Probabilistic models such as Bayesian Networks are now in widespread use in spoken dialogue systems, but their scalability to complex interaction domains remains a challenge. One central limitation is that the state space of such models grows exponentially with the problem size, which makes parameter estimation increasingly difficult, especially for domains where only limited training data is available. In this paper, we show how to capture the underlying structure of a dialogue domain in terms of probabilistic rules operating on the dialogue state. The probabilistic rules are associated with a small, compact set of parameters that can be directly estimated from data. We argue that the introduction of this abstraction mechanism yields probabilistic models that are easier to learn and generalise better than their unstructured counterparts. We empirically demonstrate the benefits of such an approach learning a dialogue policy for a human-robot interaction domain based on a Wizard-of-Oz data set.