Gaussian Process Models for Colored Graphs

Many real-world domains can naturally be represented as complex graphs, i.e., in terms of entities (nodes) and relations (edges) among them. In domains with multiple relations, represented as colored graphs, we may improve the quality of a model by exploiting the correlations among relations of different types. To this end, we develop a multi-relational Gaussian process (MRGP) model. The MRGP model introduces multiple GPs for each type of entities. Each random variable drawn from a GP represents profile/preference of an entity in some aspect, which is the function value of entity features at the aspect. These GPs are then coupled together via relations between entities. The MRGP model can be used for relation prediction and (semi-) supervised learning. We give an analysis of the MRGP model for bipartite, directed and undirected univariate relations.