Learning monadic and dyadic relations: three case studies in systems biology

In molecular biology and other subfields of biology one can encounter many machine learning problems where the goal consists of predicting relations or interactions between pairs of objects. In this article we elaborate on three applications that represent such a learning scenario: predicting functional relationships between enzymes in bioinformatics, predicting protein-ligand interactions in computational drug design and predicting heterotroph-methanotroph interactions in microbial ecology. All three case studies are analyzed using an extension of a general kernel-based framework that we proposed recently. From a mathematical perspective, we both consider monadic and dyadic relations, and we use Kronecker product feature mappings to couple feature representations of paired objects, which correspond to vertices in a graph.