While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees, and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance, but using a different set of hyperparameters, chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches not only when employed for calibrated regression, but also to inform the design of Bayesian optimization algorithms.

翻译：尽管高斯过程是各类工程和科学应用的主要工具，但其不确定性估计并不满足频率学派保证，且在实践中可能出现校准偏差。当前设计校准模型的前沿方法依赖于膨胀高斯过程后验方差，这会产生可能过于粗略的置信区间。为解决此问题，我们提出一种校准方法，该方法使用受标准高斯过程后验方差启发的计算生成预测分位数，但采用一组不同的超参数，这些参数需满足经验校准约束。这使得我们的校准方法比现有方法更具灵活性。在合理假设下，该方法可生成校准模型。此外，它不仅在校准回归任务中优于现有方法，还能为贝叶斯优化算法的设计提供信息支持。