aiqbench analysis
This research introduces Predictively Oriented Gaussian Processes (PrO-GPs), a novel framework that prioritizes predictive uncertainty calibration over traditional kernel selection. By deriving an efficient sampling scheme for nonparametric models, the method offers a robust solution for handling model misspecification in functional relationship modeling. The approach represents a significant methodological advance in Bayesian inference and probabilistic machine learning.
Predictively Oriented Gaussian Process Posteriors
arXiv:2610.03201v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.03201 [stat.ML]
(or arXiv:2610.03201v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.03201 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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