This paper presents a framework for analyzing and predicting the performances of a business process, based on historical data gathered during its past enactments. The framework hinges on an inductive-learning technique for discovering a special kind of predictive process models, which can support the run-time prediction of some performance measure (e.g., the remaining processing time or a risk indicator) for an ongoing process instance, based on a modular representation of the process, where major performance-relevant variants of it are equipped with different regression models, and discriminated through context variables. The technique is an original combination of different data mining methods (namely, non-parametric regression methods and a probabilistic trace clustering scheme) and ad hoc data transformation mechanisms, meant to bring the log traces to suitable level of abstraction. In order to overcome the severe scalability limitations of current solutions in the literature, and make our approach really suitable for large logs, both the computation of the trace clusters and of the clusters’ predictors are implemented in a parallel and distributed manner, on top of a cloud-based service-oriented infrastructure. Tests on a real-life log confirmed the validity of the proposed approach, in terms of both effectiveness and scalability.