  We propose a novel hierarchical model for multitask bipartite ranking. The
proposed approach combines a matrix-variate Gaussian process with a generative
model for task-wise bipartite ranking. In addition, we employ a novel trace
constrained variational inference approach to impose low rank structure on the
posterior matrix-variate Gaussian process. The resulting posterior covariance
function is derived in closed form, and the posterior mean function is the
solution to a matrix-variate regression with a novel spectral elastic net
regularizer. Further, we show that variational inference for the trace
constrained matrix-variate Gaussian process combined with maximum likelihood
parameter estimation for the bipartite ranking model is jointly convex. Our
motivating application is the prioritization of candidate disease genes. The
goal of this task is to aid the identification of unobserved associations
between human genes and diseases using a small set of observed associations as
well as kernels induced by gene-gene interaction networks and disease
ontologies. Our experimental results illustrate the performance of the proposed
model on real world datasets. Moreover, we find that the resulting low rank
solution improves the computational scalability of training and testing as
compared to baseline models.
