Towards combining statistical and symbolic learning: a kernel approach

 Symbolic and statistical approaches to learning have rather opposite characteristics: the former relies on an expressive and structured representation of the domain at hand and aims at producing interpretable models of the underlying concepts; the latter aims at maximizing the predictive perfomance and robustness of the learner, building on a sound generalization theory, and trades interpretability for effectiveness of the learned models. Statistical relational learning is a recent research field trying to combine the advantages of the two approaches. We take a kernel viewpoint and develop a number of algorithms where the kernel acts as an interface between a logical representation of the domain and a statistical learner. Proof tree kernels define the similarity between instances as similarity between the proofs of logical predicates they satisfy. kFOIL defines features as the truth value of clauses dynamically generated by a greedy search alogorithm. Declarative kernels rely on an axiomatic theory in order to decompose entities into parts and express relationships between them. We discuss mereotopological kernels as well as possible extensions including temporal relationships as those defined in interval temporal logic.