Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothness

Gaussian processes are ubiquitous in machine learning, statistics, and applied mathematics. They provide a flexible modelling framework for approximating functions, whilst simultaneously quantifying uncertainty. However, this is only true when the model is well-specified, which is often not the case in practice. In this paper, we study the properties of Gaussian process means when the smoothness of the model and the likelihood function are misspecified. In this setting, an important theoretical question of practical relevance is how accurate the Gaussian process approximations will be given the chosen model and the extent of the misspecification. The answer to this problem is particularly useful since it can inform our choice of model and experimental design. In particular, we describe how the experimental design and choice of kernel and kernel hyperparameters can be adapted to alleviate model misspecification.

Automated summary

Gaussian processes are widely used in machine learning, statistics, and applied mathematics given their flexibility in approximating functions and quantifying uncertainty. However, when the smoothness of the model and the likelihood function are misspecified, the accuracy of Gaussian process approximations can be affected, and adjusting experimental designs and choosing kernels and hyperparameters can help alleviate this issue.