We consider the problem of optimizing a black-box function based on noisy bandit feedback.
Kernelized bandit algorithms have shown strong empirical and theoretical performance for …

Gaussian process regression underpins countless academic and industrial applications of
machine learning and statistics, with maximum likelihood estimation routinely used to select …

This work is concerned with the convergence of Gaussian process regression. A particular
focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in …

We propose a nonparametric two-sample test procedure based on Maximum Mean
Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same …

Abstract The Expected Improvement (EI) method, proposed by Jones, Schonlau, andWelch,
is a widely used Bayesian optimization method, which makes use of a fitted Gaussian …

Gaussian process regression is widely used in many fields, for example, machine learning,
reinforcement learning and uncertainty quantification. One key component of Gaussian …

Likelihood-free inference methods typically make use of a distance between simulated and
real data. A common example is the maximum mean discrepancy (MMD), which has …

Despite the ubiquity of the Gaussian process regression model, few theoretical results are
available that account for the fact that parameters of the covariance kernel typically need to …

Gaussian processes are the model of choice in Bayesian optimization and active learning.
Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full …

This work investigates the prediction performance of the kriging predictors. We derive some
error bounds for the prediction error in terms of non-asymptotic probability under the uniform …