Process mining supports the analysis of the actual behavior and performance of business processes using event logs. % such as, e.g., sales transactions recorded by an ERP system. An essential requirement is that every event in the log must be associated with a unique case identifier (e.g., the order ID of an order-to-cash process). In reality, however, this case identifier may not always be present, especially when logs are acquired from different systems or extracted from non-process-aware information systems. In such settings, the event log needs to be pre-processed by grouping events into cases -- an operation known as event correlation. Existing techniques for correlating events have worked with assumptions to make the problem tractable: some assume the generative processes to be acyclic, while others require heuristic information or user input. Moreover, %these techniques' primary assumption is that they abstract the log to activities and timestamps, and miss the opportunity to use data attributes. % In this paper, we lift these assumptions and propose a new technique called EC-SA-Data based on probabilistic optimization. The technique takes as inputs a sequence of timestamped events (the log without case IDs), a process model describing the underlying business process, and constraints over the event attributes. Our approach returns an event log in which every event is associated with a case identifier. The technique allows users to incorporate rules on process knowledge and data constraints flexibly. The approach minimizes the misalignment between the generated log and the input process model, maximizes the support of the given data constraints over the correlated log, and the variance between activity durations across cases. Our experiments with various real-life datasets show the advantages of our approach over the state of the art.