  We propose multivariate nonstationary Gaussian processes for jointly modeling
multiple clinical variables, where the key parameters, length-scales, standard
deviations and the correlations between the observed output, are all time
dependent. We perform posterior inference via Hamiltonian Monte Carlo (HMC). We
also provide methods for obtaining computationally efficient gradient-based
maximum a posteriori (MAP) estimates. We validate our model on synthetic data
as well as on electronic health records (EHR) data from Kaiser Permanente (KP).
We show that the proposed model provides better predictive performance over a
stationary model as well as uncovers interesting latent correlation processes
across vitals which are potentially predictive of patient risk.
