Covariance functions and Bayes errors for GP regression on random graphs

We consider GP learning of functions defined on the nodes of a random graph. Covariance functions proposed for this scenario, based on diffusion processes on the graph, are shown to have some counter-intuitive properties. In particular, on graphs with tree-like structure where loops can be neglected (as is typically the case for randomly generated graphs), the "obvious" limit of a large correlation length scale does not produce a constant covariance function. In the second part, we look at Bayes errors for GP regression on graphs and study how the learning curves depend on the size of the graph, its connectivity, and the number of training examples. Joint work with Camille Coti.