Enhancing Uncertainty Estimation with Deep Gaussian Processes

Accurately estimating uncertainty in predictive models is crucial for a wide range of applications, from decision-making in landuse modelling to robust forecasting in finance and autonomous systems. Gaussian processes (GPs) offer a solid framework for uncertainty quantification but often struggle with scalability and flexibility when applied to large, high-dimensional datasets. Deep Gaussian processes (DGPs) are a powerful extension of GPs that allow for multi-layer generalisation of GPs, enabling more flexible and expressive modelling of complex data. As the complexity of the model increases, so does the computational cost, which makes it difficult to scale DGP to large-dimensional data. Although variational inference has been used with large datasets, it often produces an overconfident uncertainty estimate because it does not effectively utilise input-dependent function uncertainty. This paper introduces an approach for enhancing uncertainty estimation using the predictive log-likelihood (PLL) objective with DGP model to address these limitations. This relies on a parametric GP regression model designed for a family of predictive distributions and incorporate a modified objective function to restore a full symmetry between various contributions to predictive variance. We evaluate the performance of our methods on several benchmark regressions and large-scale environmental datasets. The results show that the model provides more reliable uncertainty estimates, particularly in regions of sparse data, making them efficient for real-world applications.