Building Undirected Influence Ontologies Using Pairwise Similarity Functions

The recovery of influence ontology structures is a useful tool within knowledge discovery, allowing for an easy and intuitive method of graphically representing the influences between concepts or variables within a system. The focus of this research is to develop a method by which undirected influence structures, here in the form of undirected Bayesian network skeletons, can be recovered from observations by means of some pairwise similarity function, either a statistical measure of correlation or some problem-specific measure. In this research, we present two algorithms to construct undirected influence structures from observations. The first makes use of a threshold value to filter out relations denoting weak influence, and the second constructs a maximum weighted spanning tree over the complete set of relations. In addition, we present a modification to the minimum graph edit distance (GED) [1], which we refer to as the modified scaled GED, in order to evaluate the performance of these algorithms in reconstructing known structures. We perform a number of experiments in reconstructing known Bayesian network structures, including a real-world medical network [2]. Our analysis shows that these algorithms outperform a random reconstruction (modified scaled GED ≈ 0.5), and can regularly achieve modified scaled GED scores better than 0.3 in sparse cases and 0.45 in dense cases. We argue that, while these methods cannot replace traditional Bayesian network structure-learning techniques, they are useful as computationally cheap data exploration tools and in knowledge discovery over structures which cannot be modelled as Bayesian networks.