  We consider a Gaussian process formulation of the multiple kernel learning
problem. The goal is to select the convex combination of kernel matrices that
best explains the data and by doing so improve the generalisation on unseen
data. Sparsity in the kernel weights is obtained by adopting a hierarchical
Bayesian approach: Gaussian process priors are imposed over the latent
functions and generalised inverse Gaussians on their associated weights. This
construction is equivalent to imposing a product of heavy-tailed process priors
over function space. A variational inference algorithm is derived for
regression and binary classification.
