Gaussian Process Regression (GPR) and Gaussian Process Latent Variable Models (GPLVM) offer a principled way of performing probabilistic non-linear regression and dimensionality reduction. In this paper we propose a hybrid between the two, the covariate-GPLVM (c-GPLVM), to perform dimensionality reduction in the presence of covariate information (e.g. continuous covariates, class labels, or censored survival times). This construction lets us adjust for covariate effects and reveals meaningful latent structure which is not revealed when using GPLVM. Furthermore, we introduce structured decomposable kernels which will let us interpret how the fixed and latent inputs contribute to feature-level variation, e.g. identify the presence of a non-linear interaction. We demonstrate the utility of this model on applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes.
Identifying biomarkers with predictive value for disease risk stratification is an important task in epidemiology. This paper describes an application of Bayesian linear survival regression to model cardiovascular event risk in diabetic individuals with measurements available on 55 candidate biomarkers. We extend the survival model to include data from a larger set of non-diabetic individuals in an effort to increase the predictive performance for the diabetic subpopulation. We compare the Gaussian, Laplace and horseshoe shrinkage priors, and find that the last has the best predictive performance and shrinks strong predictors less than the others. We implement the projection predictive covariate selection approach of Dupuis and Robert (2003) to further search for small sets of predictive biomarkers that could provide cost-efficient prediction without significant loss in performance. In passing, we present a derivation of the projective covariate selection in Bayesian decision theoretic framework.