In this presentation, a modular methodology that combines state-of-the-art methods in (stochastic) machine learning with traditional methods in rule learning is introduced to provide efficient and scalable algorithms for the classification of vast data sets, while remaining explainable. Apart from evaluating the approach on the common large-scale data sets MNIST, Fashion-MNIST and IMDB, novel results on explainable classifications of dental bills are presented. The latter case study stems from an industrial collaboration with Allianz Private Krankenversicherungs-Aktiengesellschaft which is an insurance company offering diverse services in Germany.