Effective large-scale process optimization in manufacturing industries requires close cooperation between different parties of human experts who encode their knowledge of related domains as Bayesian network models. For example, parties in the steel industry must collaboratively use their Bayesian networks on process parameters at the maker, steel properties, and application demands at the client to identify process optimizations effectively. However, business confidentiality across domains hinders collaboration, demanding alternatives to centralized inference. We propose CCBNet, the first Confidentiality-preserving Collaborative Bayesian Network inference framework. CCBNet leverages secret sharing to securely perform analysis on the combined knowledge of party models by joining two novel subprotocols: CABN, which augments probability distributions for features across modeling parties into secret shares of their normalized combination; and (ii) SAVE, which aggregate party inference result shares through distributed variable elimination. We extensively evaluate CCBNet on nine public Bayesian networks. Our results show CCBNet achieves similar predictive quality to centralized methods while preserving model confidentiality. We finally demonstrate that CCBNet scales to challenging manufacturing use cases, where involving many (16-128) parties in large networks (223-1003 features), on average, enables 45% less computation while communicating 251k values/request.

Decision trees are often desirable for classification/regression tasks thanks to their human-friendly models. Unfortunately, the construction of decision trees is a hard problem which usually implies having to rely on imperfect heuristic methods. Advancements in algorithmics and hardware processing power have rendered globally optimal trees accessible, but even state-of-the-art techniques remain limited in certain aspects. One such limitation is the use of simple, univariate predicates within the decision tree. This paper explores the practicality of further expanding the already exponentially large search space navigated by existing optimal tree algorithms in order to add support for more complex, multivariate predicates. While such an approach comes with profound negative implications on the algorithm's time complexity, it has the potential to create decision trees whose boundaries are closer to ground truth. The results of this work support such a hypothesis, but they also make it clear that further optimisation techniques are critical for multivariate optimal decision tree algorithms, especially as the variety of considered multivariate splits increases.