Network Regression with Predictive Clustering Trees

Regression inference in network data is a challenging task in machine learning and data mining. Network data describe entities represented by nodes, which may be connected with (related to) each other by edges. Many network data sets are characterized by a form of auto correlation where the values of the response variable at a given node depend on the values of the variables (predictor and response) at the nodes connected to the given node. This phenomenon is a direct violation of the assumption of independent (i.i.d.) observations: At the same time, it offers a unique opportunity to improve the performance of predictive models on network data, as inferences about one entity can be used to improve inferences about related entities. In this paper, we propose a data mining method that explicitly considers auto correlation when building regression models from network data. The method is based on the concept of predictive clustering trees (PCTs), which can be used both for clustering and predictive tasks: PCTs are decision trees viewed as hierarchies of clusters and provide symbolic descriptions of the clusters. In addition, PCTs can be used for multi-objective prediction problems, including multi-target regression and multi-target classification. Empirical results on real world problems of network regression show that the proposed extension of PCTs performs better than traditional decision tree induction when auto correlation is present in the data.