Markov blanket discovery in positive-unlabelled and semi-supervised data

Abstract. The importance of Markov blanket discovery algorithms is twofold: as the main building block in constraint-based structure learn-ing of Bayesian network algorithms and as a technique to derive the optimal set of features in filter feature selection approaches. Equally, learning from partially labelled data is a crucial and demanding area of machine learning, and extending techniques from fully to partially super-vised scenarios is a challenging problem. While there are many different algorithms to derive the Markov blanket of fully supervised nodes, the partially-labelled problem is far more challenging, and there is a lack of principled approaches in the literature. Our work derives a generaliza-tion of the conditional tests of independence for partially labelled binary target variables, which can handle the two main partially labelled scenar-ios: positive-unlabelled and semi-supervised. The result is a significantly deeper understanding of how to control false negative errors in Markov Blanket discovery procedures and how unlabelled data can help