Constraining Gaussian Processes Regression with Quasi-Likelihood Constraint Relaxation
Keywords: constrained gaussian processes, virtual point methods, bayesian inference, fusion energy
TL;DR: This paper describes a novel approach to constrained Gaussian Process regression.
Abstract: Gaussian Process regression is a popular method for nonparametric, probabilistic modelling. One of its main attractions is also, in some contexts, a significant challenge; namely its high flexibility. This flexibility can be reduced by imposing constraints on the GP prior or posterior, something that there is a large and growing body of literature on. In this paper, we present a generalisation of virtual point methods and a framework for enforcing a broad range of constraints in GP posteriors. The method involves designing a quasi-likelihood function which encodes a relaxed form of the constraints, and then conditioning the unconstrained GP posterior on this quasi-likelihood. The method leverages ideas from existing methods for constrained GP regression, namely Riihimaki and Vehtari (2010) and Hansen et al. (2024), and expands these approaches to a much broader range of constraints. The method is demonstrated with a synthetic example, where a 2-dimensional GP posterior is required to have a divergence-free gradient, as well as real-world example where the posterior GP of Thomson scattering data from the MAST tokamak is required to be both monotonically decreasing and strictly positive.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 9311
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