Bayesian networks are graphical representations of probability
distributions. In virtually all of the work on learning these networks,
the assumption is that we are presented with a data set consisting of
randomly generated instances from the underlying distribution. In many
situations, however, we also have the option of active learning,
where we have the possibility of guiding the sampling process by
querying for certain types of samples. This paper addresses the problem of
estimating the parameters of Bayesian networks in an active learning
setting. We provide a theoretical framework for this problem, and an
algorithm that chooses which active learning queries to generate based on
the model learned so far. We present experimental results showing that our
active learning algorithm can significantly reduce the need for training
data in many situations.