  Bayesian networks, and especially their structures, are powerful tools for
representing conditional independencies and dependencies between random
variables. In applications where related variables form a priori known groups,
chosen to represent different "views" to or aspects of the same entities, one
may be more interested in modeling dependencies between groups of variables
rather than between individual variables. Motivated by this, we study prospects
of representing relationships between variable groups using Bayesian network
structures. We show that for dependency structures between groups to be
expressible exactly, the data have to satisfy the so-called groupwise
faithfulness assumption. We also show that one cannot learn causal relations
between groups using only groupwise conditional independencies, but also
variable-wise relations are needed. Additionally, we present algorithms for
finding the groupwise dependency structures.
