Deep parametric predictive Gaussian processes for uncertainty estimation

Deep Gaussian processes (DGPs) are a powerful extension of Gaussian processes that allow for multi-layer generalisation of GPs, enabling more flexible and expressive modelling of complex data. However, as the depth of the model increases, so does the computational cost, making it challenging to scale deep Gaussian processes to large-dimensional data. This often leads to an underestimation of the posterior variance. Moreover, interpreting and understanding the learned representations in DGPs can be more difficult than in shallower models. We developed a model that combines a hybrid spatial factor model, which reduces the difficulty of dealing directly with high-dimensional outcomes, and a Bayesian method that integrates input variability into GP regression. The proposed model used inducing point methods with stochastic variational inference, which provides substantially improved predictive uncertainties and efficient approximation. We evaluated the benefits of our model on several benchmark regression datasets and high-dimensional data from the IMPRESSIONS Integrated Assessment Platform version 2. The performance of the input features is analysed using the proposed models and SHapley Additive exPlanations (SHAP) values for multi-task problems to help interpret the results. Our results show that the proposed integration of these techniques is efficient and accurate for the uncertainty quantification of complex models.