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This paper introduces Predictively Oriented Gaussian Processes (PrO-GPs) as a robust alternative to standard GPs, specifically addressing model misspecification by prioritizing predictive uncertainty. By deriving a reduced formulation and efficient sampling scheme, PrO-GPs enable practical computation of these predictively oriented posteriors. Experiments demonstrate that PrO-GPs yield better calibrated predictive distributions than standard GPs when the underlying data generating process is not accurately captured by the model.
Gaussian Processes can be made
Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitioners to make a number of design decisions, such as the choice of the kernel and the observation model. Suboptimal choices can produce misspecified models that do not capture the underlying data generating process. We introduce Predictively Oriented Gaussian Processes (PrO-GPs), which treat predictive uncertainty as the primary inferential target and provide a robust alternative to standard GPs. Although direct computation of a PrO posterior for nonparametric models is intractable, we derive a reduced formulation and practical sampling scheme for efficient computation. Through synthetic and real data experiments, we show that PrO-GPs produce better calibrated predictive distributions under model misspecification compared to standard GP approaches.
