Latent-Class Statistical Relational Learning
         from Formal Knowledge


      Achim Rettinger1 , Matthias Nickles2 , and Volker Tresp3
              1
               Technische Universität München, Germany,
                    achim.rettinger@cs.tum.edu
                2
                  University of Bath, United Kingdom,
                     M.L.Nickles@cs.bath.ac.uk
          3
            Siemens AG, CT, IC, Learning Systems, Germany,
                     volker.tresp@siemens.com




 Abstract. We propose a learning approach for integrating formal knowl-
 edge into statistical inference by exploiting ontologies as a semantically
 rich and fully formal representation of prior knowledge. The logical con-
 straints deduced from ontologies can be utilized to enhance and control
 the learning task by enforcing description logic satisfiability in a latent
 multi-relational graphical model. To demonstrate the feasibility of our
 approach we provide experiments using real world social network data in
 form of a SHOIN (D) ontology. SHOIN (D) or OWL DL is one of the
 knowledge representation languages endorsed by the World Wide Web
 Consortium as a basic technology for the Semantic Web. Our results
 illustrate two main practical advancements: First, entities and entity
 relationships can be analyzed via the latent model structure. Second,
 enforcing the ontological constraints guarantees that the learned model
 does not predict inconsistent relations. In our experiments, this leads to
 an improved predictive performance.