  A serious problem in learning probabilistic models is the presence of hidden
variables. These variables are not observed, yet interact with several of the
observed variables. Detecting hidden variables poses two problems: determining
the relations to other variables in the model and determining the number of
states of the hidden variable. In this paper, we address the latter problem in
the context of Bayesian networks. We describe an approach that utilizes a
score-based agglomerative state-clustering. As we show, this approach allows us
to efficiently evaluate models with a range of cardinalities for the hidden
variable. We show how to extend this procedure to deal with multiple
interacting hidden variables. We demonstrate the effectiveness of this approach
by evaluating it on synthetic and real-life data. We show that our approach
learns models with hidden variables that generalize better and have better
structure than previous approaches.
