence structure and allows to evaluate the uncertainty associated with model determination.

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