Constrained Gaussian Process Regression for Gene-Disease Association

We introduce a class of methods for Gaussian process regression with functional expectation constraints. We show that the solution can be found without the need for approximations when the constraint set satisfies a representation theorem. Further, the solution is unique when the constraint set is convex. Constrained Gaussian process regression is motivated by the modeling of transposable (matrix) data with missing entries. For such data, our approach augments the Gaussian process with a nuclear norm constraint to incorporate low rank structure. The constrained Gaussian process approach is applied to the prediction of hidden associations between genes and diseases using a small set of observed associations as well as prior covariances induced by gene-gene interaction networks and disease ontologies. We present experimental results showing the performance improvements that result from the use of additional constraints.