Nonparametric Mixture of Gaussian Processes with Constraints

Motivated by the need to identify new and clinically relevant categories of lung disease, we propose a novel clustering with constraints method using a Dirichlet process mixture of Gaussian processes in a variational Bayesian nonparametric framework. We claim that individuals should be grouped according to biological and/or genetic similarity regardless of their level of disease severity; therefore, we introduce a new way of looking at subtyping/clustering by recasting it in terms of discovering associations of individuals to disease trajectories (i.e., grouping individuals based on their similarity in response to environmental and/or disease causing variables). The nonparametric nature of our algorithm allows for learning the unknown number of meaningful trajectories. Additionally, we acknowledge the usefulness of expert guidance by providing for their input using must-link and cannot- link constraints. These constraints are encoded with Markov random fields. We also provide an efficient variational approach for performing inference on our model.