Statistical learning with graph kernels

Abstract

Several problems in chemistry, in particular for drug discovery, can be formulated as classification or regression problems over molecules. These molecules, when represented by their planar structure, can be seen as labeled graphs. One approach to solve such problems is to apply kernel methods, such as support vector machines, with labeled graphs as training patterns. This requires an implicit embedding of the labeled graphs to a Hilbert space, carried out in practice through the definition of a positive definite function over labeled graph. In this work I will review recent works that define such positive kernels. In particular we will see that although complete embeddings that separate non-isomorphic graphs, such as those obtained by counting all subgraphs or paths, are intractable in practice, fast approximations based on finite and infinite walk enumeration can be computed in polynomial time. These walk kernels and their variants give promising results on several benchmarks in computational chemistry.