Distribution free bounds for relational classi cation

Statistical Relational Learning (SRL) is a sub-area in Machine Learning which addresses the problem of performing statistical inference on data that is correlated and not independently and identically distributed (i.i.d.) { as is generally assumed. For the traditional i.i.d. setting, distribution free bounds exist, such as the Hoe ding bound, which are used to provide con dence bounds on the generalization error of a classi cation algorithm given its hold-out error on a sample size of N . Bounds of this form are currently not present for the type of interactions that are considered in the data by relational classi cation algorithms. In this paper we extend the Hoe ding bounds to the relational setting. In particular, we derive distribution free bounds for certain classes of data generation models that do not produce i.i.d. data and are based on the type of interactions that are considered by relational classi cation algorithms that have been developed in SRL. We conduct empirical studies on synthetic and real data which show that these data generation models are indeed realistic and the derived bounds are tight enough for practical use.