Choosing an appropriate kernel function is a crucial decision for many popular
statistical learning algorithms and represent the natural entry point for inserting
prior knowledge into the learning process. Inductive logic programming, on the other
hand, offers powerful and  flexible frameworks for describing existing background
knowledge and obtaining additional knowledge from the data. It therefore seems
natural to explore the synergy between these two important paradigms of machine
learning.
In this talk I will discuss a number of recent kernel-based methods that operate in
the ILP setting and present examples of successful applications. In kernels on
Prolog proof trees, the representation of an example is obtained by recording the
execution trace of a logic program expressing background knowledge. The similarity
between two examples is then computed as the similarity between the corresponding
execution traces. In declarative kernels, logic programming allows us to specify a
broad class of convolution kernels, providing a simple interface for the
incorporation of relational background knowledge. In kFOIL, features correspond to
the truth values of clauses that are dynamically generated by a greedy search
algorithm guided by the empirical risk. Unlike the previous two ideas, kFOIL learns
the kernel function from the available data and also returns a corresponding set of
clauses that are regarded as features. I will finally present a kernel based on rich
combinatorial features described by type extension trees and discuss its application
to statistical relational learning with interdependent examples.