A picture archiving and communication system (PACS) was originally designed for replacing physical films by digitizing medical images for storage and access convenience. With the maturity of communication infrastructures, e.g. 5G transmission, big data and distributed processing technologies, cloud-based PACS extends the storage and access efficiency of PACS across multiple imaging centers, hospitals and clinics without geographical bounds. In addition to the flexibility of accessing medical big data to physicians and radiologists to access medical records, fast data analytics is becoming an important part of cloud-based PACS solution. The machine learning that supports cloud-based PACS needs to provide highly accurate prediction and interpretable model, despite the model learning time should be kept as minimum as possible in the big data environment. In this paper, a framework called White Learning (WL) which hybridizes a deep learner and an incremental Bayesian network which offer the highest possible prediction accuracy and causality reasoning which are currently demanded by medical practitioners. To achieve this, several novel modifications for optimizing a WL model are proposed and studied. The efficacy of the optimized WL model is tested with empirical breast-cancer mammogram data from a local hospital.