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

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