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About this paper
George Wynne, François-Xavier Briol, Mark Girolami
Researchers from Imperial College London, University College London, and the University of Cambridge quantified the convergence accuracy of Gaussian Process predictive means under conditions of misspecified likelihoods and function smoothness. Their analysis provides rigorous error bounds, demonstrating how experimental design and kernel parameter selection influence approximation errors in these real-world scenarios and providing guidance for optimal model choices.
Key insights
- Quasi-uniform experimental designs are critical for stable and optimal convergence of Gaussian Processes, particularly under smoothness misspecification and arbitrary observation noise.
- The optimal choice for the GP kernel's smoothness parameter depends on the noise characteristics: matching the target function's smoothness (τ_f) for interpolation, but matching τ_f + d/2 for Gaussian regression.
- An adaptively chosen 'nugget' term (assumed noise variance decreasing with fill distance) significantly improves robustness and convergence when likelihoods are misspecified or data is arbitrarily corrupted.
Summary by alphaXiv.
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