One of the challenges in the Connect project is to develop techniques for learning models of networked components from exploratory interaction with the component, based on analyzing messages exchanged between the component and its environment. Many approaches to this problem employ regular inference (aka. automata learning) techniques which generate modest-size finite-state models. Most communication with real-life systems involves data values being relevant to the communication context and thus influencing the observable behavior of the communication endpoints. When applying methods from the realm of automata learning, it is desirable to handle such data occurrences. It is therefore important to extend inference techniques to handle message alphabets and state-spaces with structures containing data parameters, often with large domains. After very briefly mentioning several approaches to the problem, we give a longer account of an approach proposed by Aarts et al, which adapts ideas from of predicate abstraction, successfully used in formal verification. We illustrate the techniques by application to a simple running example, which models a simple booking service.